566 ideas
| 21979 | Wisdom emerges at the end of a process [Hegel] |
| Full Idea: The Owl of Minerva spreads its wings only with the falling of dusk. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], Pref p.13), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.4 | |
| A reaction: Hegel explains that this means that wisdom is the product of historical maturity, as the ideal emerges, and illuminates what is real. I think. |
| 19635 | Hegel produced modern optimism; he failed to grasp that consciousness never progresses [Hegel, by Cioran] |
| Full Idea: Hegel is chiefly responsible for modern optimism. How could he have failed to see that consciousness changes only its forms and modalities, but never progresses. | |
| From: report of Georg W.F.Hegel (works [1812]) by E.M. Cioran - A Short History of Decay 5 |
| 8215 | Hegel was the last philosopher of the Book [Hegel, by Derrida] |
| Full Idea: Hegel was the last philosopher of the Book. | |
| From: report of Georg W.F.Hegel (works [1812]) by Jacques Derrida - Positions p.64 | |
| A reaction: Reference to 'the Book' connects this to the great religions which rely on one holy text. The implication is that Hegel was proposing one big solution to all problems. It is doubtful if many philosophers before Hegel dreamt of that either. |
| 20109 | Hegel inserted society and history between the God-world, man-nature, man-being binary pairs [Hegel, by Safranski] |
| Full Idea: Before Hegel, people thought in binary oppositions of God and the world, man and nature, man and being. After Hegel an intervening world of society and history was inserted between these pairs. | |
| From: report of Georg W.F.Hegel (Introduction to the Philosophy of History [1840]) by Rüdiger Safranski - Nietzsche: a philosophical biography 05 | |
| A reaction: This is what Popper later called 'World Three'. This might be seen as the start of what we islanders call 'continental' philosophy, which we have largely ignored. Analytic philosophy only discovered this through philosophy of language. |
| 8927 | Philosophy moves essentially in the element of universality [Hegel] |
| Full Idea: Philosophy moves essentially in the element of universality. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 01) | |
| A reaction: I would take this to be uncontroversially correct. An interesting test case is applied ethics, which seems embedded in current cultural practices. I would always take it to be searching for what is universal in each situation. |
| 22766 | Philosophy is exploration of the rational [Hegel] |
| Full Idea: Philosophy is exploration of the rational. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], Pref) | |
| A reaction: The only problem is that Hegel (like the Stoics) thought that nature is rational all the way down, so philosophy becomes the study of everything. |
| 21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
| Full Idea: Philosophy is the supreme blossom - the concept - of the entire shape of history, the consciousness and the spiritual essence of the whole situation, the spirit of the age as the spirit present and aware of itself in thought. | |
| From: Georg W.F.Hegel (Lectures on the History of Philosophy [1830], p.25), quoted by Stephen Houlgate - An Introduction to Hegel 01 | |
| A reaction: This sees philosophy as intrinsically historical, which is a founding idea for 'continental' philosophy. Analysis is tied to science, in which the history of the subject is seen as irrelevant to its truth. Does this mean we can't go back to Aristotle? |
| 21776 | Philosophy aims to reveal the necessity and rationality of the categories of nature and spirit [Hegel, by Houlgate] |
| Full Idea: For Hegel, philosophy's principal task is to disclose the enduring necessity and rationality of the categories and forms of nature and spirit that it examines. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Stephen Houlgate - An Introduction to Hegel 4 'Phenomenology' | |
| A reaction: The idea that a miserable little evolved and transient mammal on a tiny planet has direct insight into the necessities and categories of nature and spirit looks a shade optimistic to me. You have to admire the ambition, though. |
| 19073 | True philosophy aims at absolute unity, while our understanding sees only separation [Hegel] |
| Full Idea: Everything deserving the name of philosophy has constantly been based on the consciousness of an absolute unity, where the understanding sees and accepts only separation. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §213) | |
| A reaction: Puzzled by the role of 'understanding' here. I tend to cite that as the highest aspiration of philosophy. Hegel seems to offer a higher understanding of unity, and a weaker analytic understanding, which is part of our limited psychology. |
| 21753 | If we look at the world rationally, the world assumes a rational aspect [Hegel] |
| Full Idea: Whoever looks at the world rationally will find that it in turn assumes a rational aspect; the two exist in a reciprocal relationship. | |
| From: Georg W.F.Hegel (Lectures on the Philosophy of (World) History [1837], p.29), quoted by Stephen Houlgate - An Introduction to Hegel 01 | |
| A reaction: What happens when I look at irrationality rationally? |
| 15624 | Free thinking has no presuppositions [Hegel] |
| Full Idea: Thinking that is free is without presuppositions. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §41 Add1) | |
| A reaction: Fat chance, I would have thought. Hegel's project was indeed to try to get right to the bottom of the presuppositions. My picture is always of holding one thing presupposed while you examine another, and then switching to other presuppositions. |
| 16011 | Hegel doesn't storm the heavens like the giants, but works his way up by syllogisms [Kierkegaard on Hegel] |
| Full Idea: Hegel is a Johannes Climacus who does not storm the heavens, like the giants, by putting mountain upon mountain, but climbs aboard them by way of his syllogisms. | |
| From: comment on Georg W.F.Hegel (works [1812]) by Søren Kierkegaard - The Journals of Kierkegaard 2A | |
| A reaction: [Idea from SY] This appears to be an attempt at insulting Hegel for his timidity, but it seems to be describing the cautious approach which most modern philosophers take to be correct. [PG] |
| 15631 | The ideal of reason is the unification of abstract identity (or 'concept') and being [Hegel] |
| Full Idea: Abstract identity (which is what here is also called 'concept') and being are the two moments that reason seeks to unify; this unification is the Ideal of reason. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §49) | |
| A reaction: Not sure I understand this, but I connect it to Aristotle's approach to the problem of being, which was to abandon the head-on approach, and aim to understand the identities of particulars and kinds. |
| 15612 | Older metaphysics naively assumed that thought grasped things in themselves [Hegel] |
| Full Idea: The older metaphysics has the naïve presupposition that thinking grasps what things are in-themselves, that things only are what they genuinely are when they are captured in thought. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §28 Add) | |
| A reaction: His 'older' metaphysics is prior to Kant's critique. The less naïve version is more aware of antinomies and dialectical conflicts within thought. |
| 5433 | For Hegel, things are incomplete, and contain external references in their own nature [Hegel, by Russell] |
| Full Idea: The basis of Hegel's system is that what is incomplete must not be self-subsistent, and needs the support of other things; whatever has relations to things outside itself must contain some reference to those outside things in its own nature. | |
| From: report of Georg W.F.Hegel (works [1812]) by Bertrand Russell - Problems of Philosophy Ch.14 | |
| A reaction: This leads to the idealist doctrine of 'internal relations'. It has some plausibility if you think about the physicist's definition of mass, which has to refer to forces etc. Presumably there is one essence for all of reality, instead of separate ones. |
| 21761 | If we start with indeterminate being, we arrive at being and nothing as a united pair [Hegel, by Houlgate] |
| Full Idea: Presuppositionless thinking which begins by thinking pure, indeterminate being must therefore come to think being and nothing in terms of one another. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'From indeterminate' | |
| A reaction: In Houlgate's account this seems to be the key Hegelian thought. Simply by confronting nothingness he gets the idea that one concept can lead to an alternative, and that the two can then be grasped together, which is his dialectic. |
| 21764 | Thought about being leads to a string of other concepts, like becoming, quantity, specificity, causality... [Hegel, by Houlgate] |
| Full Idea: In the course of (Hegel's) logic, we come to understand that to think being is to think becoming, quality, quantity, specificity, essence and existence, substance and causality, and, ultimately, self-determining reason itself. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'The Method' | |
| A reaction: Extraordinary! Houlgate spells out nicely what some commentators seem to gloss over, the huge a priori ambitions of Hegel's thought. I find his entire programme utterly implausible. |
| 21769 | We must start with absolute abstraction, with no presuppositions, so we start with pure being [Hegel] |
| Full Idea: The beginning must be an absolute - an abstract beginning; and so it may not presuppose anything, must not be mediated by anything or have a ground; rather it is itself to be the ground of the entire science. ...The beginning therefore is pure being. | |
| From: Georg W.F.Hegel (Science of Logic [1816], p.70), quoted by Stephen Houlgate - An Introduction to Hegel 03 'Logic' | |
| A reaction: This is the 'presuppositionless' beginning of Hegel's metaphysics, which Houlgate emphasises. Hegel's logic is very obviously a direct descendent of Descartes' Cogito. But it is pure thought, with no mention of a Self. |
| 21768 | Logic is metaphysics, the science of things grasped in thoughts [Hegel] |
| Full Idea: Logic coincides with metaphysics, with the science of things grasped in thoughts. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §24), quoted by Stephen Houlgate - An Introduction to Hegel 02 'Logic' | |
| A reaction: Not a very clear definition, given that thinking about a table appears to be a 'thing grasped in thought'. Presumably it refers to things which can only be grasped in thought, which seems to make it entirely a priori. |
| 22077 | Metaphysics is the lattice which makes incoming material intelligible [Hegel] |
| Full Idea: Metaphysics means nothing other than the range of general determinations of thought, the diamond lattice, as it were, into which we bring all material and thereby first make it intelligible. | |
| From: Georg W.F.Hegel (Philosophy of Nature (Encylopedia II) [1817], §3), quoted by Stephen Houlgate - Hegel p.95 | |
| A reaction: This sounds to me like a perfect summary of Kant's transcendental view. Metaphysics is the a priori deconstruction of our conceptual scheme. But for Kant it is fixed, and for Hegel it is dynamic. |
| 13876 | The syntactic category is primary, and the ontological category is derivative [Frege, by Wright,C] |
| Full Idea: For Frege it is the syntactic category which is primary, the ontological one derivative. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 1.iii | |
| A reaction: I take the recent revival of metaphysics to be a rebellion against precisely this thought. Ontology disappeared for a hundred years into a hopeless miasma of linguistic complexity. Language is cludge, but the world isn't. |
| 3301 | On the continent it is generally believed that metaphysics died with Hegel [Benardete,JA on Hegel] |
| Full Idea: In continental Europe it is widely believed that the metaphysical game was played out in Hegel. | |
| From: comment on Georg W.F.Hegel (works [1812]) by José A. Benardete - Metaphysics: the logical approach Intro |
| 8415 | Never lose sight of the distinction between concept and object [Frege] |
| Full Idea: Never lose sight of the distinction between concept and object. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro p.x) | |
| A reaction: Along with 8414 and 7732, we have the three axioms of modern analytical philosophy. Russell uses this distinction from Frege to attack Berkeley's idealism (see Idea 1103). The idea is strong in causal theories of reference. We realists love it. |
| 9841 | Frege was the first to give linguistic answers to non-linguistic questions [Frege, by Dummett] |
| Full Idea: Frege was the first philosopher to ask a non-linguistic question, and return a linguistic answer. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.10 | |
| A reaction: This is both heroic and infuriating. It is like erecting a road block in front of a beautiful valley. You say 'Is there a God?' and I reply 'Let us consider the semantics of that sentence'. |
| 9840 | Frege initiated linguistic philosophy, studying number through the sense of sentences [Frege, by Dummett] |
| Full Idea: §62 of Frege's 'Grundlagen' is arguably the most pregnant philosophical paragraph ever written; ..it is the very first example of what has become known as the 'linguistic turn' in philosophy. His enquiry into numbers focuses on the sense of sentences. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §62) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Dummett is a great fan of this, possibly the last great fan. It is undeniable that Frege has found one way to get at the problem, but I doubt if it is the only way. |
| 22270 | Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege] |
| Full Idea: Frege's 1879 logic transformed philosophy because it greatly expanded logic's reach - what thought can achieve unaided - and hence compelled a re-examination of everything previously said about the grounds of thought when logic gives out. | |
| From: comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 Intro | |
| A reaction: I loved the gloss on logic as 'what thought can achieve unaided'. I largely see logic in terms of what is mechanically computable. |
| 15948 | Frege developed formal systems to avoid unnoticed assumptions [Frege, by Lavine] |
| Full Idea: Frege developed a formal system to make sure that he hadn't employed unnoticed assumptions about arithmetic. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Shaughan Lavine - Understanding the Infinite VIII.2 | |
| A reaction: It is interesting that Frege seems to have had far more influence on analytic philosophy than he ever had on mathematics. |
| 8935 | Without philosophy, science is barren and futile [Hegel] |
| Full Idea: Let other sciences try to argue as much as they like without philosophy - without it they can have in them neither life, Spirit, nor truth. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 67) | |
| A reaction: To be pinned up in every physics laboratory in the world. On the whole I agree with this. My slogan is 'science is the servant of philosophy'. An unphilosophical scientist is just a technologist, an artisan. |
| 21984 | We must break up the rigidity that our understanding has imposed [Hegel] |
| Full Idea: The battle of reason is the struggle to break up the rigidity to which the understanding has reduced everything. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], I §80Z p.115), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: This sounds like a combination of Nietzsche and later Wittgenstein, and may be one of the ideas that launches 'continental' philosophy. Recent French thinkers talk continually of 'liberation'. |
| 22082 | Truth does not appear by asserting reasons and then counter-reasons [Hegel] |
| Full Idea: It is not difficult to see that the way of asserting a proposition, adducing reasons for it, and in the same way refuting its opposite by reasons, is not the form in which truth can appear. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], p.28), quoted by Stephen Houlgate - Hegel p.100 | |
| A reaction: This is a pretty good description of the way Plato and Aristotle do philosophy, so this idea, which must be a founding idea for the 'continental school', is extremely radical. Personally I identify rationality with believing things for good reasons. |
| 7083 | Highest reason is aesthetic, and truth and good are subordinate to beauty [Hegel] |
| Full Idea: I am now convinced that the highest act of reason, which embraces all ideas, is an aesthetic act, and that truth and goodness are brothers only in beauty. | |
| From: Georg W.F.Hegel (Oldest System Prog. of German Idealism [1796]), quoted by Simon Critchley - Continental Philosophy - V. Short Intro Append | |
| A reaction: This seems to be the distinctive value framework of the romantic movement and the nineteenth century, where art is destined to replace religion. However, Plato in the Symposium is an interesting ally. Aim for beauty, and the rest follows? |
| 21974 | The world seems rational to those who look at it rationally [Hegel] |
| Full Idea: To him who looks at the world rationally, the world looks rationally back; the two exist in reciprocal relationship. | |
| From: Georg W.F.Hegel (Lectures on the Philosophy of (World) History [1837], Intro p.29), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.4 | |
| A reaction: This is a nice variation on the stoic idea that nature is essentially rational. If we are capable of rationality, then nature has made us that way. Romantics seem to prefer looking at nature less rationally, so what do they see in nature? |
| 22081 | Let thought follow its own course, and don't interfere [Hegel] |
| Full Idea: Let thought follow its own course; and I think badly whenever I add something of my own. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §24 Add 2), quoted by Stephen Houlgate - Hegel p.100 | |
| A reaction: The idea that reason has a course of its own is a mega-assumption, which I would only accept after a lot of persuasion, which I doubt that Hegel can provide. The modern analytic idea of metaphysics as logic has a similar basis. |
| 10804 | Thoughts have a natural order, to which human thinking is drawn [Frege, by Yablo] |
| Full Idea: Burge has argued that Frege's rationalism runs very deep. Frege holds that there is a natural order of thoughts to which human thinking is naturally drawn. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stephen Yablo - Carving Content at the Joints § 8 | |
| A reaction: [Yablo cites Burge 1984,1992,1998] What an intriguing idea. I always start from empiricist beginnings, but some aspects of rationalism just sieze you by the throat. |
| 22037 | Objectivity is not by correspondence, but by the historical determined necessity of Geist [Hegel, by Pinkard] |
| Full Idea: What gives objectivity to a judgment about an object is not correspondence, but the way in which a judgement is located within a pattern of reasonng that is determined by the way in which Geist is historically determined as necessarily taking the object. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816], Intro) by Terry Pinkard - German Philosophy 1760-1860 | |
| A reaction: I quote this, but I'm blowed if I can make sense of how objectivity could be achieved in such a way. How can a historical process create a necessary judgement? Sorry, I'm fairly new to Hegel. Pinker says it is the practice of giving reasons. |
| 15626 | Categories create objective experience, but are too conditioned by things to actually grasp them [Hegel] |
| Full Idea: It is the categories that elevate mere perception into objectivity, into experience; but these concepts ...are conditioned by the given material. ...Hence the understanding, or cognition through categories, cannot become cognizant of things-in-themselves. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §43-4) | |
| A reaction: As one often fears with Hegel, this sounds like a deep insight, but is less persuasive when translated into simpler English (if I've got it right!). Being 'conditioned by the material' strikes me as just what is needed for good categories. |
| 22768 | Subjective and objective are not firmly opposed, but merge into one another [Hegel] |
| Full Idea: It is usually believed that the subjective and objective are firmly opposed to one another. But this is not the case; they in fact pass over into one another. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 026 add) | |
| A reaction: I take this to mean that they are on a spectrum, rather than being binary opposites. This seems reasonable to me, since I take there to be degrees of objectivity. |
| 9832 | Frege sees no 'intersubjective' category, between objective and subjective [Dummett on Frege] |
| Full Idea: Frege left no place for a category of the intersubjective, intermediate between the wholly objective and the radically subjective. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.7 | |
| A reaction: Interesting. More sophisticated accounts of language (with the Private Language Argument as background) hold out possibilities of objectivity arising from an articulate community. See Idea 95. |
| 8414 | Keep the psychological and subjective separate from the logical and objective [Frege] |
| Full Idea: Always separate sharply the psychological from the logical, the subjective from the objective. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro p.x) | |
| A reaction: This (with Ideas 7732 and 8415) is said to be the foundation of modern analytical philosophy. It contrasts with Husserl's 'Logical Investigations', which are the foundations of phenomenology. I think it is time someone challenged Frege here. |
| 7740 | There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner] |
| Full Idea: There is, in addition to the external world of physical objects and the internal world of ideas, a third realm of non-spatio-temporal objective objects, among which are thoughts. | |
| From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Joan Weiner - Frege Ch.7 | |
| A reaction: This seems to be Platonism, and, in particular, to give a Platonic existent status to propositions. Personally I believe in propositions, but as glimpses of how our brains actually work, not as mystical objects. |
| 22035 | The structure of reason is a social and historical achievement [Hegel, by Pinkard] |
| Full Idea: The lesson of Hegel's Phenomenology was that the structure of reason was social, and was therefore a historical achievement. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Terry Pinkard - German Philosophy 1760-1860 10 | |
| A reaction: This must be one of the most influential ideas to have filtered into the modern world. It is a predecessor of Marxist sociology. The idea that stands against it is Frege's platonist view of logic, making it necessary, despite being historical. |
| 8932 | Truth does not come from giving reasons for and against propositions [Hegel] |
| Full Idea: The way of asserting a proposition, adducing reasons for it, and in the same way refuting its opposite by reasons, is not the form in which truth can appear. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 48) | |
| A reaction: I can't see Plato or Aristotle agreeing with this. It is obviously the prelude to Hegel's dialectical account of reasoning. However, if we don't believe things because we have good reason to, I'm not sure where we shoud start. |
| 8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
| Full Idea: Frege disagree that logic should merely describe the laws of thought - how people actually did reason. Logic is essentially normative, not descriptive. We want the one logic which successfully tracks the truth. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Jennifer Fisher - On the Philosophy of Logic 1.III | |
| A reaction: This explains Frege's sustained attack on psychologism, and it also explains we he ended up as a platonist about logic - because he wanted its laws to be valid independently of human thinking. A step too far, perhaps. Brains are truth machines. |
| 19661 | Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux] |
| Full Idea: Hegel saw that the absolutization of the principle of sufficient reason (which marked the culmination of the belief in the necessity of what is) required the devaluation of the principle of non-contradiction. | |
| From: report of Georg W.F.Hegel (works [1812], 3) by Quentin Meillassoux - After Finitude; the necessity of contingency 3 | |
| A reaction: I pass this on without understanding it, though a joint study of my collection of ideas on sufficient reason and non-contradiction might make it clear. [Let me know if you can explain it!] |
| 15616 | If truth is just non-contradiction, we must take care that our basic concepts aren't contradictory [Hegel] |
| Full Idea: If truth were nothing more than lack of contradiction, one would have to examine first of all, with regard to each concept, whether it does not on its own account, contain an inner contradiction. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §33 Rem) | |
| A reaction: This is a very nice thought, which modern analytic philosophers, steeped in logic, should think about. It is always presumed that a contradiction is between a proposition and its negation, not some inner feature. |
| 21983 | Being and nothing are the same and not the same, which is the identity of identity and non-identity [Hegel] |
| Full Idea: Pure being and pure nothing are the same, ...but on the contrary they are not the same ...they are absolutely distinct. ...This is the identity of identity and non-identity. | |
| From: Georg W.F.Hegel (Science of Logic [1816], I.i.i.1C p.82,74), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: Even Moore, who is very patient with Hegel, gets cross at this point, describing such talk as 'shocking'. He's not wrong. Moore later says that the reason in reality tolerates contradictions, but human understanding can't. |
| 21985 | The so-called world is filled with contradiction [Hegel] |
| Full Idea: The so-called world is never and nowhere without contradiction. (...but it is unable to endure it) | |
| From: Georg W.F.Hegel (Science of Logic [1816], I.i.ii.2C(b)), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: [Second bit in Ency I §11] To clarify this one would need to understand 'so-called'. Note that his claim is not that the world contains occasional contradictions, but that the whole of reality is contradictory. I think this idea is nonsense. |
| 21978 | Hegel's dialectic is not thesis-antithesis-synthesis, but usually negation of negation of the negation [Hegel, by Moore,AW] |
| Full Idea: The dialectic is often described in terms of thesis, antithesis, and synthesis - though this is not a Hegelian way of speaking. Hegel himself sometimes describes it in terms of negation and negation of the negation. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816], I.i.i.C(c) p.150) by A.W. Moore - The Evolution of Modern Metaphysics 07.4 | |
| A reaction: A footnote says the first form of description only occurs once in Hegel's work. I am guessing that Marx is responsible for the standard misrepresentation. |
| 15615 | Older metaphysics became dogmatic, by assuming opposed assertions must be true and false [Hegel] |
| Full Idea: The older metaphysics became dogmatism because, given the nature of finite determinations, it had to assume that of two opposed assertions (of the kind that those propositions were) one must be true and the other false. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §32) | |
| A reaction: While dialethism in logic looks very dubious to me, I have every sympathy with Hegel when it comes to the reasonings of ordinary language. There it is much harder to know whether you are addressing truly opposed assertions. |
| 20952 | Rather than in three stages, Hegel presented his dialectic as 'negation of the negation' [Hegel, by Bowie] |
| Full Idea: Hegel's 'dialectic' is often characterised in terms of the triad of thesis, antithesis and synthesis. This is, however, not the way he presents it. The core of the dialectic is rather what Hegel terms the 'negation of the negation'. | |
| From: report of Georg W.F.Hegel (works [1812]) by Andrew Bowie - Introduction to German Philosophy | |
| A reaction: Interestingly, this connects it to debates about intuitionist logic, which denies that double-negation necessarily makes a positive. Presumably Marx emphasised the first reading. |
| 21766 | Dialectic is the instability of thoughts generating their opposite, and then new more complex thoughts [Hegel, by Houlgate] |
| Full Idea: The dialectical principle, for Hegel, is the principle whereby apparently stable thoughts reveal their inherent instability by turning into their opposites and then into new, more complex thoughts (as being turns to nothing, and then becoming). | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'The Method' | |
| A reaction: Houlgate says this is unique to Hegel, and is NOT the familiar thesis-antithesis-synthesis idea of dialectic, found in Kant and Engels. Hegelian idea shares the Greek idea of insights arising from oppositions. |
| 21767 | Dialectic is seen in popular proverbs like 'pride comes before a fall' [Hegel] |
| Full Idea: In the domain of individual ethics, we find the consciousness of dialectic in those universally familiar proverbs 'pride goes before a fall' and 'too much wit outwits itself'. ...Joy relieves itself in tears, and melancholy can be revealed in a smile. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §81), quoted by Stephen Houlgate - An Introduction to Hegel 02 'The Method' | |
| A reaction: 'Too clever by half' is the English version. Hegel's dialectic suggests that each concept somehow implies its opposite, rather than a mere mercurial drift from one extreme to the other. Most pride doesn't lead to a fall. |
| 15638 | Dialectic is the moving soul of scientific progression, the principle which binds science together [Hegel] |
| Full Idea: The dialectical constitutes the moving soul of scientific progression, and it is the principle through which alone immanent coherence and necessity enter into the content of science. ..[Add 1] It is the principle of all motion, of all life. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §81) |
| 15639 | Socratic dialectic is subjective, but Plato made it freely scientific and objective [Hegel] |
| Full Idea: It is in the Platonic philosophy that dialectic first occurs in a form which is freely scientific, and hence also objective. With Socrates, dialectical thinking still has a predominantly subjective shape, consistent with his irony. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §81 Add1) | |
| A reaction: I don't understand how dialectic can be 'objective', given that it is a method rather than a belief. Plato certainly seems to elevate dialectic into something almost mystical, because of what is said to be within its power. |
| 9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
| Full Idea: Frege expressly denies that a correct definition need capture the sense of the expression it defines: it need only get the reference right. | |
| From: report of Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.3 | |
| A reaction: This might hit up against the renate/cordate problem, of two co-extensive concepts, where the definition gets the extension right, but the intension wrong. |
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
| A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| Full Idea: We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a 'constructive definition', but we prefer to call it a 'definition' tout court. It contrasts with an 'analytic' definition. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.210) | |
| A reaction: An analytic definition is evidently a deconstruction of a past constructive definition. Fregean definition is a creative activity. |
| 9844 | Originally Frege liked contextual definitions, but later preferred them fully explicit [Frege, by Dummett] |
| Full Idea: In his middle period, Frege became hostile to contextual definitions, and any definition other than an explicit one, ..but at the time of the 'Grundlagen' he conceived of his context principle as licensing contextual definitions. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.11 | |
| A reaction: His context principle says words only have a meaning in a context. Intuitively, I would say that there is no correct answer to how something should be defined. Totally circularity is hopeless, but presuppositions just weaken a definition. |
| 9822 | Nothing should be defined in terms of that to which it is conceptually prior [Frege, by Dummett] |
| Full Idea: Frege appeals to a general principle that nothing should be defined in terms of that to which it is conceptually prior. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64) by Michael Dummett - Frege philosophy of mathematics Ch.3 | |
| A reaction: The point is that the terms of the definition would depend on the thing being defined. But of all the elusive concepts, that of 'conceptual priority' is one of the slipperiest. An example is the question of precedence between 'parallel' and 'direction'. |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
| A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| Full Idea: Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced. | |
| From: report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3 | |
| A reaction: This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts. |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
| A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
| 17495 | Proof aims to remove doubts, but also to show the interdependence of truths [Frege] |
| Full Idea: Proof has as its goal not only to raise the truth of a proposition above all doubts, but additionally to provide insight into the interdependence of truths. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §02) | |
| A reaction: This is a major idea in Frege's thinking, and a reason why he is the father of modern metaphysics as well as the father of modern logic. You study the framework of truths by studying the logic that connects them. |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| Full Idea: It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.212) | |
| A reaction: Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step. |
| 8632 | You can't transfer external properties unchanged to apply to ideas [Frege] |
| Full Idea: It would be remarkable if a property abstracted from external things could be transferred without any change of sense to events, to ideas and to concepts, like speaking of 'blue ideas' or 'salty concepts'. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §24) | |
| A reaction: Since those phrases make perfectly good metaphorical sense, I presume the Frege was a fairly literal sort of chap. Is this the earliest emergence of the idea of a category mistake? |
| 19070 | Superficial truth is knowing how something is, which is consciousness of bare correctness [Hegel] |
| Full Idea: Truth is at first taken to mean that I know how something is. This is truth, however, only in reference to consciousness; it is formal truth, bare correctness. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §213) | |
| A reaction: I would translate this idea as saying that bare correctness is conscious awareness of the truthmaker for some statement. Hegel then offers a 'deeper' account of the nature of truth. I would say awareness is quite separate from the concept of truth. |
| 21793 | Genuine truth is the resolution of the highest contradiction [Hegel] |
| Full Idea: The highest truth, truth as such, is the resolution of the highest opposition and contradiction. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], I: 99), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Art' | |
| A reaction: Uneasy about the word 'highest', and the general Hegelian dream of 'resolving' contradictions, rather than just eliminating at least one component of them. No one else uses the word 'truth' like this. I suppose this Truth has a capital 'T'. |
| 19466 | The word 'true' seems to be unique and indefinable [Frege] |
| Full Idea: It seems likely that the content of the word 'true' is sui generis and indefinable | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.327 (60)) | |
| A reaction: This is the view I associate with Davidson, though fans of Axiomatic Truth give up defining it, and just describe how it behaves. Defining it is very elusive, but I don't accept that nothing can be said about the contents of the concept of truth. |
| 21795 | What I hold true must also be part of my feelings and character [Hegel] |
| Full Idea: Whatever I hold as true, whatever ought to be valid for me, must also be in my feeling, must belong to my being and character. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], I: 97), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Philosophy' | |
| A reaction: I can see that truths do tend to become part of our character, but not that they ought to do so. I suppose I try to live my life enmeshed in the many truths which I have personally selected from the maelstrom of possibilities that engulf us. |
| 5644 | In Hegel's logic it is concepts (rather than judgements or propositions) which are true or false [Hegel, by Scruton] |
| Full Idea: The terms of Hegel's logic are not judgements or propositions, but rather concepts: and it is concepts, in this view, that are true or false. | |
| From: report of Georg W.F.Hegel (Logic (Encyclopedia I) [1817]) by Roger Scruton - Short History of Modern Philosophy Ch.12 | |
| A reaction: Quite alien to normal studies of logic, but I can make sense of a correspondence theory of truth for concepts, which might be more interesting than normal propositional or predicate logic. Does the concept of, say, a 'natural law' correspond to anything? |
| 8187 | Frege was strongly in favour of taking truth to attach to propositions [Frege, by Dummett] |
| Full Idea: Frege was strongly in favour of taking truth to attach to propositions, which he called 'thoughts' and regarded as being expressed by sentences. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Truth and the Past 1 | |
| A reaction: Sometimes it is necessary to know the time, the place, and the speaker before one can evaluate the truth of a proposition. Not just indexical words, but the indexical aspect of, say, "the team played badly". |
| 22317 | Truth does not admit of more and less [Frege] |
| Full Idea: What is only half true is untrue. Truth does not admit of more and less. | |
| From: Gottlob Frege (works [1890], CP 353), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 48 'Truth' | |
| A reaction: What about a measurement which is accurate to three decimal places? Maybe being 'close to' the truth is not the same as being 'more' true. The truth about a distance between two points is unknowable? |
| 19072 | In the deeper sense of truth, to be untrue resembles being bad; badness is untrue to a thing's nature [Hegel] |
| Full Idea: When truth is viewed in the deeper sense, to be untrue means much the same as to be bad. A bad man is an untrue man, and man who does not behave as his notion or his vocation requires. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §213) | |
| A reaction: See Idea 19071 for the 'deeper sense'. This seems to confirm that Hegel's deeper concept of truth resembles authenticity. I guess it will be something fulfilling the essence of the thing. Doctors must be proper doctors. Gold must be true gold? |
| 13881 | We need to grasp not number-objects, but the states of affairs which make number statements true [Frege, by Wright,C] |
| Full Idea: For Frege (as opposed to Gödel) the epistemological aim is not to relate to the objects which are the subject-matter of number theory, but to relate to the states of affairs that make for the truth of number-theoretic statements. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 1.v | |
| A reaction: I am beginning to see that this is a key issue in modern philosophy, of whether we build our metaphysics on the things of the world or on the truths about the world. I vote for the things, because the other way slides into anti-realism. |
| 19071 | The deeper sense of truth is a thing matching the idea of what it ought to be [Hegel] |
| Full Idea: Truth in the deeper sense is the identity between objectivity and the notion. It is in this deeper sense of truth that we speak of a true state or work of art. These are true if they are as they ought to be (their reality corresponds to their notion). | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §213) | |
| A reaction: This seems to be a correspondence theory, but not as we know it, Jim. He seems to have a value built into truth, which sounds to me like existentialist 'authenticity'. I like what he is saying, but I would analyse it into two or more components. |
| 19465 | There cannot be complete correspondence, because ideas and reality are quite different [Frege] |
| Full Idea: It is essential that the reality shall be distinct from the idea. But then there can be no complete correspondence, no complete truth. | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.327 (60)) | |
| A reaction: He thinks that logic can give a perfect account of truth, or at least the extension of truth, where ordinary language will always fail. I wonder what he would have thought of Tarski's theory? |
| 7077 | The true is the whole [Hegel] |
| Full Idea: The true is the whole. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 20) | |
| A reaction: This is the full idealist coherence view of truth, that one only approaches the Truth (capital T) as one builds up a more and more coherent picture. It makes truth unattainable, and that strikes me as a bit silly. |
| 19468 | The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege] |
| Full Idea: The sentence 'I smell the scent of violets' has just the same content as 'It is true that I smell the scent of violets'. So it seems that nothing is added to the thought by my ascribing to it the property of truth. | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.328 (61)) | |
| A reaction: This idea predates Ramsey's similar proposal, for which, oddly, Ramsey always seems to get the credit. To a logician they may have identical content, but pragmatically they are likely to differ in context. 'True' certainly doesn't add to the thought. |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2 | |
| A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped. |
| 9154 | Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge] |
| Full Idea: Frege maintained a sophisticated version of the Euclidean position that knowledge of the axioms and theorems of logic, geometry, and arithmetic rests on the self-evidence of the axioms, definitions, and rules of inference. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority Intro | |
| A reaction: I am inclined to agree that they are indeed self-evident, but not in a purely a priori way. They are self-evident general facts about how reality is and how (it seems) that it must be. It seems to me closer to a perception than an insight. |
| 9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
| Full Idea: Since every definition is an equation, one cannot define equality itself. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327) | |
| A reaction: This seems a particularly nice instance of the general rule that 'you have to start somewhere'. It is a nice test case for the nature of meaning to ask 'what do you understand when you understand equality?', given that you can't define it. |
| 4971 | I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege] |
| Full Idea: A distinction of subject and predicate finds no place in my way of representing a judgement. | |
| From: Gottlob Frege (Begriffsschrift [1879], §03) | |
| A reaction: Perhaps this sentence could be taken as the beginning of modern analytical philosophy. The old view doesn't seem to me entirely redundant - merely replaced by a much more detailed analysis of what makes a 'subject' and what makes a 'predicate'. |
| 17745 | For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki] |
| Full Idea: 'All A's are B's' meant for Frege that the concept A implies the concept B, or that to be A implies also to be B. Moreover this applies to arbitrary x which happens to be A. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Michal Walicki - Introduction to Mathematical Logic History D.2 | |
| A reaction: This seems to hit the renate/cordate problem. If all creatures with hearts also have kidneys, does that mean that being enhearted logically implies being kidneyfied? If all chimps are hairy, is that a logical requirement? Is inclusion implication? |
| 13455 | Frege did not think of himself as working with sets [Frege, by Hart,WD] |
| Full Idea: Frege did not think of himself as working with sets. | |
| From: report of Gottlob Frege (works [1890]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: One can hardly blame him, given that set theory was only just being invented. |
| 9157 | The null set is only defensible if it is the extension of an empty concept [Frege, by Burge] |
| Full Idea: Frege regarded the null set as an indefensible entity from the point of view of iterative set theory. It collects nothing. He thought a null entity (a null extension) is derivable only as the extension of an empty concept. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority II | |
| A reaction: Frege is right, if you like sets. Othewise all the other sets are going to be defined simply by their extension, and the empty set has to be defined in a different way, which looks like appalling theory. Empty concepts bother me though! |
| 9835 | It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett] |
| Full Idea: Since he thought of classes as extensions of concepts, ...it is because a concept can be empty that there is such a thing as the empty class. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.8 | |
| A reaction: Frege was already up against the awaiting Russell Paradox, but this view also seems to imply that there are many empty classes, since the absences of sandwiches would be different from the absence of heroism. |
| 16895 | The null set is indefensible, because it collects nothing [Frege, by Burge] |
| Full Idea: Frege regarded the null set as an indefensible entity from the point of view of iterative set theory. It collects nothing. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Apriority (with ps) 2 | |
| A reaction: The null set defines the possibility that something could be collected. At the very least, it introduces curly brackets into the language. |
| 14238 | A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege] |
| Full Idea: A class consists of objects; it is an aggregate, a collective unity, of them; if so, it must vanish when these objects vanish. If we burn down all the trees of a wood, we thereby burn down the wood. Thus there can be no empty class. | |
| From: Gottlob Frege (Elucidation of some points in E.Schröder [1895], p.212), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? | |
| A reaction: This rests on Cantor's view of a set as a collection, rather than on Dedekind, which allows null and singleton sets. |
| 9854 | We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett] |
| Full Idea: We can introduce a new type of object from the obtaining of some equivalence relation between objects of some already known kind, by identifying the new objects as equivalence classes of the old ones under that equivalence relation. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.14 | |
| A reaction: Some accounts of abstraction merely describe the concept, but this is a rival to the traditional pyschological abstractionism that Frege attacked so vigorously. Should we take a platonist or constructivist view of the new objects? |
| 9883 | Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett] |
| Full Idea: Frege decided that all logical objects, or at least all those needed for mathematics, could be defined by logical abstraction, except the classes needed for such definitions. ..This definition by equivalence classes has been adopted as a standard device. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64-68) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: This means if we are to understand modern abstraction (instead of the psychological method of ignoring selected properties of objects), we must understand the presuppositions needed for a definition by equivalence. |
| 18104 | Frege, unlike Russell, has infinite individuals because numbers are individuals [Frege, by Bostock] |
| Full Idea: Frege was able to prove that there are infinitely many individuals by taking the numbers themselves to be individuals, but this course was not open to Russell. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by David Bostock - Philosophy of Mathematics 5.2 |
| 9834 | A class is, for Frege, the extension of a concept [Frege, by Dummett] |
| Full Idea: A class is, for Frege, the extension of a concept. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.8 | |
| A reaction: This simple idea was the source of all his troubles, because there are concepts which can't have an extension, because of contradiction. ...And yet all intuition says Frege is right.. |
| 3328 | Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA] |
| Full Idea: Contrary to Dedekind's anti-realism, Frege proposed a realist definition of a set as the extension of a predicate (or concept, or function). | |
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.13 |
| 7728 | Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner] |
| Full Idea: Frege distinguished between asserting a proposition and expressing it, and he introduced the judgement stroke (a small vertical line, assertion) and the content stroke (a long horizontal line, expression) to represent them. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege Ch.3 | |
| A reaction: There are also strokes for conditional and denial. |
| 16881 | The laws of logic are boundless, so we want the few whose power contains the others [Frege] |
| Full Idea: Since in view of the boundless multitude of laws that can be enunciated we cannot list them all, we cannot achieve completeness except by searching out those that, by their power, contain all of them. | |
| From: Gottlob Frege (Begriffsschrift [1879], §13) | |
| A reaction: He refers to these laws in the previous sentence as the 'core'. His talk of 'power' is music to my ears, since it implies a direction of explanation. Burge says the power is that of defining other concepts. |
| 7622 | In 1879 Frege developed second order logic [Frege, by Putnam] |
| Full Idea: By 1879 Frege had discovered an algorithm, a mechanical proof procedure, that embraces what is today standard 'second order logic'. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Hilary Putnam - Reason, Truth and History Ch.5 | |
| A reaction: Note that Frege did more than introduce quantifiers, and the logic of predicates. |
| 9179 | Frege frequently expressed a contempt for language [Frege, by Dummett] |
| Full Idea: Frege frequently expressed a contempt for language. | |
| From: report of Gottlob Frege (works [1890], p.228) by Michael Dummett - Frege's Distinction of Sense and Reference p.228 | |
| A reaction: This strikes me as exactly the right attitude for a logician to have. Russell seems to have agreed. Attitudes to vagueness are the test case. Over-ambitious modern logicians dream of dealing with vagueness. Forget it. Stick to your last. |
| 16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
| Full Idea: A proof does not only serve to convince us of the truth of what is proved: it also serves to reveal logical relations between truths. Hence we find in Euclid proofs of truths that appear to stand in no need of proof because they are obvious without one. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: This is a key idea in Frege's philosophy, and a reason why he is the founder of modern analytic philosophy, with logic placed at the centre of the subject. I take the value of proofs to be raising questions, more than giving answers. |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| Full Idea: Are there perhaps modes of inference peculiar to mathematics which …do not belong to logic? Here one may point to inference by mathematical induction from n to n+1. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: He replies that it looks as if induction can be reduced to general laws, and those can be reduced to logic. |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| Full Idea: Mathematics has closer ties with logic than does almost any other discipline; for almost the entire activity of the mathematician consists in drawing inferences. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: The interesting question is who is in charge - the mathematician or the logician? |
| 13473 | Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD] |
| Full Idea: Frege thinks there is a single right deductive order of the truths. This is not an epistemic order, but a logical order, and it is our job to arrange our beliefs in this order if we can make it out. | |
| From: report of Gottlob Frege (works [1890]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Frege's dream rests on the belief that there exists a huge set of logical truths. Pluralism, conventionalism, constructivism etc. about logic would challenge this dream. I think the defence of Frege must rest on Russellian rooting of logic in nature. |
| 21595 | Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel] |
| Full Idea: The law of excluded middle is ...the maxim of the definite understanding, which would fain avoid contradiction, but in doing so falls into it. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], p.172), quoted by Timothy Williamson - Vagueness 1.5 | |
| A reaction: Not sure how this works, but he would say this, wouldn't he? |
| 7729 | Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner] |
| Full Idea: Frege's regimentation is based on the view of the simplest sort of statement as having, not subject/predicate form (as in Aristotle), but function/argument form. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege | |
| A reaction: This looks like being a crucial move into the modern world, where one piece of information is taken in and dealt with, as in computer procedures. Have educated people reorganised their minds along Fregean lines? |
| 8645 | Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege] |
| Full Idea: The proposition "Jupiter has four moons" can be converted into "the number of Jupiter's moons is four". | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §57) | |
| A reaction: This seems to be the beginning of the modern exploration of the whole idea of logical form. It is one thing to find a logical forms which suits your current thesis (here, that numbers are not adjectival), but another to prove that it is the right form. |
| 4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
| Full Idea: A thought can be split up in many ways, so that now one thing, now another, appears as subject or predicate | |
| From: Gottlob Frege (On Concept and Object [1892], p.199) | |
| A reaction: Thus 'the mouse is in the box', and 'the box contains the mouse'. A simple point, but important when we are trying to distinguish thought from language. |
| 21777 | Negation of negation doubles back into a self-relationship [Hegel, by Houlgate] |
| Full Idea: For Hegel, the 'negation of negation' is negation that, as it were, doubles back on itself and 'relates itself to itself'. | |
| From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 6 'Space' | |
| A reaction: [ref VNP 1823 p.108] Glad we've cleared that one up. |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions. | |
| From: Gottlob Frege (Function and Concept [1891], p.38) | |
| A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions. |
| 8492 | Relations are functions with two arguments [Frege] |
| Full Idea: Functions of one argument are concepts; functions of two arguments are relations. | |
| From: Gottlob Frege (Function and Concept [1891], p.39) | |
| A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions. |
| 3319 | Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA] |
| Full Idea: The whole point of Frege's functional account of predication lies in its allowing us to dispense with all properties across the board. | |
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.9 |
| 6076 | For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn] |
| Full Idea: For Frege, a predicate does not refer to the objects of which it is true, but to the function that maps these objects onto the True and False; ..a predicate is a name for this function. | |
| From: report of Gottlob Frege (works [1890]) by Colin McGinn - Logical Properties Ch.3 | |
| A reaction: McGinn says this is close to the intuitive sense of a property. Perhaps 'predicates are what make objects the things they are?' |
| 16891 | Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge] |
| Full Idea: Gödel undermined Frege's assumption that all but the basic truths are provable in a system, but insofar as one conceives of proof informally as an epistemic ordering among truths, one can see his vision as worth developing. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority (with ps) 1 | |
| A reaction: [compressed] This 'epistemic ordering' fits my thesis of seeing the world through our explanations of it. |
| 16906 | The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion] |
| Full Idea: The primitive truths contain the core of arithmetic because their constituents are simples which define the essential boundaries of the subject. …The primitive truths are the most general ones, containing the basic, essence determining elements. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Robin Jeshion - Frege's Notion of Self-Evidence 2 | |
| A reaction: This presents Frege as explicable in essentialist terms, as identifying the core of an abstract discipline, from which the rest of it is generated. Jeshion says 'simples are the essence'. |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| Full Idea: Usually a truth is only called a 'theorem' when it has not merely been obtained by inference, but is used in turn as a premise for a number of inferences in the science. ….Proofs use non-theorems, which only occur in that proof. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) |
| 8447 | In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege] |
| Full Idea: The reference of 'Etna' cannot be Mount Etna itself, because each piece of frozen lava which is part of Mount Etna would then also be part of the thought that Etna is higher than Vesuvius. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.43) | |
| A reaction: This seems to be a straight challenge to Kripke's baptismal account of reference. I think I side with Kripke. Frege is allergic to psychological accounts, but the mind only has the capacity to think of the aspect of Etna that is relevant. |
| 18772 | We can treat designation by a few words as a proper name [Frege] |
| Full Idea: The designation of a single object can also consist of several words or other signs. For brevity, let every such designation be called a proper name. | |
| From: Gottlob Frege (On Sense and Reference [1892]), quoted by Bernard Linsky - Quantification and Descriptions 1 | |
| A reaction: Frege regards names and descriptions as in the same class. Russell, and then Kripke, had things to say about that. |
| 14075 | Proper name in modal contexts refer obliquely, to their usual sense [Frege, by Gibbard] |
| Full Idea: According to Frege, a proper name in a modal context refers obliquely; its reference there is its usual sense. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Allan Gibbard - Contingent Identity V | |
| A reaction: [he cites the fourth page of Frege's 'Sense and Reference'] One can foresee problems with the word 'usual' here. Frege might be offering something better than Kripke does here. |
| 10424 | A Fregean proper name has a sense determining an object, instead of a concept [Frege, by Sainsbury] |
| Full Idea: We could think of a referring expression in Fregean terms as what he calls a proper name (Eigenname): its Sinn (sense) is supposed to determine an object as opposed to a concept as its Bedeutung (referent). | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Mark Sainsbury - The Essence of Reference 18.1 | |
| A reaction: The problem would be that the same expression could precisely indicate an object on one occasion, nearly do so on another, and totally fail on a third. |
| 18773 | People may have different senses for 'Aristotle', like 'pupil of Plato' or 'teacher of Alexander' [Frege] |
| Full Idea: In the case of an actual proper name such as 'Aristotle' opinions as to the sense may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. | |
| From: Gottlob Frege (On Sense and Reference [1892], note), quoted by Bernard Linsky - Quantification and Descriptions 1 | |
| A reaction: This note is 'notorious', and was a central target for Kripke's critique. Frege says people's senses may vary on this, and thinks the sense of 'Aristotle' can be accurately expressed. |
| 8448 | Any object can have many different names, each with a distinct sense [Frege] |
| Full Idea: An object can be determined in different ways, and every one of these ways of determining it can give rise to a special name, and these different names then have different senses. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.44) | |
| A reaction: This seems right. No name is an entirely neutral designator. Imagine asking a death-camp survivor their name, and they give you their prison number. Sense clearly intrudes into names. But picking out the object is what really matters. |
| 4978 | The meaning of a proper name is the designated object [Frege] |
| Full Idea: The meaning of a proper name is the object itself which we designate by using it. | |
| From: Gottlob Frege (On Sense and Reference [1892], p.30) | |
| A reaction: I can't actually make sense of this. How can a physical object be identical with a meaning? What sort of thing is a 'meaning'? Meanings are just 'in the head', I suspect. |
| 10510 | Frege ascribes reference to incomplete expressions, as well as to singular terms [Frege, by Hale] |
| Full Idea: Frege ascribes reference not only to singular terms, but equally to expressions of other kinds (the various kinds of incomplete expressions). | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Bob Hale - Abstract Objects Ch.3 Intro | |
| A reaction: The incomplete expressions presumably make reference to concepts. Frege may not seem, therefore, to have a notion of reference as what plugs language into reality - except that he is presumably a platonist about concepts. |
| 18937 | If sentences have a 'sense', empty name sentences can be understood that way [Frege, by Sawyer] |
| Full Idea: Frege's theory of 'sense' showed how sentences with empty names can have meaning and be understood. One just has to grasp the sense of the sentence (the thought expressed), and this is available even in the absence of a referent for the name. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Sarah Sawyer - Empty Names 2 | |
| A reaction: My immediate reaction is that this provides a promising solution to the empty names problem, which certainly never bothered me before I started reading philosophy. Sawyer says co-reference and truth problems remain. |
| 18940 | It is a weakness of natural languages to contain non-denoting names [Frege] |
| Full Idea: Languages have the fault of containing expressions which fail to designate an object. | |
| From: Gottlob Frege (On Sense and Reference [1892], p.40) | |
| A reaction: Wrong, Frege! This is a strength of natural languages! Names are tools. It isn't a failure of your hammer if you can't find any nails. |
| 18939 | In a logically perfect language every well-formed proper name designates an object [Frege] |
| Full Idea: A logically perfect language should satisfy the conditions that every expression grammatically well constructed as a proper name out of signs already introduced shall in fact designate an object. | |
| From: Gottlob Frege (On Sense and Reference [1892], p.41) | |
| A reaction: This seems to cramp your powers of reasoning, if you must know the object to use the name ('Jack the Ripper'), and reasoning halts once you deny the object's existence ('Pegasus'), or you don't know if names co-refer ('Hesperus/Phosphorus'). |
| 13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
| Full Idea: Frege (1893) considered a definite description to be a genuine singular term (as we do), so that a sentence like 'The present King of France is bald' would have the same logical form as 'Harry Truman is bald'. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by M Fitting/R Mendelsohn - First-Order Modal Logic | |
| A reaction: The difficulty is what the term refers to, and they embrace a degree of Meinongianism - that is that non-existent objects can still have properties attributed to them, and so can be allowed some sort of 'existence'. |
| 9950 | A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman] |
| Full Idea: The contribution of the quantifier to the truth conditions of sentences of which it is a part cannot be adequately explained if it is treated as other than a second-level predicate (for instance, if it is viewed as name). | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: They suggest that this makes it something like a 'property of properties'. With this account it becomes plausible to think of numbers as quantifiers (since they do, after all, specify quantities). |
| 9991 | For Frege the variable ranges over all objects [Frege, by Tait] |
| Full Idea: For Frege the variable ranges over all objects. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by William W. Tait - Frege versus Cantor and Dedekind XII | |
| A reaction: The point is that Frege had not yet seen the necessity to define the domain of quantification, and this leads him into various difficulties. |
| 10536 | Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege] |
| Full Idea: For Frege there is no need to specify the domain of the individual variables, which is taken as the totality of all objects. This contrasts with the standard notion of an interpretation, which demands that we first fix the domain. | |
| From: comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: What intrigues me is how domains of quantification shift according to context in ordinary usage, even in mid-sentence. I ought to go through every idea in this database, specifying its domain of quantification. Any volunteers? |
| 9871 | Frege always, and fatally, neglected the domain of quantification [Dummett on Frege] |
| Full Idea: Frege persistently neglected the question of the domain of quantification, which proved in the end to be fatal. | |
| From: comment on Gottlob Frege (works [1890]) by Michael Dummett - Frege philosophy of mathematics Ch.16 | |
| A reaction: The 'fatality' refers to Russell's paradox, and the fact that not all concepts have extensions. Common sense now says that this is catastrophic. A domain of quantification is a topic of conversation, which is basic to all language. Cf. Idea 9874. |
| 7730 | Frege introduced quantifiers for generality [Frege, by Weiner] |
| Full Idea: In order to express generality, Frege introduced quantifier notation. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege | |
| A reaction: This is the birth of predicate logic, beloved of analytical philosophers (but of no apparent interest to phenomenalists, deconstructionists, existentialists?). Generality is what you get from induction (which is, of course, problematic). |
| 7742 | Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh] |
| Full Idea: Frege treated 'everything' as basic, and suggested ways of recasting propositions containing other quantifiers so that this was the only one remaining. He recast 'something' as 'at least one thing', and defined this in terms of 'everything' and 'not'. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Gregory McCullogh - The Game of the Name 1.6 | |
| A reaction: Extreme parsimony seems highly desirable in logic as well as ontology, but it can lead to frustrations, especially over the crucial question of the existence of things quantified over. See Idea 6068. |
| 9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
| Full Idea: The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17 | |
| A reaction: In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it. |
| 14236 | Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege] |
| Full Idea: Frege says the number four is assigned to the concept 'horse that draws the Kaiser's carriage', but the four horses that drew the carriage did so together, not separately. No horses, not four, fall under the Fregean concept. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §46) by Oliver,A/Smiley,T - What are Sets and What are they For? Intro | |
| A reaction: They say that Frege stumbles because he is blind to irreducibly plural predicates. |
| 13824 | Proof theory began with Frege's definition of derivability [Frege, by Prawitz] |
| Full Idea: Frege's formal definition of derivability is perhaps the first investigation in general proof theory. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Dag Prawitz - Gentzen's Analysis of First-Order Proofs 2 n2 | |
| A reaction: In 'On General Proof Theory §1' Prawitz says "proof theory originated with Hilbert" in 1900. Presumably Frege offered a theory, and then Hilbert saw it as a general project. |
| 13609 | Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan] |
| Full Idea: Frege's work supplied a set of axioms for logic itself, at least partly because it was a well-known way of presenting the foundations in other disciplines, especially mathematics, but it does not nowadays strike us as natural for logic. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by David Kaplan - Dthat 5.1 | |
| A reaction: What Bostock has in mind is the so-called 'natural' deduction systems, which base logic on rules of entailment, rather than on a set of truths. The axiomatic approach uses a set of truths, plus the idea of possible contradictions. |
| 16884 | Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge] |
| Full Idea: In Frege's view axioms are basic truth, and basic truths do not need proof. Basic truths can be (justifiably) recognised as true by understanding their content. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 1 | |
| A reaction: This is the underpinning of the rationalism in Frege's philosophy. |
| 9462 | Frege is intensionalist about reference, as it is determined by sense; identity of objects comes first [Frege, by Jacquette] |
| Full Idea: Intensionalism of reference is owing to Frege (in his otherwise extensionalist philosophy of language). Sense determines reference, so intension determines extension. An object must first satisfy identity requirements, and is thus in a set. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Dale Jacquette - Intro to 'Philosophy of Logic' §4 | |
| A reaction: The notion that identity of objects comes first sounds right - you can't just take objects as basic - they have to be individuated in order to be discussed. |
| 18936 | Frege moved from extensional to intensional semantics when he added the idea of 'sense' [Frege, by Sawyer] |
| Full Idea: Frege moved from an extensional semantic theory (that countenances only linguistic expressions and their referents) to an intensional theory that invokes in addition a notion of sense. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Sarah Sawyer - Empty Names 2 | |
| A reaction: This was because of Frege's famous 'puzzles', such as the morning/evening star. Quine loudly proclaimed himself an 'extensionalist', implying that he had extensional solutions for Frege's Puzzles. |
| 22294 | We can show that a concept is consistent by producing something which falls under it [Frege] |
| Full Idea: We can only establish that a concept is free from contradiction by first producing something that falls under it. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §095), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist' | |
| A reaction: Potter quotes this as an example of proof by modelling. If it has one model then it must be consistent. Then we ask whether all the models are or are not consistent with one another. Circular squares fail the test. |
| 16886 | The truth of an axiom must be independently recognisable [Frege] |
| Full Idea: It is part of the concept of an axiom that it can be recognised as true independently of other truths. | |
| From: Gottlob Frege (On Euclidean Geometry [1900], 183/168), quoted by Tyler Burge - Frege on Knowing the Foundations 4 | |
| A reaction: Frege thinks the axioms of arithmetic all reside in logic. |
| 17624 | To understand axioms you must grasp their logical power and priority [Frege, by Burge] |
| Full Idea: Understanding the axioms depends not only on understanding Frege's elucidatory remarks about the interpretation of his symbols, but also on understanding their logical structure - their power to entail other truths, and their reason-giving priority. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 4) by Tyler Burge - Frege on Knowing the Foundations 4 | |
| A reaction: This is a distinctively Burgean spin put on what Frege has to say about axioms, but I like it, and it seems well enough supported in Frege's writings (e.g. 1914). |
| 16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
| Full Idea: We can trace the chains of inference backwards, …and the circle of theorems closes in more and more. ..We must eventually come to an end by arriving at truths can cannot be inferred, …which are the axioms and postulates. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: The rival (more modern) view is that that all theorems are equal in status, and axioms are selected for convenience. |
| 16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
| Full Idea: Science must endeavour to make the circle of unprovable primitive truths as small as possible, for the whole of mathematics is contained in this kernel. The essence of mathematics has to be defined by this kernel of truths. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204-5) | |
| A reaction: [compressed] I will make use of this thought, by arguing that mathematics may be 'explained' by this kernel. |
| 16871 | A truth can be an axiom in one system and not in another [Frege] |
| Full Idea: It is possible for a truth to be an axiom in one system and not in another. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: Frege aspired to one huge single system, so this is a begrudging concession, one which modern thinkers would probably take for granted. |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| Full Idea: The axioms are theorems, but truths for which no proof can be given in our system, and no proof is needed. It follows from this that there are no false axioms, and we cannot accept a thought as an axiom if we are in doubt about its truth. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: He struggles to be as objective as possible, but has to concede that whether we can 'doubt' the axiom is one of the criteria. |
| 15628 | The idea that contradiction is essential to rational understanding is a key modern idea [Hegel] |
| Full Idea: The thought that the contradiction which is posited by the determinations of the understanding in what is rational is essential and necessary, has to be considered one of the most important and profound advances of the philosophy of modern times. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48) | |
| A reaction: This is the aspect of Kant's philosophy which launched the whole career of Hegel. Hegel is the philosopher of the antinomies. Graham Priest is his current representative on earth. |
| 15629 | Tenderness for the world solves the antinomies; contradiction is in our reason, not in the essence of the world [Hegel] |
| Full Idea: The solution to the antinomies is as trivial as they are profound; it consists merely in a tenderness for the things of this world. The stain of contradiction ought not to be in the essence of what is in the world; it must belong only to thinking reason. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48 Rem) | |
| A reaction: A rather Wittgensteinian remark. I love his 'tenderness for the things of this world'! I'm not clear why our thinking should be considered to be inescapably riddled with basic contradictions, as Hegel seems to imply. Just make more effort. |
| 15630 | Antinomies are not just in four objects, but in all objects, all representations, all objects and all ideas [Hegel] |
| Full Idea: The main point that has to be made is that antinomy is found not only in Kant's four particular objects taken from cosmology, but rather in all objects of all kinds, in all representations, concepts and ideas. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48 Rem) | |
| A reaction: I suppose Heraclitus and Empedocles, with their oppositional accounts of reality, are the ancestors of this worldview. I just don't feel that sudden flood of insight from this idea of Hegel that comes from some of the other great philsophical theories. |
| 16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
| Full Idea: We cannot long remain content with the present fragmentation [of mathematics]. Order can be created only by a system. But to construct a system it is necessary that in any step forward we take we should be aware of the logical inferences involved. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19 | |
| A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals. |
| 18256 | Quantity is inconceivable without the idea of addition [Frege] |
| Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit' | |
| A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree. |
| 8640 | We cannot define numbers from the idea of a series, because numbers must precede that [Frege] |
| Full Idea: We cannot define number by the generalized concept of a series. Positions in the series cannot be the basis on which we distinguish the objects, since they must already have been distinguished somehow or other, for us to arrange them in a series. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §42) | |
| A reaction: You can arrange things in a line without the use of numbers. You need prior mastery of counting, though, to say where an item comes in the line. And yet... why shouldn't you define counting by the use of some original primitive line? Numbers map onto it. |
| 18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
| Full Idea: If 'number' is the referent of a numerical symbol, a real number is the same as a ratio of quantities. ...A length can have to another length the same ratio as a mass to another mass. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], III.1.73), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' | |
| A reaction: This is part of a critique of Cantor and the Cauchy series approach. Interesting that Frege, who is in the platonist camp, is keen to connect the real numbers with natural phenomena. He is always keen to keep touch with the application of mathematics. |
| 18253 | I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege] |
| Full Idea: You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities. | |
| From: Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' | |
| A reaction: Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc. |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton). | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
| A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'? |
| 9838 | Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett] |
| Full Idea: Frege's point was that by treating 0 as a number, we run into none of the antinomies that result from treating 'never' as the name of a time, or 'nobody' as the name of a person. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.8 | |
| A reaction: I don't think that is a good enough reason. Daft problems like that are solved by settling the underlying proposition or logical form (of a sentence containing 'nobody') before one begins to reason. Other antinomies arise with zero. |
| 9564 | For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined [Frege, by Chihara] |
| Full Idea: In Frege's system 'concept' and 'extension of a concept' are primitive notions; whereas 'zero' and 'successor' are defined. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Charles Chihara - A Structural Account of Mathematics 7.5 | |
| A reaction: This is in contrast to the earlier Peano Postulates for arithmetic, which treat 'zero' and 'successor' as primitive. Interesting, given that Frege is famous for being a platonist. |
| 10551 | If objects exist because they fall under a concept, 0 is the object under which no objects fall [Frege, by Dummett] |
| Full Idea: On Frege's approach (of accepting abstract objects if they fall under a concept) the existence of the number 0, from which the series of numbers starts, is of course guaranteed by the citation of a concept under which nothing falls. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: Frege cites the set of all non-self-identical objects, but he could have cited the set of circular squares. Given his Russell Paradox problems, this whole claim is thrown in doubt. Actually doesn't Frege's view make 0 impossible? Am I missing something? |
| 8653 | Nought is the number belonging to the concept 'not identical with itself' [Frege] |
| Full Idea: I define nought as the Number which belongs to the concept 'not identical with itself'. ...I choose this definition as it can be proved on purely logical grounds. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §74) | |
| A reaction: An important part of Frege's logicist programme, along with his use of Hume's Principle (Idea 8649). He needed a prior definition of 'Number' (in §68). Clever, but intuitively a rather weird idea of zero. It is more of an example than a definition. |
| 8636 | We can say 'a and b are F' if F is 'wise', but not if it is 'one' [Frege] |
| Full Idea: We combine 'Solon was wise' and 'Thales was wise' into 'Solon and Thales were wise', but we can't say 'Solon and Thales were one', which implies that 'one' is not a property in the same way 'wise' is. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §29) | |
| A reaction: Maybe 'one' is still a property, but of a different sort. However, Frege builds up a very persuasive case that just because numbers function as adjectives it does not follow that they are properties. See Idea 8637. |
| 8654 | One is the Number which belongs to the concept "identical with 0" [Frege] |
| Full Idea: One is the Number which belongs to the concept "identical with 0". | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §77) | |
| A reaction: This follows from Idea 8653, which defined zero. Zero is the number of a non-existent set, and one is how many sets you have when you have only got zero. Very clever. |
| 8641 | You can abstract concepts from the moon, but the number one is not among them [Frege] |
| Full Idea: What are we supposed to abstract from to get from the moon to the number 1? We do get certain concepts, such as satellite, but 1 is not to be met with. In the case of 0 we have no objects at all. ..The essence of number must work for 0 and 1. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §44) | |
| A reaction: Note that Frege seems to be conceding psychological abstraction for most other concepts. But why can't you abstract from your abstractions, to reach high-level abstractions? And why should numbers not emerge at those higher levels? |
| 9989 | Units can be equal without being identical [Tait on Frege] |
| Full Idea: The fact that units are equal does not mean that they are identical. The units can be equal just in the sense that once can be substituted for any other without altering the name assigned, i.e. the number. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54) by William W. Tait - Frege versus Cantor and Dedekind XI | |
| A reaction: [this is in reference to Thomae 1880] Presumably this might mean that units have type-identity, rather than token-dentity. 'This' unit might be a token, but 'a' unit would be a type. I am extremely reluctant to ditch the old concept of a unit. |
| 17429 | Frege says only concepts which isolate and avoid arbitrary division can give units [Frege, by Koslicki] |
| Full Idea: It is Frege's view that only concepts which satisfy isolation and non-arbitrary division can play the role of dividing up what falls under them into countable units. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1 | |
| A reaction: Compare Idea 17429. If I count out a 'team of players', I need this unit concept to get what a 'player' is, but then need the 'team' concept to do the counting. Number doesn't attach to the unit concept. |
| 17427 | Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Frege, by Koslicki] |
| Full Idea: Frege's proposal can be isolation as discreteness, i.e. absence of overlap, between the objects counted; and isolation as drawing of conceptual boundaries. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 1 |
| 17437 | Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki] |
| Full Idea: Non-arbitrary division concerns the internal structure of the things falling under a concept. Its point is to ensure that we cannot go on dividing these units arbitrarily and still expect to find more things of the same kind. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.3 | |
| A reaction: Counting something red is given as an example. This seems to define mass-terms, or stuff. |
| 17438 | Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Frege, by Koslicki] |
| Full Idea: For Frege, the distinction between what we count and what we do not count is drawn by our concepts. ...We can describe the very same external phenomena either as the leaves of a tree or its foliage. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 3 | |
| A reaction: Hm. We can't obey 'count the foliage', but we all know that foliage is countable stuff, where water isn't. Nature has a say here - it isn't just a matter of our concepts. |
| 17426 | A concept creating a unit must isolate and unify what falls under it [Frege] |
| Full Idea: Only a concept which isolates what falls under it in a definite manner, and which does not permit any arbitrary division of it into parts, can be a unit relative to finite Number. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54), quoted by Kathrin Koslicki - Isolation and Non-arbitrary Division 1 | |
| A reaction: This is the key modern proposal for the basis of counting, by trying to get at the sort of concept which will turn something into a 'unit'. The concept must isolate and unify. Why should just one concept do that each time? |
| 17428 | Frege says counting is determining what number belongs to a given concept [Frege, by Koslicki] |
| Full Idea: Roughly, Frege's picture of counting is this. When we count something, we determine what number belongs to a given concept. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1 | |
| A reaction: If the concept were 'herd of sheep' that would need a context before there could be a fixed number. You can count until you get bored, like counting stars to get to sleep. 'Count off 20 sheep' has the number before the counting starts. |
| 15916 | Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine] |
| Full Idea: Frege assumed that since infinite collections cannot be counted, he needed a theory of number that is independent of counting. He therefore took one-to-one correspondence to be basic, not well-orderings. Hence cardinals are basic, not ordinals. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Shaughan Lavine - Understanding the Infinite III.4 |
| 17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
| Full Idea: Counting rests itself on a one-one correlation, namely of numerals 1 to n and the objects. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]), quoted by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: Parsons observes that counting will establish a one-one correspondence, but that doesn't make it the aim of counting, and so Frege hasn't answered Husserl properly. Which of the two is conceptually prior? How do you decide. |
| 9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
| Full Idea: When Husserl says that sameness of number can be shown by one-one correlation, he forgets that this counting itself rests on a univocal one-one correlation, namely that between the numerals 1 to n and the objects of the set. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326) | |
| A reaction: This is the platonist talking. Neo-logicism is attempting to build numbers just from the one-one correlation of objects. |
| 10034 | The number of natural numbers is not a natural number [Frege, by George/Velleman] |
| Full Idea: Frege shows that the number of natural numbers is not identical to any natural number. This is because, while no natural number is identical to its successor, the number of natural numbers is. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: Frege is notorious for the lack of respect shown in his writings for the great Cantor, and this seems to have blocked him from a more sophisticated account of infinity, but this idea seems a nice one. |
| 18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
| Full Idea: It cannot be demanded that everything be proved, because that is impossible; but we can require that all propositions used without proof be expressly declared as such, so that we can see distinctly what the whole structure rests upon. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.2), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 'What' |
| 16883 | Arithmetical statements can't be axioms, because they are provable [Frege, by Burge] |
| Full Idea: For Frege, no arithmetical statement is an axiom, because all are provable. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Knowing the Foundations 1 | |
| A reaction: This is Frege's logicism, in which the true and unprovable axioms are all found in the logic, not in the arithmetic. Compare that view with the Dedekind/Peano axioms. |
| 16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
| Full Idea: If the law [of induction] can be proved, it will be included amongst the theorems of mathematics; if it cannot, it will be included amongst the axioms. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: This links Frege with the traditional Euclidean view of axioms. The question, then, is how do we know them, given that we can't prove them. |
| 17855 | It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C] |
| Full Idea: Frege's account of the ancestral has made it possible, in effect, to define the natural numbers as entities for which induction holds. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Crispin Wright - Frege's Concept of Numbers as Objects 4.xix | |
| A reaction: This is the opposite of the approach in the Peano Axioms, where induction is used to define the natural numbers. |
| 10625 | Frege had a motive to treat numbers as objects, but not a justification [Hale/Wright on Frege] |
| Full Idea: It has been observed that Frege has a motive to treat numbers as objects, but not a justification for doing so. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' §3.2 |
| 13871 | Frege claims that numbers are objects, as opposed to them being Fregean concepts [Frege, by Wright,C] |
| Full Idea: When Frege urges that numbers are to be thought of as objects, the content of this claim has to be derived from its opposition to the claim that numbers are Fregean concepts. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 1.ii |
| 13872 | Numbers are second-level, ascribing properties to concepts rather than to objects [Frege, by Wright,C] |
| Full Idea: Frege had the insight that statements of number, like statements of existence, are in a sense second-level. That is, they are most fruitfully and least confusingly seen as ascribing a property not to an object, but to a concept. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 1.iii | |
| A reaction: This sounds neat, but I'm immediately wondering whether he is just noticing how languages work, rather than how things are. If I say red is a bright colour, I am saying something about red objects. |
| 9816 | For Frege, successor was a relation, not a function [Frege, by Dummett] |
| Full Idea: Frege was operating with a successor relation, rather than a successor function. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.2 | |
| A reaction: That is, succession is a given fact, not a construction. 4 may be the successor of 3 in natural numbers, but not in rational or real numbers, so we can't take the relation for granted. |
| 9953 | Numbers are more than just 'second-level concepts', since existence is also one [Frege, by George/Velleman] |
| Full Idea: Frege needs more than just saying that numbers are second-level concepts under which first-level concepts fall, because they can fall under many second-level concepts, such as that of existence. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This marks the end of the first stage of Frege's theory, which leads him on to objects and Hume's Principle. After you have written 'level' a few times, you begin to wonder whether thought and world really are carved up in such a neat way. |
| 9954 | "Number of x's such that ..x.." is a functional expression, yielding a name when completed [Frege, by George/Velleman] |
| Full Idea: We can view "the number of x's such that ...x..." as a functional expression that is completed by a first-level predicate and yields a name (which is of the right kind to denote an object). | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This is how Frege gets, in his account, from numbers being predicates to numbers being objects. He was a clever lad. |
| 10139 | Frege gives an incoherent account of extensions resulting from abstraction [Fine,K on Frege] |
| Full Idea: Frege identifies each conceptual abstract with the corresponding extension of concepts. But the extensions themselves are among the abstracts, so each extension is identical with the class of all concepts that have that extension, which is absurd. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kit Fine - The Limits of Abstraction I.2 | |
| A reaction: Fine says this point is 'from the standpoint of a general theory of abstracts', which presumably was implied in Frege, but not actually spelled out. |
| 10028 | For Frege the number of F's is a collection of first-level concepts [Frege, by George/Velleman] |
| Full Idea: Frege defines 'the number of F's' as the extension of the concept 'equinumerous with F'. The extension of such a concept will be a collection of first-level concepts, namely, just those that are equinumerous with F. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This must be reconciled with Frege's platonism, which tells us that numbers are objects, so the objects are second-level sets. Would there be third-level object/sets, such as the set of all the second-level sets perfectly divisible by three? |
| 17636 | A cardinal number may be defined as a class of similar classes [Frege, by Russell] |
| Full Idea: Frege showed that a cardinal number may be defined as a class of similar classes. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Bertrand Russell - Regressive Method for Premises in Mathematics p.277 |
| 9586 | In a number-statement, something is predicated of a concept [Frege] |
| Full Idea: In a number-statement, something is predicated of a concept. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.328) | |
| A reaction: A succinct statement of Frege's theory of numbers. By my lights that would make numbers at least second-order abstractions. |
| 10029 | Numbers need to be objects, to define the extension of the concept of each successor to n [Frege, by George/Velleman] |
| Full Idea: The fact that numbers are objects guarantees the availability of a supply of n+1 objects, which can be used to define the concept F for the successor of n, by defining the objects which fall under F. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: [compressed] This is the key step which takes from from numbers being adjectival to numbers being objectual. One wonders whether physical objects might do the necessary job at the next level down. Numbers need countables. |
| 9973 | The number of F's is the extension of the second level concept 'is equipollent with F' [Frege, by Tait] |
| Full Idea: Frege's definition is that the number N F(x) of F's, where F is a concept, is the extension of the second level concept 'is equipollent with F'. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by William W. Tait - Frege versus Cantor and Dedekind III | |
| A reaction: In trying to pin Frege down precisely, we must remember that an extension can be a collection of sets, as well as a collection of concrete particulars. |
| 16500 | Frege showed that numbers attach to concepts, not to objects [Frege, by Wiggins] |
| Full Idea: It was a justly celebrated insight of Frege that numbers attach to the concepts under which objects fall, and not to the objects themselves. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by David Wiggins - Sameness and Substance 1.6 | |
| A reaction: A combination of this idea, and Aristotle's 'Categories', give us the roots of the philosophy of David Wiggins. Frege's example of two boots (or one 'pair' of boots) is the clearest example. …But the world dictates our concepts. |
| 9990 | Frege replaced Cantor's sets as the objects of equinumerosity attributions with concepts [Frege, by Tait] |
| Full Idea: Frege's contribution with respect to the definition of equinumerosity was to replace Cantor's sets as the objects of number attributions by concepts. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by William W. Tait - Frege versus Cantor and Dedekind XII | |
| A reaction: This pinpoints Frege's big idea, which is a powerful one, and may be right. The difficulty seems to be that the extension is ultimately what counts (because that is where plurality resides), and it is tricky getting the concept to determine the extension. |
| 7738 | Zero is defined using 'is not self-identical', and one by using the concept of zero [Frege, by Weiner] |
| Full Idea: Zero is the extension of 'is equinumerous with the concept "is not self-identical"' (which holds of no objects); ..one is defined as the extension of 'is equinumerous with the concept "is identical to zero"'. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.4 | |
| A reaction: It sounds like some sort of cheating to define zero in terms of objects, but one in terms of concepts. |
| 23456 | Frege said logical predication implies classes, which are arithmetical objects [Frege, by Morris,M] |
| Full Idea: Frege's idea is that the logical notion of predication is enough to generate appropriate objects. Every predicate defines a class, which is in turn an object to which predicates apply; and the notion of a class can be used to generate arithmetic. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H | |
| A reaction: At last, a lovely clear account of what Frege was doing - and why Russell's paradox was Frege's disaster. Logicism must take the ingredients of logic, and generate arithmetical 'objects' from them alone. But do we need 'objects'? |
| 13887 | Frege started with contextual definition, but then switched to explicit extensional definition [Frege, by Wright,C] |
| Full Idea: Frege abandoned contextual definition of numerical singular terms, and decided to go for explicit definitions in terms of extension-denoting terms instead. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv |
| 13897 | Each number, except 0, is the number of the concept of all of its predecessors [Frege, by Wright,C] |
| Full Idea: In Frege's definition of numbers, each number, except 0, is defined as the number belonging to the concept under which just its predecessors fall. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 4.xvii | |
| A reaction: This would make the numbers dependent on all of the predecessors, just as Dedekind's numbers do. Dedekind's progression has to continue, but why should Frege's? Frege's are just there, where Dedekind's are constructed. Why are Frege's ordered? |
| 9856 | Frege's account of cardinals fails in modern set theory, so they are now defined differently [Dummett on Frege] |
| Full Idea: In standard set theory, Frege's cardinals could not be members of classes, and his proof of the infinity of natural numbers fails. Nowadays they are defined as sets each representative of its cardinality, comprising ordinals of lower cardinality. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.14 | |
| A reaction: Pinning something down in a unique way is not the same as telling you its intrinsic nature. But a completely successful definition seems to have locked on to some deep truth about its target. |
| 9902 | Frege's incorrect view is that a number is an equivalence class [Benacerraf on Frege] |
| Full Idea: Frege view (which has little to commend it) was that the number 3 is the extension of the concept 'equivalent with some 3-membered set'; that is, for Frege a number was an equivalence class - the class of all classes equivalent with a given class. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Paul Benacerraf - What Numbers Could Not Be II | |
| A reaction: Frege is a platonist, who takes numbers to be objects, so this equivalence class must be identical with an object. What exactly was Frege claiming? I mean, really exactly? |
| 17814 | The natural number n is the set of n-membered sets [Frege, by Yourgrau] |
| Full Idea: Frege defines the natural number n in terms of the set of n-membered sets. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Palle Yourgrau - Sets, Aggregates and Numbers 'Two' | |
| A reaction: He says this view 'has been treated rudely by history', because Frege's view of sets was naive, and because independence results have undermined set-theoretic platonism. |
| 17819 | A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau on Frege] |
| Full Idea: Given the set {Carter, Reagan} ...I still want to know How many what? Members? 2. Sets? 1. Feet of members? 4. Relatives of members? 44. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Palle Yourgrau - Sets, Aggregates and Numbers 'New Problem' | |
| A reaction: This is his 'new problem' for Frege. Frege want a concept to divide a pack of cards, by cards, suits or pips. You choose 'pips' and form a set, but then the pips may have a number of corners. Solution: pick your 'objects' or 'units', and stick to it. |
| 17820 | If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on Frege] |
| Full Idea: If we are allowed in the case of sets to construe the number question as 'really': How many (elements)?, then we could just as well construe Frege's famous question about the deck of cards as: How many (cards)? | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Palle Yourgrau - Sets, Aggregates and Numbers 'New Problem' | |
| A reaction: My view is that counting is not entirely relative to the concept employed, but that the world imposes objects on us which thus impose their concepts and their counting. This is 'natural', but we can then counter nature with pragmatics and whimsy. |
| 3331 | If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege] |
| Full Idea: There is a suspicion that Frege's definition of 5 (as the set of all sets with 5 members) may be infected with circularity, …and how can we be sure on a priori grounds that 4 and 5 are not both empty sets, and hence identical? | |
| From: comment on Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.14 |
| 9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
| Full Idea: For Frege, the extension of the concept F is an object, as revealed by the fact that we use a name to refer to it. ..We must distinguish the concept, the object that falls under it, and the extension of the concept, which is the set containing the object. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This I take to be the key distinction needed if one is to grasp Frege's account of what a number is. When we say that Frege is a platonist about numbers, it is because he is committed to the notion that the extension is an object. |
| 10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
| Full Idea: Frege opts for his famous definition of numbers in terms of extensions of the concept 'equal to the concept F', but he then (in 'Grundgesetze') needs a theory of extensions or classes, which he provided by means of Basic Law V. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' §1 |
| 17460 | A statement of number contains a predication about a concept [Frege] |
| Full Idea: A statement of number [Zahlangabe] contains a predication about a concept. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §46), quoted by Ian Rumfitt - Concepts and Counting Intro | |
| A reaction: See Rumfitt 'Concepts and Counting' for a discussion. |
| 16890 | Frege's problem is explaining the particularity of numbers by general laws [Frege, by Burge] |
| Full Idea: The worry with the attempt to derive arithmetic from general logical laws (which is required for it to be analytic apriori) is that it is incompatible with the particularity of numbers. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §13) by Tyler Burge - Frege on Apriority (with ps) 1 | |
| A reaction: Burge cites §13 (end) of Grundlagen, and then the doomed Basic Law V as his attempt to bridge the gap from general to particular. |
| 8630 | Individual numbers are best derived from the number one, and increase by one [Frege] |
| Full Idea: The individual numbers are best derived from the number one together with increase by one. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §18) | |
| A reaction: Frege rejects the empirical approach partly because of the intractability of zero, but this approach has the same problem. I suggest a combination of empiricism for simple numbers, and pure formalism for extensions into complexity, and zero. |
| 11029 | 'Exactly ten gallons' may not mean ten things instantiate 'gallon' [Rumfitt on Frege] |
| Full Idea: To the question 'How many gallons of water are in the tank', the correct answer might be 'exactly ten'. But this does not mean that exactly ten things instantiate the concept 'gallon of water in the tank'. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §46) by Ian Rumfitt - Concepts and Counting p.43 | |
| A reaction: The difficulty for Frege that is being raised is that whole numbers are used to designate quantities of stuff, as well as for counting denumerable things. Rumfitt notes that 'ten' answers 'how much?' as well as Frege's 'how many?'. |
| 10013 | Numerical statements have first-order logical form, so must refer to objects [Frege, by Hodes] |
| Full Idea: Summary: numerical terms are singular terms designating objects; numerical predicates are level 1 concepts and relations; quantification over mathematics is referential; hence arithmetic has first-order form, and mathematical objects exist, non-spatially. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §55?) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.123 | |
| A reaction: [compressed] So the heart of Frege is his translation of 'Jupiter has four moons' into a logical form which only refers to numerical objects. Commentators seem vague as to whether the theory is first-order or second-order. |
| 18181 | The Number for F is the extension of 'equal to F' (or maybe just F itself) [Frege] |
| Full Idea: My definition is as follows: the Number which belongs to the concept F is the extension of the concept 'equal to the concept F' [note: I believe that for 'extension of the concept' we could simply write 'concept']. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §68) | |
| A reaction: The note has caused huge discussion [Maddy 1997:24]. No wonder I am confused about whether a Fregean number is a concept, or a property of a concept, or a collection of things, or an object. Or all four. Or none of the above. |
| 18103 | Numbers are objects because they partake in identity statements [Frege, by Bostock] |
| Full Idea: One can always say 'the number of Jupiter's moons is 4', which is explicitly a statement of identity, and for Frege identity is always to be construed as a relation between objects. This is really all he gives to argue that numbers are objects. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 55-57) by David Bostock - Philosophy of Mathematics | |
| A reaction: I struggle to understand why numbers turn out to be objects for Frege, given that they are defined in terms of sets of equinumerous sets. Is the number not a property of that meta-set. Bostock confirms my uncertainty. Paraphrase as solution? |
| 9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
| Full Idea: Cantor pointed out explicitly to Frege that it is a mistake to take the notion of a set (i.e. of that which has a cardinal number) to simply mean the extension of a concept. ...Frege's later assumption of this was an act of recklessness. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by William W. Tait - Frege versus Cantor and Dedekind III | |
| A reaction: ['recklessness' is on p.61] Tait has no sympathy with the image of Frege as an intellectual martyr. Frege had insufficient respect for a great genius. Cantor, crucially, understood infinity much better than Frege. |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139 | |
| A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble. |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 |
| 9956 | 'The number of Fs' is the extension (a collection of first-level concepts) of the concept 'equinumerous with F' [Frege, by George/Velleman] |
| Full Idea: Frege defines 'the number of Fs' as equal to the extension of the concept 'equinumerous with F'. The extension of such a concept will be a collection of first-level concepts, namely those that are equinumerous with F. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: Presumably this means equinumerous with 'instances' of F, if F is a predicate. The problem of universals looms. I was clear about this idea until I tried to draw a diagram illustrating it. You try! |
| 13527 | Frege's cardinals (equivalences of one-one correspondences) is not permissible in ZFC [Frege, by Wolf,RS] |
| Full Idea: Frege defined a cardinal as an equivalence class of one-one correspondences. The cardinal 3 is the class of all sets with three members. This definition is intuitively appealing, but it is not permissible in ZFC. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Robert S. Wolf - A Tour through Mathematical Logic 2.2 | |
| A reaction: This is why Frege's well known definition of cardinals no longer figures in standard discussions of the subject. His definition is acceptable in Von Neumann-Bernays-Gödel set theory (Wolf p.73). |
| 22292 | Hume's Principle fails to implicitly define numbers, because of the Julius Caesar [Frege, by Potter] |
| Full Idea: Frege rejected Hume's Principle as an implicit definition of number terms, because of the Julius Caesar problem. ....[128] Instead Frege adopted an explicit definition of the number-of function. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Uniq' |
| 17442 | Frege thinks number is fundamentally bound up with one-one correspondence [Frege, by Heck] |
| Full Idea: Frege's answer is that the concept of number is fundamentally bound up with the notion of one-one correspondence. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1 | |
| A reaction: Birds seem to find a mate with virtually no concept of number. I'm beginning to think that the essence of numbers is that they are both ordinals and cardinals. Frege, of course, thinks identity is basic to metaphysics. |
| 11030 | The words 'There are exactly Julius Caesar moons of Mars' are gibberish [Rumfitt on Frege] |
| Full Idea: The word 'Julius Caesar is prime' may well involve some kind of category error, but the still compose a grammatical sentence. The words 'There are exactly Julius Caesar moons of Mars', by contrast, are gibberish. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Ian Rumfitt - Concepts and Counting p.48 |
| 10030 | 'Julius Caesar' isn't a number because numbers inherit properties of 0 and successor [Frege, by George/Velleman] |
| Full Idea: 'Julius Caesar' is not a natural number in Frege's account because he does not fall under every concept under which 0 falls and which is hereditary with respect to successor. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: Significant for structuralist views. One might say that any object can occupy the structural place of '17', but if you derive your numbers from 0, successor and induction, then the 17-object must also inherit the properties of zero and successors. |
| 8690 | From within logic, how can we tell whether an arbitrary object like Julius Caesar is a number? [Frege, by Friend] |
| Full Idea: The 'Julius Caesar problem' in Frege's theory is that from within logic we cannot tell if an arbitrary objects such as Julius Caesar is a number or not. Logic itself cannot tell us enough to distinguish numbers from other sorts of objects. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.4 | |
| A reaction: What a delightful problem (raised by Frege himself). A theory can look beautiful till you ask a question like this. Only a logician would, I suspect, get into this mess. Numbers can be used to count or order things! "I've got Caesar pencils"? |
| 10219 | Frege said 2 is the extension of all pairs (so Julius Caesar isn't 2, because he's not an extension) [Frege, by Shapiro] |
| Full Idea: Frege proposed that the number 2 is a certain extension, the collection of all pairs. Thus, 2 is not Julius Caesar because, presumably, persons are not extensions. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stewart Shapiro - Philosophy of Mathematics 3.2 | |
| A reaction: Unfortunately, as Shapiro notes, Frege's account of extension went horribly wrong. Nevertheless, this seems to show why the Julius Caesar problem does not matter for Frege, though it might matter for the neo-logicists. |
| 13889 | Fregean numbers are numbers, and not 'Caesar', because they correlate 1-1 [Frege, by Wright,C] |
| Full Idea: We cannot reasonably suppose that any numerical singular term has the same reference as 'Caesar', because Frege's numbers (unlike persons) are to be identified and distinguished by appeal to facts about 1-1 correlation among concepts. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv |
| 18142 | One-one correlations imply normal arithmetic, but don't explain our concept of a number [Frege, by Bostock] |
| Full Idea: Frege inferred from the Julius Caesar problem that even though Hume's Principle sufficed as a single axiom for deducing the arithmetic of the finite cardinal numbers, still it does not explain our ordinary understanding of those numbers. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by David Bostock - Philosophy of Mathematics 9.A.2 |
| 9046 | Our definition will not tell us whether or not Julius Caesar is a number [Frege] |
| Full Idea: We can never decide by means of our definitions whether any concept has the number JULIUS CAESAR belonging to it, or whether that same familiar conqueror of Gaul is a number or not. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §56) | |
| A reaction: This has become a famous modern problem. The point is that the definition of a number must explain why this is a number, and not something else. Must you mention that you could use it to count? Count you count using emperors? |
| 16896 | If numbers can be derived from logic, then set theory is superfluous [Frege, by Burge] |
| Full Idea: Frege thought that if one could derive the existence of numbers from logical concepts, one would not need set theory to explain number theory, or for any other good purpose. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority (with ps) 2 | |
| A reaction: Note that we have two possible routes to 'explain' numbers. I'm inclined to see set theory as modelling numbers rather than explaining them. Frege did better at explanation, but I suspect he is wrong too. |
| 8639 | If numbers are supposed to be patterns, each number can have many patterns [Frege] |
| Full Idea: Patterns can be completely different while the number of their elements remains the same, so that here we would have different distinct fives, sixes and so forth. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §41) | |
| A reaction: A blow to my enthusiasm for Michael Resnik's account of maths as patterns. See, for example, Ideas 6296 and 6301. We are clearly set up to spot patterns long before we arrive at the abstract concepts of numbers. We see the same number in two patterns. |
| 13874 | Numbers seem to be objects because they exactly fit the inference patterns for identities [Frege] |
| Full Idea: The most important consideration for numbers being objects is that they sustain the patterns of inference demanded by the reflexivity, transitivity and symmetry of identity. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]), quoted by Crispin Wright - Frege's Concept of Numbers as Objects 1.iii | |
| A reaction: But then if I say that the 'whereabouts of Jack' is identical to the 'whereabouts of Jill', that would seem to make whereaboutses into objects. |
| 13875 | Frege's platonism proposes that objects are what singular terms refer to [Frege, by Wright,C] |
| Full Idea: The basis of Frege's platonism is the thesis that objects are what singular terms, in the ordinary intuitive sense of 'singular term', refer to. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 1.iii | |
| A reaction: This claim strikes me as very bizarre, and is at the root of all the daft aspects of twentieth century linguistic philosophy. See Bob Hale on singular terms, who defends the Fregean view against obvious problems like 'for THE SAKE of the children'. |
| 7731 | How can numbers be external (one pair of boots is two boots), or subjective (and so relative)? [Frege, by Weiner] |
| Full Idea: If the number one is a property of external things, how can one pair of boots be the same as two boots? ...but if the number one is subjective, then the number a thing has for me need not be the same number the object has for you. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.4 | |
| A reaction: This nicely captures the initial dilemma over the nature of numbers. It is the commonest dilemma in all of philosophy, struggling between subjective and objective accounts of things. Hence Putnam's nice definition of philosophy (Idea 2352). |
| 7737 | Identities refer to objects, so numbers must be objects [Frege, by Weiner] |
| Full Idea: Identity statements are about objects. If we can say that 1 is identical (or not) to 0, then 1 must be an object. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.4 | |
| A reaction: This seems to point to Platonism about numbers, but maybe we can accept it as being about physical objects. If numbers are essentially patterns, then identity is hypothetical one-to-one identity between sets of objects. |
| 8635 | Numbers are not physical, and not ideas - they are objective and non-sensible [Frege] |
| Full Idea: Number is neither spatial and physical, like Mill's pile of pebbles, nor yet subjective like ideas, but non-sensible and objective. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §27) | |
| A reaction: This doesn't require commitment to full-blown universals, nor to a dualist world of mind. The thinking of the brain moves far away from the areas of sensation, and the brain's capacity for truth is its capacity for objectivity. |
| 8652 | Numbers are objects, because they can take the definite article, and can't be plurals [Frege] |
| Full Idea: Individual numbers are objects, as is indicated by the use of the definite article in expressions like 'the number two', and by the impossibility of speaking of ones, twos, etc. in the plural. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §68 n) | |
| A reaction: Hm. The beginnings of linguistic philosophy, with all its problems. It is well known that 'for the sake of the children' doesn't make an ontological commitment to 'sakes'. The children might 'enter in threes', but the second half is a good point. |
| 9580 | Our concepts recognise existing relations, they don't change them [Frege] |
| Full Idea: The bringing of an object under a concept is merely the recognition of a relation which previously already obtained, [but in the abstractionist view] objects are essentially changed by the process, so that objects brought under a concept become similar. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: Frege's view would have to account for occasional misapplications of concepts, like taking a dolphin to be a fish, or falsely thinking there is someone in the cellar. |
| 9589 | Numbers are not real like the sea, but (crucially) they are still objective [Frege] |
| Full Idea: The sea is something real and a number is not; but this does not prevent it from being something objective; and that is the important thing. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.337) | |
| A reaction: This seems a qualification of Frege's platonism. It is why people start talking about abstract items which 'subsist', instead of 'exist'. It shows Frege's motivation in all this, which is to secure logic and maths from the vagaries of psychology. |
| 17816 | Frege's logicism aimed at removing the reliance of arithmetic on intuition [Frege, by Yourgrau] |
| Full Idea: In reducing arithmetic to logic Frege was precisely trying to show the independence of this study from any peculiarly mathematical intuitions. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Palle Yourgrau - Sets, Aggregates and Numbers 'Two' |
| 9831 | Geometry appeals to intuition as the source of its axioms [Frege] |
| Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged. |
| 8633 | There is no physical difference between two boots and one pair of boots [Frege] |
| Full Idea: One pair of boots may be the same visible and tangible phenomenon as two boots. This is a difference in number to which no physical difference corresponds; for 'two' and 'one pair' are by no means the same thing. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §25) | |
| A reaction: He is attacking Mill. Those of us who are seeking an empirical account of arithmetic have certainly got to face up to this example. Not insurmountable, I think. |
| 9577 | The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege] |
| Full Idea: The most naïve opinion of number is that it is something like a heap in which things are contained. The next most naïve view is the conception of number as the property of a heap, cleansing the objects of their particulars. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.323) | |
| A reaction: A hundred toothbrushes and a hundred sponges can be seen to contain the same number (by one-to-one mapping), without actually knowing what that number is. There is something numerical in the heap, even if the number is absent. |
| 9951 | It appears that numbers are adjectives, but they don't apply to a single object [Frege, by George/Velleman] |
| Full Idea: Numbers as adjectives appear to attribute a property - but to what? Superficially it seems to be to the objects themselves, as it makes sense to say that a plague is 'deadly', but not that it is 'ten'. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: Surely they could be adjectival if they were properties of groups? Groups can be 'numerous', or 'more than a hundred', or 'too many for this taxi'. |
| 9952 | Numerical adjectives are of the same second-level type as the existential quantifier [Frege, by George/Velleman] |
| Full Idea: A numerical adjective forms part of a predicate of second-level, needing supplementation from the first level (F). So the second-level predicate is of the same type as the existential quantifier, and can be called a 'numerical quantifier'. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This seems like a highly plausible account of how numbers work in language, but it leaves you wondering what the ontological status of a quantifier is. I presume platonic heaven is not full of elite entities called quantifiers, marshalling the others. |
| 11031 | 'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many' [Rumfitt on Frege] |
| Full Idea: 'Jupiter has four moons' is semantically and syntactically on all fours with 'Jupiter has many moons'. But it would be brave to construe the latter proposition as a transformation of 'The number of Jupiter's moons is identical with the number many'. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Ian Rumfitt - Concepts and Counting p.49 | |
| A reaction: I take this to be an important insight. Number words are continuous with (are in the same category as) words for general numerical quantity, such as 'just a few' or 'many' or 'rather a lot'. Numbers are part of normal language. |
| 8637 | The number 'one' can't be a property, if any object can be viewed as one or not one [Frege] |
| Full Idea: How can it make sense to ascribe the property 'one' to any object whatever, when every object, according as to how we look at it, can be either one or not one? | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §30) | |
| A reaction: This remark seems to point to numbers being highly subjective, but the interest of Frege is that he then makes out a case for numbers being totally objective, despite being entirely non-physical in nature. How do they do that? |
| 9999 | For science, we can translate adjectival numbers into noun form [Frege] |
| Full Idea: We want a concept of number usable for science; we should not, therefore, be deterred by everyday language using numbers in attributive constructions. The proposition 'Jupiter has four moons' can be converted to 'the number of Jupiter's moons is four'. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §57) | |
| A reaction: Critics are quick to point out that this could work the other way (noun-to-adjective), so Frege hasn't got an argument here, only an escape route. How about the verb version ('the moons of Jupiter four'), or the adverb ('J's moons behave fourly')? |
| 7739 | Arithmetic is analytic [Frege, by Weiner] |
| Full Idea: Frege's project was to show that arithmetic is analytic. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.7 | |
| A reaction: This particularly opposes Kant (e.g. Idea 5525). My favoured view (which may have few friends) is that arithmetic is a set of facts about the necessary pattern relationships within any possible physical world. That will make it synthetic. |
| 9945 | Logicism shows that no empirical truths are needed to justify arithmetic [Frege, by George/Velleman] |
| Full Idea: Frege claims that his logicist project directly shows that no empirical truths about the natural world need be employed in the justification of arithmetic (nor need any truths that are apprehended through some kind of intuition). | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This simple way of putting it creates a sticking-point for me. It occurs to me that the best description of arithmetic is that it 'models' the natural world. If a beautiful system failed to count objects, it wouldn't be accepted as 'arithmetic'. |
| 8782 | Frege offered a Platonist version of logicism, committed to cardinal and real numbers [Frege, by Hale/Wright] |
| Full Idea: Since Frege's defence of his thesis that the laws of arithmetic are analytic depended upon a realm of independently existing objects - the finite cardinal numbers and the real numbers - his view amounted to a Platonist version of logicism. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by B Hale / C Wright - Logicism in the 21st Century 1 | |
| A reaction: Nice to have this spelled out. Along with Gödel, Frege is the most distinguished Platonist since the great man. Frege has lots of modern fans, but I would have thought that this makes his position a non-starter. Alternatives are needed. |
| 13608 | Mathematics has no special axioms of its own, but follows from principles of logic (with definitions) [Frege, by Bostock] |
| Full Idea: Frege's logicism is the theory that mathematics has no special axioms of its own, but follows just from the principles of logic themselves, when augmented with suitable definitions. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by David Bostock - Intermediate Logic 5.1 | |
| A reaction: Thus logicism is opposed to the Dedekind-Peano axioms, which are not logic, but are specific to mathematics. Hence modern logicists try to derive the Peano Axioms from logical axioms. Logicism rests on logical truths, not inference rules. |
| 16905 | Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion] |
| Full Idea: For Frege, that arithmetic is essentially general, governing (applying to) everything, entails that its ultimate building blocks are purely logical. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Robin Jeshion - Frege's Notion of Self-Evidence 2 | |
| A reaction: Put like that, it doesn't sound very persuasive. If any truth is totally general, then it must be purely logical? |
| 5658 | Numbers are definable in terms of mapping items which fall under concepts [Frege, by Scruton] |
| Full Idea: Frege defines numbers in terms of 'equinumerosity', which says two concepts are equinumerous if the items falling under one of them can be placed in one-to-one correspondence with the items falling under the other. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Roger Scruton - Short History of Modern Philosophy Ch.17 | |
| A reaction: This doesn't sound quite enough. What is the difference between three and four? The extensions of items generate separate sets, but why does one follow the other, and how do you count the items to get the one-to-one correspondence? |
| 8655 | Arithmetic is analytic and a priori, and thus it is part of logic [Frege] |
| Full Idea: It is probable that the laws of arithmetic are analytic and consequently a priori; arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §87) | |
| A reaction: I'm not sure about 'thus', without more explication. Empiricists loved this, because it placed arithmetic firmly among Hume's 'relations of ideas', thus avoiding the difficulties Mill encountered trying to explain arithmetic through piles of pebbles. |
| 16880 | Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge] |
| Full Idea: Frege saw arithmetical judgements as resting on a foundation of logical principles, and the discovery of this foundation as a discovery of the nature and structure of the justification of arithmetical truths and judgments. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations Intro | |
| A reaction: Burge's point is that the logic justifies the arithmetic, as well as underpinning it. |
| 8689 | Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend] |
| Full Idea: After the problem with Russell's paradox, Frege did not publish for fourteen years, and he then tried to re-found arithmetic in Euclidean geometry, rather than in logic. | |
| From: report of Gottlob Frege (works [1890], 3.4) by Michèle Friend - Introducing the Philosophy of Mathematics 3.4 | |
| A reaction: I take it that his new road would have led him to modern Structuralism, so I think he was probably on the right lines. Unfortunately Frege had already done enough for one good lifetime. |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise. |
| 18165 | My Basic Law V is a law of pure logic [Frege] |
| Full Idea: I hold that my Basic Law V is a law of pure logic. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.4), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: This is, of course, the notorious law which fell foul of Russell's Paradox. It is said to be pure logic, even though it refers to things that are F and things that are G. |
| 18166 | The loss of my Rule V seems to make foundations for arithmetic impossible [Frege] |
| Full Idea: With the loss of my Rule V, not only the foundations of arithmetic, but also the sole possible foundations of arithmetic, seem to vanish. | |
| From: Gottlob Frege (Letters to Russell [1902], 1902.06.22) | |
| A reaction: Obviously he was stressed, but did he really mean that there could be no foundation for arithmetic, suggesting that the subject might vanish into thin air? |
| 10607 | Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P] |
| Full Idea: Frege's general logical system involves a type hierarchy, distinguishing objects from properties from properties-of-properties etc., with every item belonging to a determinate level. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Peter Smith - Intro to Gödel's Theorems 14.1 | |
| A reaction: The Theory of Types went on to apply this hierarchy to classes, where Frege's disastrous Basic Law V flattens the hierarchy of classes, putting them on the same level (Smith p.119) |
| 10831 | Frege only managed to prove that arithmetic was analytic with a logic that included set-theory [Quine on Frege] |
| Full Idea: Frege claimed to have proved that the truths of arithmetic are analytic, but the logic capable of encompassing this reduction was logic inclusive of set theory. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Willard Quine - Philosophy of Logic Ch.5 |
| 13864 | Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects [Wright,C on Frege] |
| Full Idea: Frege's platonism seems to be in some tension with logicism: for the thought is unprepossessing that logic should dictate the existence of infinitely many objects of some kind. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects Intro | |
| A reaction: Obviously Frege didn't think this, but then the crux seems to be that Frege believed that there was a multitude of logical truths awaiting discovery, while modern logic just seems to be about the logical consequences of things. |
| 10033 | Why should the existence of pure logic entail the existence of objects? [George/Velleman on Frege] |
| Full Idea: If a distinguishing features of logic is its complete generality, focusing on truth in general, why should the existence of logic entail the existence of infinitely many objects? ..How can it be completely general if it has ontological commitments? | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This strikes me as simple and devastating. It depends how you conceive logic, but I only conceive it as the formalised rules of successful reasoning. I can't comprehend the claim that without certain objects, reasoning would be impossible. |
| 10010 | Frege's belief in logicism and in numerical objects seem uncomfortable together [Hodes on Frege] |
| Full Idea: Frege's views on arithmetic centred on two central theses, that mathematics is really logic, and that it is about distinctively mathematical sorts of objects, such as cardinal numbers. These theses seem uncomfortable passengers in a single boat. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic | |
| A reaction: This question pinpoints precisely my unease about Frege. I take logic to be the rules for successful reasoning, so I don't see how they can have ontological implications. It is very extreme platonism to say that right reasoning requires logical objects. |
| 9545 | Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara] |
| Full Idea: Near the end of his life, Frege completely abandoned his logicism, and came to the conclusion that the source of our arithmetical knowledge is what he called 'the Geometrical Source of Knowledge'. | |
| From: report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3 | |
| A reaction: We have, rather crucially, lost touch with the geometrical origins of arithmetic (such as 'square' numbers), which is good news for the practice of mathematics, but probably a disaster for the philosophy of the subject. |
| 9631 | Formalism fails to recognise types of symbols, and also meta-games [Frege, by Brown,JR] |
| Full Idea: Early formalism (Thomae etc) was crushed by Frege: first, mathematics must be about classes of symbols (abstract types), not the symbols themselves (the tokens); second, games may be meaningless, but meta-games are not. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: Brown goes on to show how Hilbert revived the formalist project. A really austere formalist view of mathematics clearly seems to be missing something basic, either in physical nature, or in the world of ideas. |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising. |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2 | |
| A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism. |
| 9875 | Frege was completing Bolzano's work, of expelling intuition from number theory and analysis [Frege, by Dummett] |
| Full Idea: Frege was completing Bolzano's work, of expelling intuition from number theory and analysis (while leaving it its due place in geometry). | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: It was Kant who had placed the emphasis on intuition. Frege eventually thought arithmetic might be geometric, and so intuition had to triumph after all. |
| 8642 | Abstraction from things produces concepts, and numbers are in the concepts [Frege] |
| Full Idea: What we actually get by means of abstraction from things is the concept, and in this we then discover the number. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §47) | |
| A reaction: And how do we 'discover' it, if not by a process of further abstraction? The concept of the moon (see Idea 8641) no more contains the number one than the actual moon does |
| 8621 | Mental states are irrelevant to mathematics, because they are vague and fluctuating [Frege] |
| Full Idea: Sensations and mental pictures, formed from the amalgamated traces of earlier sense-impressions, are absolutely no concern of arithmetic; they are characteristically fluctuating and indefinite, in contrast to the concepts and objects of mathematics. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro) | |
| A reaction: Sounds very like Plato's distinction between the worlds of opinion and knowledge (Ideas 1170 and 2133). This view is fine amidst the implicit dualism of all nineteenth century thought, but how does abstract mathematics link to the soggy brain? |
| 11008 | Existence is not a first-order property, but the instantiation of a property [Frege, by Read] |
| Full Idea: When Kant said that existence was not a property, what he meant was, according to Frege, that existence is not a first-order property - it is not a property of individuals but a property of properties, that the property has an instance. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Stephen Read - Thinking About Logic Ch.5 |
| 8643 | Affirmation of existence is just denial of zero [Frege] |
| Full Idea: Affirmation of existence is nothing but denial of the number nought. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §53) | |
| A reaction: Mathematicians - don't you luv 'em. No doubt this is helpful in placing existence within the great network of logical inferences, but his 'nothing but' is laughable. I don't see much existential anguish in the denial of zero. |
| 19470 | Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege] |
| Full Idea: Thoughts are neither things in the external world nor ideas. A third realm must be recognised. Anything in this realm has it in common with ideas that it cannot be perceived by the senses, and does not need an owner to belong with his consciousness. | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.337(69)) | |
| A reaction: This important idea is the creed for modern platonists. We don't have to accept Forms, or any particular content, but there is a mode of existence which is distinct from both mental and physical, and is the residence of 'abstracta'. I deny it! |
| 5645 | The dialectical opposition of being and nothing is resolved in passing to the concept of becoming [Hegel, by Scruton] |
| Full Idea: The concept of being contains within itself it own negation - nothing - and the dialectical opposition between these two concepts is resolved only in the passage to a new concept, becoming, which contains the truth of the passage from nothing to being. | |
| From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Short History of Modern Philosophy Ch.12 | |
| A reaction: The idea that one concept 'contains' another, or that an opposition could be 'resolved' by a new concept, sounds doubtful to me. For most analytical philosophers, and for Aristotle, oppositions are contradictions, and cannot and should not be 'resolved'. |
| 21762 | To grasp an existence, we must consider its non-existence [Hegel, by Houlgate] |
| Full Idea: It is only to the extent that we can say that something is not, that we can say what it actually is. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'From indeterminate' | |
| A reaction: A key idea for Hegel, but it leaves me flat. Thinking about the non-being of something throws no light at all for me on the inexpressible actuality of its existence. |
| 21977 | Nothing exists, as thinkable and expressible [Hegel] |
| Full Idea: Nothing can be thought of, imagined, spoken of, and therefore it is. | |
| From: Georg W.F.Hegel (Science of Logic [1816], I.i.i.C.1 Rem 3 p.101), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.4 | |
| A reaction: This sounds like Meinong on circular squares. Does this mean that the negation of every truth also somehow exists? I struggle with this idea. Lewis Carroll nailed it. |
| 21760 | Thinking of nothing is not the same as simply not thinking [Hegel, by Houlgate] |
| Full Idea: Thinking of nothing is not the same as simply not thinking. Thought that suspends all its presuppositions and so ends up thinking of nothing determinate still remains thought, albeit utterly indeterminate and inchoate thought. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'From indeterminate' | |
| A reaction: This is the very starting point of Hegel's dialectical inferences in his 'Logic'. It is hard to entirely disagree, though I wonder whether the exercise is actually possible. What are you aware of if you have a thought with no content? |
| 22772 | Personality overcomes subjective limitations and posits Dasein as its own [Hegel] |
| Full Idea: Personality is that which overcomes the limitation of being merely subjective and gives itself reality - or, what amounts to the same thing, to posit that existence [Dasein] as its own. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 039) | |
| A reaction: This looks like the source for Heidegger's distinctive concept of Dasein. The emphasis in Hegel is on creating it out of subjectivity by an act of choice. For Heidegger Dasein seems to be a primitive concept. |
| 5657 | Frege's logic showed that there is no concept of being [Frege, by Scruton] |
| Full Idea: Frege's quantificational logic vindicates Kant's insight that existence is not a predicate and leads to fallacies when treated as one; and we might also say, despite Hegel, that there is no concept of being. | |
| From: report of Gottlob Frege (works [1890]) by Roger Scruton - Short History of Modern Philosophy Ch.17 | |
| A reaction: I notice that Colin McGinn has questioned the value of quantificational logic. It is difficult to assert that 'there is no concept of x', if several people have written large books about it. |
| 8911 | If abstracta are non-mental, quarks are abstracta, and yet chess and God's thoughts are mental [Rosen on Frege] |
| Full Idea: Frege's identification of the abstract with the realm of non-mental things entails that unobservables such as quarks are abstract. The abstract nature of chess, and the possibility of abstracta in the mind of God, show they can be mind-dependent. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Gideon Rosen - Abstract Objects 'Way of Neg' | |
| A reaction: I like the robust question 'if a is said to 'exist', what is it said to be made of?' I consider the views of Frege to have had too much influence in this area, and recognising the role of the mind (psychology!) in abstraction is a start. |
| 8634 | The equator is imaginary, but not fictitious; thought is needed to recognise it [Frege] |
| Full Idea: We speak of the equator as an imaginary line, but it is not a fictitious line; it is not a creature of thought, the product of a psychological process, but is only recognised or apprehended by thought. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §26) | |
| A reaction: Nice point. The same goes for the apparently very abstract and theoretical concept of a 'circle', because a perfect circle could be imagined in a very specific location, perhaps passing through three specified points. |
| 5646 | Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton] |
| Full Idea: It would not be unfair to say that Hegel's metaphysics consists of an ontological proof of the existence of everything. | |
| From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Short History of Modern Philosophy Ch.12 | |
| A reaction: This is so gloriously far from David Hume that we must all find some appeal in it. The next question would be whether necessary existence has been proved. If so, given death, decay and entropy, what is it that has to exist? 2nd Law of Thermodynamics? |
| 18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
| Full Idea: Frege's theory treats existence as a property, not of things we call existent, but of concepts instantiated by those things. 'Biden exists' says our Biden-concept has instances. That is certainly not how it feels! We speak of the thing, not of concepts. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by Stephen Yablo - Aboutness 01.4 | |
| A reaction: Yablo's point is that you must ask what the sentence is 'about', and then the truth will refer to those things. Frege gets into a tangle because he thinks remarks using concepts are about the concepts. |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism' |
| 21765 | The ground of a thing is not another thing, but the first thing's substance or rational concept [Hegel, by Houlgate] |
| Full Idea: Hegel's logic reveals that the true ground of something is not something other than it is, but the substance of that thing itself, or the rational concept that makes the thing what it is. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'The Method' | |
| A reaction: This seems to be classic Aristotelian essentialism, though Aristotle was also interested in dependence relations. |
| 17443 | Many of us find Frege's claim that truths depend on one another an obscure idea [Heck on Frege] |
| Full Idea: Frege sometimes speaks of 'the dependence of truths upon one another' (1884:§2), but I find such ideas obscure, and suspect I'm not the only one who does. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §02) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1 | |
| A reaction: He refers to Burge 'struggling mightily' with this aspect of Frege's thought. I intend to defend Frege. See his 1914 lectures. I thought this dependence was basic to the whole modern project of doing metaphysics through logic? |
| 17445 | Parallelism is intuitive, so it is more fundamental than sameness of direction [Frege, by Heck] |
| Full Idea: Frege says that parallelism is more fundamental than sameness of direction because all geometrical notions must originally be given in intuition. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: If Frege thinks some truths are more fundamental, this gives an indication of his reasons. But intuition is not a very strong base. |
| 10539 | Frege refers to 'concrete' objects, but they are no different in principle from abstract ones [Frege, by Dummett] |
| Full Idea: Frege employs the notion of 'concrete' (wirklich, literally 'actual') objects, in arguing that not every object is concrete, but it does not work; abstract objects are just as much objects as concrete ones. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §26,85) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: See Idea 10516 for why Dummett is keen on the distinction. Frege strikes me as being wildly irresponsible about ontology. |
| 9578 | If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege] |
| Full Idea: If an object is just presentation, we can pay less attention to a property and it disappears. By letting one characteristic after another disappear, we obtain concepts that are increasingly more abstract. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: Frege despises this view. Note there is scope in the despised view for degrees or levels of abstraction, defined in terms of number of properties ignored. Part of Frege's criticism is realist. He retains the object, while Husserl imagines it different. |
| 22059 | Kant's thing-in-itself is just an abstraction from our knowledge; things only exist for us [Hegel, by Bowie] |
| Full Idea: For Hegel there is no thing-in-itself, because the thing only becomes a something by being for us. Kant's thing-in-itself is the result of abstracting from the thing everything we know about it. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Andrew Bowie - German Philosophy: a very short introduction 3 | |
| A reaction: This seems to pinpoint why Hegel is an idealist philosopher. Frege objected to abstraction for similar reasons. I don't understand how the tree outside my window can only exist 'for me'. I have a much better theory about the tree. |
| 22083 | Hegel believe that the genuine categories reveal things in themselves [Hegel, by Houlgate] |
| Full Idea: Hegel believed, unlike Kant, that the categories of the understanding, when properly understood, disclose the nature of things in themselves and not just the character of things as they appear to us. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - Hegel p.101 | |
| A reaction: 'Properly understood' sounds like 'no true Scotsman'. This is thoroughgoing idealism, because reality is determined by the activity of the mind, and not from outside. The Hegel story makes more sense if you see the categories as evolutionary. |
| 19471 | A fact is a thought that is true [Frege] |
| Full Idea: A fact is a thought that is true. | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.342(74)) | |
| A reaction: It strikes me as pretty obvious that facts are not thoughts, because they concern the contents of thoughts. You can't discuss facts without the notion of what a thought is 'about'. If I think about my garden, the relevant fact is aspects of my garden. |
| 17431 | Vagueness is incomplete definition [Frege, by Koslicki] |
| Full Idea: Frege seems to assimilate vagueness to incompleteness of definition. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1 |
| 13879 | For Frege, ontological questions are to be settled by reference to syntactic structures [Frege, by Wright,C] |
| Full Idea: For Frege, syntactic categories are prior to ontological ones, and it is by reference to the syntactic structure of true statements that ontological questions are to be understood and settled. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 1.v |
| 10642 | Second-order quantifiers are committed to concepts, as first-order commits to objects [Frege, by Linnebo] |
| Full Idea: Frege claims that second-order quantifiers are committed to concepts, just as singular first-order quantifiers are committed to objects. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Øystein Linnebo - Plural Quantification 5.3 | |
| A reaction: It increasingly strikes me that Fregeans try to get away with this nonsense by diluting both the notion of a 'concept' and the notion of an 'object'. |
| 22078 | Even simple propositions about sensations are filled with categories [Hegel] |
| Full Idea: Categories, like 'being', or 'individuality', are already mingled into every proposition, even when it has a completely sensible content, such as "this leaf is green". | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §246 Add), quoted by Stephen Houlgate - Hegel p.95 | |
| A reaction: This is the source of the idea that observation is theory-laden (which tracks back to Kant). Not Duhem, who gets the credit among analytic philosophers. Quine obviously never read Hegel. But the idea is overrated. |
| 15634 | Thought about particulars is done entirely through categories [Hegel] |
| Full Idea: As an activity of the particular, thinking has the categories as its only product and content. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §62) | |
| A reaction: There seems to be an interesting implication in this remark (taken in isolation!) that one can somehow transcend the categories when one begins to think about the universal. Are the universal and the categories not connected? |
| 21755 | For Hegel, categories shift their form in the course of history [Hegel, by Houlgate] |
| Full Idea: For Hegel, the categories of thought are not fixed, eternal forms that remain unchanged throughout history, but are concepts that alter their meaning in history. | |
| From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01 | |
| A reaction: This results from a critique of Kant's rather rigid view of categories. This idea is very influential, and certainly counts among Hegel's better ideas. |
| 21754 | Our concepts and categories disclose the world, because we are part of the world [Hegel, by Houlgate] |
| Full Idea: For Hegel, the structure of our concepts and categories is identical with, and thus discloses, the structure of the world itself, because we ourselves are born into and so share the character of the world we encounter. | |
| From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01 | |
| A reaction: This is a reasonable speculation, but it makes more sense in the context of natural selection, and an empiricist theory of concepts. |
| 22079 | Hegel said Kant's fixed categories actually vary with culture and era [Hegel, by Houlgate] |
| Full Idea: Hegel's disagreement with Kant is that categories are not unambiguously universal forms of human understanding, but are conceived in subtly different ways in different cultures and in different historical epochs. | |
| From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - Hegel p.95 | |
| A reaction: This may be Hegel's most influential idea. Though he hoped that categories would contain truth, by arising untrammelled from reason, and thereby matching reality. His successors seem to have given up on that hope, and settled for relativism. |
| 22080 | The nature of each category relates itself to another [Hegel] |
| Full Idea: In the categories, something through its own nature relates itself to the other. | |
| From: Georg W.F.Hegel (Science of Logic [1816], p.125), quoted by Stephen Houlgate - Hegel p.99 | |
| A reaction: This is the doctrine of internal relations rejected by Moore and Russell, and also the key idea in Hegel's logic - that ideas give rise to other ideas, without contribution by the thinker. |
| 10032 | 'Ancestral' relations are derived by iterating back from a given relation [Frege, by George/Velleman] |
| Full Idea: Any relation will yield a new relation, called the 'ancestral', which is the iterated relation which leads up to it, as when 'x is the parent of y' can lead us to the relation 'x is an ancestor of y' | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §79) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This idea is one of Frege's notable discoveries. The ancestral seems to be a generalisation of a given relation. |
| 10606 | Frege treats properties as a kind of function, and maybe a property is its characteristic function [Frege, by Smith,P] |
| Full Idea: Frege urges us to regard properties as just a special kind of function, and in the case of numerical properties he comes close to identifying a property with its characteristic function. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Peter Smith - Intro to Gödel's Theorems 11.3 n 5 | |
| A reaction: Every now and then really interesting bits of metaphysics pop out of Frege, though it usually needs commentators to show the implications. Does the 'characteristic' imply a teleological view? |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property. | |
| From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2 | |
| A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects. |
| 10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
| Full Idea: Expositors of Frege's views have disagreed over whether abstract qualities are to be reckoned among his objects. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by Bob Hale - Abstract Objects Ch.2.II | |
| A reaction: [he cites Dummett 1973:70-80, and Wright 1983:25-8] There seems to be a danger here of a collision between Fregean verbal approaches to ontological commitment and the traditional views about universals. No wonder they can't decide. |
| 10533 | We can't get a semantics from nouns and predicates referring to the same thing [Frege, by Dummett] |
| Full Idea: Frege is denying that on a traditional basis we can construct a workable semantics for a language; we can't regard terms like 'wisdom' as standing for the very same thing as the predicate 'x is wise' stands for. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: This follows from Idea 10532, indicating how to deal with the problem of universals. So predicates refer to concepts, and singular terms to objects. But I see no authoritative way of deciding which is which, given that paraphrases are possible. |
| 8647 | Not all objects are spatial; 4 can still be an object, despite lacking spatial co-ordinates [Frege] |
| Full Idea: To give spatial co-ordinates for the number four makes no sense; but the only conclusion to be drawn from that is, that 4 is not a spatial object, not that it is not an object at all. Not every object has a place. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §61) | |
| A reaction: This is the modern philosophical concept of an 'object', though I find such talk very peculiar. It sounds like extreme Platonism, though this is usually denied. This is how logicians seem to see the world. |
| 10309 | Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale] |
| Full Idea: Frege's argument for abstract objects is: 1) singular terms in true expressions must denote objects, 2) numerals function as singular terms, 3) there must exist numbers denoted by those expressions. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Bob Hale - Abstract Objects Ch.1 | |
| A reaction: [compressed] Given that most of the singular term usages can be rephrased adjectively, this strikes me as a weak argument, though Hale pins his whole book on it. |
| 10550 | Frege establishes abstract objects independently from concrete ones, by falling under a concept [Frege, by Dummett] |
| Full Idea: For Frege it is legitimate, in order to establish the existence of a certain number, to cite a concept under which only abstract objects fall, and in such a way guarantee the existence of the number quite independently of what concrete objects there are. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: This approach of Frege's got into trouble with Russell's Paradox, which gave a concept under which nothing could fall. It strikes me as misguided even without that problem. I say abstracta are rooted in the concrete. |
| 18269 | Logical objects are extensions of concepts, or ranges of values of functions [Frege] |
| Full Idea: How are we to conceive of logical objects? My only answer is, we conceive of them as extensions of concepts or, more generally, as ranges of values of functions ...what other way is there? | |
| From: Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr | |
| A reaction: This is the clearest statement I have found of what Frege means by an 'object'. But an extension is a collection of things, so an object is a group treated as a unity, which is generally how we understand a 'set'. Hence Quine's ontology. |
| 8785 | For Frege, objects just are what singular terms refer to [Frege, by Hale/Wright] |
| Full Idea: In Frege's 'Grundlagen' objects, as distinct from entities of other types (properties, relations, or various functions), just are what (actual or possible) singular terms refer to. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by B Hale / C Wright - Logicism in the 21st Century 2 | |
| A reaction: This seems to be the key claim that results in twentieth century metaphysics being done through analysis of language. The culmination is, of course, a denial of metaphysics, and then an eventual realisation that Frege was wrong. |
| 10278 | Without concepts we would not have any objects [Frege, by Shapiro] |
| Full Idea: Frege is known for the idea that we do not have objects without concepts. Without concepts, there is nothing - no thing - to count. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stewart Shapiro - Philosophy of Mathematics 8.4 | |
| A reaction: A very helpful clarification. Thinking about the probable mental life of higher and lower animals, the proposal seems extremely plausible. Dogs have some concepts, slugs have none, so slugs do not exist in a world of objects. I like it. |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place. | |
| From: Gottlob Frege (Function and Concept [1891], p.32) | |
| A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them. |
| 10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
| Full Idea: Frege's notion of an object plays two roles in his semantics. Objects are the referents of proper names, and they are equally what predicates are true and false of. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.4 | |
| A reaction: Frege is the source of a desperate desire to turn everything into an object (see Idea 8858!), and he has the irritating authority of the man who invented quantificational logic. Nothing but trouble, that man. |
| 9877 | Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett] |
| Full Idea: Earlier, Frege divided objects into subjective, actual objective, and non-actual objective; in the 'Grundgesetze' he emphasised logical objects; but in 'The Thought' the non-actual objects become exclusively thoughts and their constituent senses. | |
| From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: Sounds to me like Frege was finally waking up and taking a dose of common sense. The Equator is the standard example of a non-actual objective object. |
| 17432 | Frege's universe comes already divided into objects [Frege, by Koslicki] |
| Full Idea: Frege's universe is one that comes already divided into objects. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1 | |
| A reaction: Nice to have this spelled out. I get frustrated with metaphysics built on logic, with domains of objects, without worry about where all these objects came from. They're axiomatic, it seems. She cites Geach as having a universe of 'goo'. |
| 21981 | The one substance is formless without the mediation of dialectical concepts [Hegel] |
| Full Idea: As intuitively accepted by Spinoza without a previous mediation by dialectic, substance is as it were a dark shapeless abyss which engulfs all definite content as radically null, and produces from itself nothing that has a positive substance of its own. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], I §151Z p.215), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.6 | |
| A reaction: This seems to be an expression of idealism, since only what is conceptualised can exist. |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| Full Idea: The first demand of logic is of a sharp boundary. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22 | |
| A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are. |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| Full Idea: Of any concept, we must require that it have a sharp boundary. Of any object it must hold either that it falls under the concept or it does not. We may not allow a third case in which it is somehow indeterminate whether an object falls under a concept. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.229), quoted by Ian Rumfitt - The Logic of Boundaryless Concepts p.1 n1 | |
| A reaction: This is the voice of the classical logician, which has echoed by Russell. I'm with them, I think, in the sense that logic can only work with precise concepts. The jury is still out. Maybe we can 'precisify', without achieving total precision. |
| 15637 | Essence is the essential self-positing unity of immediacy and mediation [Hegel] |
| Full Idea: The entire second part of the 'Logic', the doctrine of Essence, deals with the essential self-positing unity of immediacy and mediation. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §65) | |
| A reaction: He is referring to his book 'Science of Logic'. I don't really understand this, but that essence 'posits' the unity of a thing catches my attention. |
| 15613 | Real cognition grasps a thing from within itself, and is not satisfied with mere predicates [Hegel] |
| Full Idea: In genuine cognition ...an object determines itself from within itself, and does not acquire its predicates in an external way. If we proceed by way of predication, the spirit gets the feeling that the predicates cannot exhaust what they are attached to. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §28 Add) | |
| A reaction: I take this to be a glimpse of Hegel's notoriously difficult account of essence. Place this alongside Locke's distinction between Nominal and Real essences. Once we have the predicates, we want to grasp their source. |
| 16022 | The idea of a criterion of identity was introduced by Frege [Frege, by Noonan] |
| Full Idea: The notion of a criterion of identity was introduced into philosophical terminology in Frege's 'Grundlagen', and was strong emphasised in Wittgenstein's 'Philosophical Investigations'. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Harold Noonan - Identity §4 | |
| A reaction: For Frege a thing can only have an intrinsic identity if it can participate in an equality relation. For abstract objects (such as directions or numbers) the relation is an equivalence. The general idea is that identical objects must relate in some way. |
| 11100 | Frege's algorithm of identity is the law of putting equals for equals [Frege, by Quine] |
| Full Idea: Frege's algorithm of identity is the law of putting equals for equals. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Willard Quine - Identity, Ostension, and Hypostasis 4 | |
| A reaction: Quine, and most modern philosophers, seem to accept universal substitutivity as a sufficient condition for identity. But you then get the problem of coextensionality (renate/cordate), which can only be solved by introducing modality. |
| 4893 | Frege was asking how identities could be informative [Frege, by Perry] |
| Full Idea: A problem which Frege called to our attention is: how can identities be informative? | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by John Perry - Knowledge, Possibility and Consciousness §5.2 | |
| A reaction: E.g. (in Russell's example) how is "Scott is the author of 'Waverley'" more informative than "Scott is Scott"? A simple answer might just be that informative identities also tell you of a thing's properties. "The red ball is the heavy ball". |
| 12153 | Geach denies Frege's view, that 'being the same F' splits into being the same and being F [Perry on Frege] |
| Full Idea: Frege's position is that 'being the same F as' splits up into a general relation and an assertion about the referent ('being the same' and 'being an F'). This is what Geach denies, when he says there is no such thing as being 'just the same'. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by John Perry - The Same F I | |
| A reaction: It looks as if you can take your pick - whether two things are perfectly identical, or whether they are identical in some respect. Get an unambiguous proposition before you begin the discussion. Identify referents, not kinds of identity, says Perry. |
| 3318 | Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA] |
| Full Idea: It was Frege who first made identity a logical notion, enshrining it above all in the formula (x) x=x. | |
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.9 |
| 9853 | Identity between objects is not a consequence of identity, but part of what 'identity' means [Frege, by Dummett] |
| Full Idea: Part of Frege's profound new idea of identity is that the criteria for identity of objects of a given kind is not a consequence of the way that kind of object is characterised, but has to be expressly stipulated as part of that characterisation. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.13 | |
| A reaction: This makes identity a relative concept, rather than an instrinsic concept. Does a unique object have an identity? Do properties have intrinsic identity conditions, making them usable to identify two objects. Deep waters. Has Frege muddied them? |
| 16885 | To understand a thought, understand its inferential connections to other thoughts [Frege, by Burge] |
| Full Idea: Frege famously realised that understanding a thought requires understanding its inferential connections to other thoughts. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 1 | |
| A reaction: If true, this is probably our greatest advance in grasping the concept of 'understanding' since Aristotle - but is it true? It is a striking and interesting idea, and central to the importance of Frege in modern analytic philosophy. |
| 17623 | To understand a thought you must understand its logical structure [Frege, by Burge] |
| Full Idea: For Frege, coming to a full understanding of logical structure is necessary to full understanding of a thought. And understanding logical structure derives from seeing what structures are most fruitful in accounting for the patterns of inference. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Knowing the Foundations 4 | |
| A reaction: To me, the notion of finding what is 'fruitful' implies finding the essence of the structure. |
| 21772 | In absolute knowing, the gap between object and oneself closes, producing certainty [Hegel] |
| Full Idea: In absolute knowing ...the separation of the object from the certainty of oneself is completely eliminated: truth is now equated with certainty and this certainty with truth. | |
| From: Georg W.F.Hegel (Science of Logic [1816], p.49), quoted by Stephen Houlgate - An Introduction to Hegel 03 'Absolute' | |
| A reaction: I don't understand this, but I note it because Hegel is evidently not a fallibilist about knowledge. I take this idea to be Descartes' 'clear and distinct ideas', wearing a grand rhetorical uniform. |
| 15611 | I develop philosophical science from the simplest appearance of immediate consciousness [Hegel, by Hegel] |
| Full Idea: In my 'Phenomenology of Spirit' the procedure adopted was to begin from the first and simplest appearance of the spirit, from immediate consciousness, and to develop the dialectic right up to the standpoint of philosophical science. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Georg W.F.Hegel - Logic (Encyclopedia I) §25 Rem | |
| A reaction: I take metaphysics to be either Parmenidean (starting from Being) or Cartesian (starting from mind), and this (surprisingly, given his lengthy talk of Being) shows Hegel to be a quintessentially Cartesian philosopher. Aristotle is the great Parmenidean. |
| 15636 | The Cogito is at the very centre of the entire concern of modern philosophy [Hegel] |
| Full Idea: The proposition 'Cogito Ergo Sum' stands at the very centre, so to speak, of the entire concern of modern philosophy. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §64 Rem) | |
| A reaction: I distinguish two approaches to philosophy: the Parmenidean (which starts from the nature of being), and the Cartesian (which starts from the fact of consciousness). This remark confirms that Hegel is firmly in the latter school. |
| 20954 | The 'absolute idea' is when all the contradictions are exhausted [Hegel, by Bowie] |
| Full Idea: The point in philosophy at which the contradictions are exhausted is what Hegel means by the 'absolute idea'. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Andrew Bowie - Introduction to German Philosophy 4 'Questions' | |
| A reaction: {Can't think of a response to this one) |
| 8928 | The Absolute is not supposed to be comprehended, but felt and intuited [Hegel] |
| Full Idea: The Absolute is not supposed to be comprehended, it is to be felt and intuited. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 06) | |
| A reaction: Hegel was a rather romantic philosopher. Where does the 'supposed' come from? If the Absolute is only felt and intuited, can the resulting apprehensions be reported to others? Is this, in fact, mysticism? |
| 8929 | In the Absolute everything is the same [Hegel] |
| Full Idea: In the Absolute everything is the same. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 16) | |
| A reaction: This is indistinguishable from the great spherical reality of Parmenides. It is not unreasonable to enquire about the epistemology of this claim. Is Hegel a seer, or can we all intuit this insight into reality? |
| 21774 | Genuine idealism is seeing the ideal structure of the world [Hegel, by Houlgate] |
| Full Idea: Genuine (as opposed to subjective) idealism, for Hegel, is the point of view that knows the world to have a rational, and therefore 'ideal', structure. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Stephen Houlgate - An Introduction to Hegel 04 'The Unhappy' | |
| A reaction: Compare Leibniz, whose monad theory is said to be a sort of idealism, because it places ideas at the heart of reality. Is Plato also this sort of 'genuine' idealism? Do we need different terms for 'genuine' and 'subjective' idealism? And 'transcendental'? |
| 21972 | Hegel, unlike Kant, said how things appear is the same as how things are [Hegel, by Moore,AW] |
| Full Idea: Hegel rejected the fundamental Kantian distinction between how things knowably appear and how they unknowably are in themselves. This was anathema to him. For Hegel how things knowably appear is how they manifestly are. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by A.W. Moore - The Evolution of Modern Metaphysics 07.2 | |
| A reaction: We shouldn't assume that Hegel was therefore a realist, because Berkeley would agree with this idea. Hegel rejected transcendental idealism for this reason. Hegel wanted to get rid of the immanent/transcendent distinction |
| 22038 | Hegel's non-subjective idealism is the unity of subjective and objective viewpoints [Hegel, by Pinkard] |
| Full Idea: The unity of the two points of view (subjective and objective) constitutes Hegel's idealism. ...He kept emphasising that it was not 'subjective' idealism. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Terry Pinkard - German Philosophy 1760-1860 10 | |
| A reaction: Subjective idealism denies the objective point of view. [**20th June 2019, 10:49 am. This is the 20,000th idea in the database. The project was begun in 1997, as organised notes to help with teaching. For the last ten years today has been my target**]. |
| 22044 | Hegel claimed his system was about the world, but it only mapped conceptual interdependence [Pinkard on Hegel] |
| Full Idea: In the view of the later Schelling, although Hegel's system only really laid out the ways in which the senses of various concepts depended on each other, it claimed to be a system about the world itself. | |
| From: comment on Georg W.F.Hegel (Science of Logic [1816]) by Terry Pinkard - German Philosophy 1760-1860 | |
| A reaction: I'm no expert, but I'm inclined to agree with Schelling. Since I am suspicious of the idea that each concept generates its own negation, I also doubt the accuracy of Hegel's map. I'm a hopeless case. |
| 21464 | The Absolute is the primitive system of concepts which are actualised [Hegel, by Gardner] |
| Full Idea: In Hegel the Absolute is the exhaustive, unconditioned and self-grounding system of concepts made concrete in actuality, the world of experience. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Sebastian Gardner - Kant and the Critique of Pure Reason 10 'Absolute' | |
| A reaction: If I collect multiple attempts to explain what the Absolute is, I may one day drift toward a hazy understanding of it. Right now this idea means nothing to me, but I pass it on. His notion of 'concept' seems a long way from the normal modern one. |
| 22084 | Authentic thinking and reality have the same content [Hegel] |
| Full Idea: Thinking in its immanent determination and the true nature of things form one and the same content. | |
| From: Georg W.F.Hegel (Science of Logic [1816], p.45), quoted by Stephen Houlgate - Hegel p.101 | |
| A reaction: This is not much use unless we have a crystal clear idea of 'immanent determination', because we need to eliminate errors. |
| 21975 | The absolute idea is being, imperishable life, self-knowing truth, and all truth [Hegel] |
| Full Idea: The absolute idea alone is being, imperishable life, self-knowing truth, and is all truth. ....All else is error, confusion, opinion, endeavour, caprice, and transitoriness. | |
| From: Georg W.F.Hegel (Science of Logic [1816], II.iii.3 p.824), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.4 | |
| A reaction: Hegel sounding a bit too much like an over-excited preacher here. The absolute idea seems to be the unified totality of all truths about reality. For Hegel human self-awareness is a big part of that. The idea is being because there is only one substance. |
| 21976 | The absolute idea is the great unity of the infinite system of concepts [Hegel, by Moore,AW] |
| Full Idea: We can think of the absolute idea roughly as the entire infinite system of interrelated concepts, in their indissoluble unity, as exercised in the self-consciousness towards which the process [of thought] leads. It is the 'telos' of the process. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816], II.iii.3 p.825) by A.W. Moore - The Evolution of Modern Metaphysics 07.4 | |
| A reaction: This expounds the quotation in Idea 21975. Moore emphasises concepts, where Hegel emphasises the truth. The connection is in Idea 5644. |
| 8934 | Being is Thought [Hegel] |
| Full Idea: Being is Thought. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 54) | |
| A reaction: You won't find a more succinct slogan for idealism than that. Speaking as what Tim Williamson (referring to himself) calls a 'rottweiler realist', I can't quite get the hang of Hegel's claim. What does he think thought is, if it isn't about the world? |
| 22300 | Existence is just a set of relationships [Hegel] |
| Full Idea: Everything that exists stands in correlation, and this correlation is the veritable nature of existence. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], p.235 (1892)), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 23 'Abs' |
| 9158 | For Frege a priori knowledge derives from general principles, so numbers can't be primitive [Frege] |
| Full Idea: If one took the numbers as primitive, one would not be deriving their existence and character from general principles- thus controverting Frege's view of the nature of an a priori subject. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]), quoted by Tyler Burge - Frege on Apriority II | |
| A reaction: He seems to be in tune with Leibniz on this. His view begs the obvious question of where the general principles come from. I would have thought that relationships between concepts might be known a priori, without principles being involved. |
| 16887 | Frege's concept of 'self-evident' makes no reference to minds [Frege, by Burge] |
| Full Idea: Frege's terms that translate 'self-evident' usually make no explicit reference to actual minds. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 4 | |
| A reaction: This follows the distinction in Aquinas, between things that are intrinsically self-evident, and things that are self-evident to particular people. God, presumably, knows all of the former. |
| 8657 | Mathematicians just accept self-evidence, whether it is logical or intuitive [Frege] |
| Full Idea: The mathematician rests content if every transition to a fresh judgement is self-evidently correct, without enquiring into the nature of this self-evidence, whether it is logical or intuitive. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §90) | |
| A reaction: Note the suggestion that there are two different sorts of self-evidence. But see Idea 1410. Frege presumably drifted into philosophy because he wasn't happy with this blissful ignorance. |
| 16894 | An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge] |
| Full Idea: Generality for Frege is simply universal quantification; what makes a truth apriori is that its ultimate grounds are universally quantified. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Apriority (with ps) 2 |
| 9352 | An a priori truth is one derived from general laws which do not require proof [Frege] |
| Full Idea: If the proof of a truth can be derived exclusively from general laws, which themselves neither need nor admit of proof, then the truth is a priori. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03) | |
| A reaction: Presumably the unproved general laws from which the derivation comes are more securely a priori, as are the principles used to make the derivation. As Frege says, he is trying to spell out Kant's view; see Idea 9345. |
| 16889 | A truth is a priori if it can be proved entirely from general unproven laws [Frege] |
| Full Idea: If it is possible to derive a proof purely from general laws, which themselves neither need nor admit of proof, then the truth is a priori. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03), quoted by Tyler Burge - Frege on Apriority (with ps) 1 | |
| A reaction: Burge brings out the contrast with Kant, for whom a priori truths are derived from particular facts, not general ones. |
| 9225 | Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H] |
| Full Idea: Hegel is reputed to have claimed to have deduced on a priori grounds that the number of planets is exactly five. | |
| From: report of Georg W.F.Hegel (works [1812]) by Hartry Field - Recent Debates on the A Priori 1 | |
| A reaction: Even if this is a wicked travesty of Hegel, it will do nicely to represent the extremes of claims to a priori synthetic knowledge. Field doesn't offer any evidence. I would love it to be true. |
| 2514 | Frege tried to explain synthetic a priori truths by expanding the concept of analyticity [Frege, by Katz] |
| Full Idea: Frege challenged synthetic a priori truths by expanding the concept of analyticity, undertaken in order to provide a semantic basis for his logicist explanation of mathematical truth as analytic truth. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Jerrold J. Katz - Realistic Rationalism Int.xx |
| 15609 | The sensible is distinguished from thought by being about singular things [Hegel] |
| Full Idea: The distinction of the sensible from thought is to be located in that fact that the determination of the sensible is singularity. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §20 Rem) | |
| A reaction: Compare Idea 15608, where we find that thought concerns universals. What a very clear thinker Hegel was! |
| 21773 | Experience is immediacy, unity, forces, self-awareness, reason, culture, absolute being [Hegel, by Houlgate] |
| Full Idea: Experience moves from 1) immediacy, to 2) united objects with properties, 3) its forces and laws, 4) self-consciousness in the process, 5) seeing a rational realm, 6) seeing a cultural realm, 7) seeing the absolute being of consciousness. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Stephen Houlgate - An Introduction to Hegel 03 'From certainty' | |
| A reaction: [My summary of Houlgate's summary of the key sequence of ideas in The Phenomenology of Spirit]. I stare at it with bewilderment, but cannot decide whether or not Hegel is pursuing a worthwhile project. [also Houlgate p.77 and 102] |
| 22033 | Hegel tried to avoid Kant's dualism of neutral intuitions and imposed concepts [Hegel, by Pinkard] |
| Full Idea: Hegel tried to avoid the untenable Kantian dualism between concepts and intuitions, and the Kantian mechanism of the 'imposition' of concepts on sensibility entailed by that dualism (with intuition having neutral content). | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Terry Pinkard - German Philosophy 1760-1860 09 | |
| A reaction: [Pinker is describing the opening of Phenomenology] In modern discussions this concerns the idea of The Given, which is wholly uninterpreted raw experience. Sellars and MacDowell. Kant seems to split an agent into two (Master/Slave). |
| 15625 | Sense perception is secondary and dependent, while thought is independent and primitive [Hegel] |
| Full Idea: What can be perceived by the senses is really secondary and not self-standing, while thoughts, on the contrary, are what is genuinely independent and primitive. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §41 Add2) | |
| A reaction: Although this is post-Kant, it strikes me as a perfect slogan for rationalism. Personally I would say that such a dichotomy is becoming a historical relic, in the light of modern understanding of the brain. Experience and thought are inextricable. |
| 15619 | Empiricism made particular knowledge possible, and blocked wild claims [Hegel] |
| Full Idea: Empiricism resulted from a need for concrete content, as opposed to abstract theories that cannot advance from universal generalizations to the particular, and for a firm hold against the possibility of proving any claim at all in the field. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §37) | |
| A reaction: That sounds about right, and makes you wonder why Hegel wasn't an empiricist. |
| 15620 | Empiricism contains the important idea that we should see knowledge for ourselves, and be part of it [Hegel] |
| Full Idea: We must recognise the important principle of freedom that lies in Empiricism; namely, that what ought to count in our human knowing, we ought to see for ourselves, and to know ourselves as present in it. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §38 Rem) | |
| A reaction: Like Idea 15619, this is an interesting and perceptive remark, from a philosopher who seems a long way from empiricism. I presume he will be thinking mainly of Hume, via Kant. Personally I prefer Locke. |
| 15622 | Empiricism unknowingly contains and uses a metaphysic, which underlies its categories [Hegel] |
| Full Idea: Empiricism operates without knowing that it contains a metaphysics and is engaged in it, and that it is using categories and their connections in a totally uncritical and unconscious manner. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §38 Rem) | |
| A reaction: I doubt whether this is true of modern empiricists, who have been challenged so often from within their own ranks on so many things. I'm not even sure that it is true of Locke and Hume, apart from the way in which all philosophers are unaware of things. |
| 15621 | Empiricism of the finite denies the supersensible, and can only think with formal abstraction [Hegel] |
| Full Idea: Inasmuch as Empiricism restricts itself to what is finite, the consistent carrying through of its programme denies the supersensible altogether, ..and it leaves thinking with abstraction only, [i.e.] with formal universality and identity. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §38 Rem) | |
| A reaction: I'm not clear how a denial of empiricism allows you (with intellectual integrity) to embrace 'the supersensible'. The set theoretic account of higher levels of infinity looks like a nice test case. |
| 15632 | The Humean view stops us thinking about perception, and finding universals and necessities in it [Hegel] |
| Full Idea: The Humean standpoint proclaims the thinking of our perceptions to be inadmissible; i.e. the eliciting of the universal and necessary out of those perceptions. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §50) | |
| A reaction: Obviously Hume permits 'relations of ideas', but presumably the point is that his approach only legitimates a rather passive abstraction from experience, rather than an active application of a priori concepts to it. A fair criticism. See Bonjour. |
| 16900 | Intuitions cannot be communicated [Frege, by Burge] |
| Full Idea: Frege makes a notorious claim that what is intuitable is not communicable. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §26) by Tyler Burge - Frege on Apriority (with ps) 4 |
| 21771 | Consciousness derives its criterion of knowledge from direct knowledge of its own being [Hegel] |
| Full Idea: In what consciousness affirms from within itself as being-in-itself or the True we have the standard which consciousness itself sets up by which to measure what it knows. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], p.053), quoted by Stephen Houlgate - An Introduction to Hegel 03 'The Method' | |
| A reaction: This seems to be a very close relation of Descartes' 'clear and distinct conceptions'. This certainly places Hegel in the Rationalist camp. |
| 16903 | Justifications show the ordering of truths, and the foundation is what is self-evident [Frege, by Jeshion] |
| Full Idea: Frege thought that the relations of epistemic justification in a science mirrors the natural ordering of truths: in particular, what is self-evident is selbstverstandlich. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §02) by Robin Jeshion - Frege's Notion of Self-Evidence 1 | |
| A reaction: I'm not sure that I can accept a 'natural ordering of truths'. Is there a natural ordering of the facts of the world? The most I can see is a direction to causation. Maybe inferences have a direction, but humans intrude on those. |
| 22058 | Hegel's 'absolute idea' is the interdependence of all truths to justify any of them [Hegel, by Bowie] |
| Full Idea: Hegel's system culminates in the 'absolute idea', the explanation of why all particular truths depend on the relationship to other truths for their justification. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Andrew Bowie - German Philosophy: a very short introduction 3 | |
| A reaction: The 'hyper-coherence' theory of justification. The normal claim is that there must be considerable local coherence to provide decent support. Hegel's picture sounds like part of the Enlightenment Dream. Is the idea of 'all truths' coherent? |
| 11052 | Psychological logic can't distinguish justification from causes of a belief [Frege] |
| Full Idea: With the psychological conception of logic we lose the distinction between the grounds that justify a conviction and the causes that actually produce it. | |
| From: Gottlob Frege (Logic [1897] [1897]) | |
| A reaction: Thus Frege kicked the causal theory of justification well into touch long before it had even been properly formulated. That is not to say that there is no psychological aspect to logic, because there is. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 15623 | Humean scepticism, unlike ancient Greek scepticism, accepts the truth of experience as basic [Hegel] |
| Full Idea: Humean scepticism should be very carefully distinguished from Greek scepticism. In Humean scepticism, the truth of the empirical, the truth of feeling and intuition is taken as basic. ..Greek scepticism turned itself against the sensible. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §39 Rem) | |
| A reaction: This seems right, and Hume himself was quite contemptuous of the sort of scepticism found in the ideas of Sextus Empiricus. |
| 22780 | It is a rejection of intellectual dignity to say that we cannot know the truth [Hegel] |
| Full Idea: The assertion that human beings cannot know the truth, but have to do only with appearances …deprives the spirit of intellectual dignity. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 132) | |
| A reaction: It is a relief to find Hegel making this assertion. His later followers seem to have slid into an extreme cultural relativism. I'm not sure that 'intellectual dignity' is a very secure foundation for his claim. |
| 16882 | The building blocks contain the whole contents of a discipline [Frege] |
| Full Idea: The ultimate building blocks of a discipline contain, as it were in a nutshell, its whole contents. | |
| From: Gottlob Frege (works [1890]), quoted by Tyler Burge - Frege on Knowing the Foundations 1 | |
| A reaction: [Burge gives a reference] I would describe this nutshell as the 'essence' of the subject, and it fits Aristotle's concept of an essence perfectly. Does it fit biology or sociology, in the way it might fit maths or logic? Think of DNA or cells in biology. |
| 8624 | Induction is merely psychological, with a principle that it can actually establish laws [Frege] |
| Full Idea: Induction depends on the general proposition that the inductive method can establish the truth of a law, or the probability for it. If we deny this, induction becomes nothing more than a psychological phenomenon. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03 n) | |
| A reaction: The problem is that we can't seem to 'establish' the requisite proposition, even for probability, since probability is in part subjective. I think induction needs the premiss that nature has underlying uniformity, which we then tease out by observation. |
| 8626 | In science one observation can create high probability, while a thousand might prove nothing [Frege] |
| Full Idea: The procedure of the sciences, with its objective standards, will at times find a high probability established by a single confirmatory instance, while at others it will dismiss a thousand as almost worthless. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §10) | |
| A reaction: This thought is presumably what pushes theorists away from traditional induction and towards Bayes's Theorem (Idea 2798). The remark is a great difficulty for anyone trying to defend traditional induction. |
| 8648 | Ideas are not spatial, and don't have distances between them [Frege] |
| Full Idea: Spatial predicates are not applicable to ideas; an idea is neither to the right nor to the left of another idea; we cannot give the distances between ideas in millimetres. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §61) | |
| A reaction: This Fregean thought should be music to the ears of Cartesians, though it does not seem intended as support for dualism. This is the logicians' view of reality, where true inferences are what matter, and brains and souls are irrelevant. |
| 20741 | Consciousness is shaped dialectically, by opposing forces and concepts [Hegel, by Aho] |
| Full Idea: In 'The Phenomenology of Spirit' Hegel offers a panoptic account of Western consciousness as a dialectical process shaped by opposing principles - such as subject/object, freedom/determinism, temporal/eternal, and particular/universal. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Kevin Aho - Existentialism: an introduction 2 'Subjective' | |
| A reaction: A helpful pointer, for us poor analytic philosophers, who stare in bewilderment at Hegel's stuff, despite its apparent importance. At moment it is the politics that strikes me as most interesting in Hegel. This is cultured consciousness, pre-Marx. |
| 21770 | Consciousness is both of objects, and of itself [Hegel] |
| Full Idea: Consciousness is, on the one hand, consciousness of the object, and on the other, consciousness of itself. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], p.052), quoted by Stephen Houlgate - An Introduction to Hegel 03 'The Method' | |
| A reaction: Hume challenges whether there is any knowledge of consciousness purely in itself. Schopenhauer flatly disagreed (Idea 4166) - but then he would, wouldn't he? |
| 5647 | Hegel claims knowledge of self presupposes desire, and hence objects [Hegel, by Scruton] |
| Full Idea: Hegel seems to argue that the immediate knowledge of self (the Cartesian premise) presupposes the activity that constitutes the self, and this presupposes desire, and hence the knowledge of objects. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Roger Scruton - Short History of Modern Philosophy Ch.12 | |
| A reaction: This hardly amounts to an argument, but I find it quite sympathetic as a claim. It fits comfortably with modern externalist accounts of thought. While solipsism seems a logical possibility, it hardly amounts to a coherent account of mental life. |
| 22770 | A person is a being which is aware of its own self-directed and free subjectivity [Hegel] |
| Full Idea: A person is a subject which is aware of its subjectivity, for as a person, I am completely for myself: the person is the individuality of freedom in pure being-for-itself. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 035 add) | |
| A reaction: Sartre's being 'pour-soi'. Presumably the freedom is for action as well as thought. He ignores Spinoza's claim that such freedom is just an illusion. |
| 5648 | For Hegel knowledge of self presupposes objects, and also a public and moral social world [Hegel, by Scruton] |
| Full Idea: Hegel tries to show that knowledge of self as subject presupposes not just knowledge of objects, but knowledge of a public social world, in which there is moral order and civic trust. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Roger Scruton - Short History of Modern Philosophy Ch.12 | |
| A reaction: This is not far off Wittgenstein's private language argument. It is also Popper's 'World Three', of society and language. Human reality is incomprehensible without some recognition of the culture in which we immerse, like fish in water. |
| 22788 | A human only become a somebody as a member of a social estate [Hegel] |
| Full Idea: When we say that a human being must be somebody, we mean that he must belong to a particular estate. …A human being with no estate is merely a private person and does not possess universality. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 207 add) | |
| A reaction: The first rebellion in Europe against the rising individual liberalism which started with Descartes and was clarified in Kant. Hegel's idea is hugely influential, especially through Marx. I don't believe being a person is a wholly social matter. |
| 22792 | Individuals attain their right by discovering their self-consciousness in institutions [Hegel] |
| Full Idea: Individuals attain their essential right by discovering their essential self-consciousness in social institutions, as that universal aspect of their particular interests which has being in itself. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 264) | |
| A reaction: This is the source of the influential idea made famous by Marx. Hegel seems to have a rather rigid and deterministic view of society, which fixes self-consciousness. The modern view is that self-consciousness is endlessly malleable, by society. |
| 21780 | A free will primarily wills its own freedoom [Hegel, by Houlgate] |
| Full Idea: For Hegel, the content or 'object' which any free will wills simply by virtue of being free is nothing other than its own freedom. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 027) by Stephen Houlgate - An Introduction to Hegel 8 'The Limits' | |
| A reaction: Personally I take the concept of a wholly 'free' will to be vacuous, but this is a very interesting idea. I would delete 'by virtue of being free', and say that what we mean by free will is the will's desperation to be as free as possible. Love it. |
| 22040 | Freedom is produced by the activity of the mind, and is not intrinsically given [Hegel] |
| Full Idea: Actual freedom is not something immediately existent in mindedness, but is something to be produced by the mind's own activity. It is thus as the producer of its freedom that we have to consider mindedness in philosophy. | |
| From: Georg W.F.Hegel (Philosophy of Mind (Encylopedia III) [1817], §382, Zusatz), quoted by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Pinkard glosses this as an agent being free by being the centre of a group of social responsibilities. Hence I presume small children have no freedom. Presumably we could deprive citizens of all responsibility, and hence of metaphysical freedom. |
| 15617 | In abstraction, beyond finitude, freedom and necessity must exist together [Hegel] |
| Full Idea: Considered as abstractly confronting one another, freedom and necessity pertain to finitude only and are valid only on its soil. A freedom with no necessity in it, and a mere necessity without freedom, are determinations that are abstract and thus untrue. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §35 Add) | |
| A reaction: This is, presumably, the Hegelian dialectical nature of things, that contradictories are bound together. We must struggle hard to undestand a freedom bound by necessity, and a necessity which contains freedom. (Good luck). |
| 22039 | Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard] |
| Full Idea: Hegel argued that it was the impossibility of a naturalistic account of normativity that distinguished Geist from nature, not Geist's being any kind of metaphysical substance. | |
| From: report of Georg W.F.Hegel (Philosophy of Mind (Encylopedia III) [1817]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Hegel always seems to want to have his cake and eat it. Without a mental substance, how can Geist not be part of nature? What is Geist made of? Is his view functionalist? But that is usually naturalistic. Is normativity magic? |
| 19469 | We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege] |
| Full Idea: We distinguish the grasp of a thought, which is 'thinking', from the acknowledgement of the truth of a thought, which is the act of 'judgement', from the manifestation of this judgement, which is an 'assertion'. | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.329 (62)) |
| 15608 | The act of thinking is the bringing forth of universals [Hegel] |
| Full Idea: Thinking as an activity is the active universal, and indeed the self-actuating universal, since the act, or what is brought forth, is precisely the universal. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §20) | |
| A reaction: One should contemplate animal thought in the light of this remark. Thought requires the recognition of types of things, and resemblances, and repetitions, and patterns. Language consists almost entirely of universals. |
| 8620 | Thought is the same everywhere, and the laws of thought do not vary [Frege] |
| Full Idea: Thought is in essentials the same everywhere: it is not true that there are different kinds of laws of thought to suit the different kinds of objects thought about. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro) | |
| A reaction: Different kinds of thinker might also be candidates for different laws of thought. I'm unsure of Frege's grounds for this claim; most continental philosophers would probably reject it. |
| 9581 | Many people have the same thought, which is the component, not the private presentation [Frege] |
| Full Idea: The same thought can be grasped by many people. The components of a thought, and even more so the things themselves, must be distinguished from the presentations which in the soul accompany the grasping of a thought. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.325) | |
| A reaction: This is the basic realisation, also found in Russell, of how so much confusion has crept into philosophy, in Berkeley, for example. Frege starts down the road which leads to the externalist view of content. |
| 8162 | Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett] |
| Full Idea: For Frege, thoughts belong to a special realm of reality, which he called the 'realm of sense' and distinguished from the 'realm of reference'. | |
| From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Michael Dummett - Thought and Reality 1 | |
| A reaction: A thought is, for Frege, a proposition. There is a halfway Platonism possible here, where the 'realm' for such things exists, but within that realm the objects might be conventional, or some such. Real possible worlds containing fictions! |
| 9818 | A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett] |
| Full Idea: On Frege's view, what distinguishes thoughts from everything else is that they may meaningfully be called 'true' and 'false'. | |
| From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Michael Dummett - Frege philosophy of mathematics Ch.2 | |
| A reaction: A lot of thinking is imagistic, and while the image may or may not truly picture the world, we tend to think that the truth or otherwise of daydreaming is simply irrelevant. Does Frege take all thought to be propositional? |
| 18265 | We don't judge by combining subject and concept; we get a concept by splitting up a judgement [Frege] |
| Full Idea: Instead of putting a judgement together out of an individual as subject and an already previously formed concept as predicate, we do the opposite and arrive at a concept by splitting up the content of possible judgement. | |
| From: Gottlob Frege (Boole calculus and the Concept script [1881], p.17) | |
| A reaction: This is behind holistic views of sentences, and hence of whole languages, and behind Quine's rejection of 'properties' inferred from the predicates in judgements. |
| 16379 | Thoughts about myself are understood one way to me, and another when communicated [Frege] |
| Full Idea: When Dr Lauben thinks he has been wounded, ..only Dr Lauben can grasp thoughts determined in this way. But he cannot communicate a thought which only he can grasp. To say 'I have been wounded' he must use 'I' in a sense graspable by others. | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918]), quoted by François Recanati - Mental Files 16.1 | |
| A reaction: [compressed] This seems to be the first, and very influential, attempt to explain the unusual and revealing semantics of indexicals. It seems to be the ultimate source of 2-D semantics, by introducing two modes of meaning for one term. |
| 21986 | Hegel's system has a vast number of basic concepts [Hegel, by Moore,AW] |
| Full Idea: For Hegel the full system of concepts ...contains many more than Kant's twelve. | |
| From: report of Georg W.F.Hegel (Logic (Encyclopedia I) [1817], I §60Z) by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: This offers some sort of conceptual scheme, but not the structured one that Kant proposes. The sequence of dialectical mediation imposes some sort of shape on the concepts. |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| Full Idea: If we need such signs, we also need definitions so that we can cram this sense into the receptacle and also take it out again. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: Has anyone noticed that Frege is the originator of the idea of the mental file? Has anyone noticed the role that definition plays in his account? |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| Full Idea: We often need to use a sign with which we associate a very complex sense. Such a sign seems a receptacle for the sense, so that we can carry it with us, while being always aware that we can open this receptacle should we need what it contains. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: This exactly the concept of a mental file, which I enthusiastically endorse. Frege even talks of 'opening the receptacle'. For Frege a definition (which he has been discussing) is the assigment of a label (the 'definiendum') to the file (the 'definiens'). |
| 20953 | Every concept depends on the counter-concepts of what it is not [Hegel, by Bowie] |
| Full Idea: Hegel relies on the claim that every concept depends for its determinacy upon its relation to other concepts which it is not (so that even the concept of being depends, for example, upon the concept of nothing). | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Andrew Bowie - Introduction to German Philosophy 4 'Questions' | |
| A reaction: How does he know this? A question I keep asking about continental philosophers. The negation concepts must be entirely non-conscious. Which negation concepts are relevant to the concept 'tree'? |
| 15607 | We don't think with concepts - we think the concepts [Hegel] |
| Full Idea: There is a saying that, when we have grasped a concept, we still do not know what to think with it. But there is nothing to be thought with a concept save the concept itself. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §03 Rem) | |
| A reaction: Analytic philosophers should read Hegel on concepts, because he approaches the matter so very differently, and seems to be the root of the continental approach to such things. He seems to me to talk more sense than Frege on the subject. |
| 15610 | Active thought about objects produces the universal, which is what is true and essential of it [Hegel] |
| Full Idea: When thinking is taken as active with regard to ob-jects, as the thinking-over of something, then the universal - as the product of the activity - contains the value of the matter, what is essential, inner, true. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §21) | |
| A reaction: I prefer to talk of 'general terms' rather than 'universals'. If 'tiger' is coined for the first one, but must be applicable to subsequent tigers, it has to generalise what they all have in common. Locke's 'nominal' essence, I would say. |
| 9870 | Early Frege takes the extensions of concepts for granted [Frege, by Dummett] |
| Full Idea: In the 'Grundlagen' Frege takes the notion of the extension of a concept for granted as unproblematic. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.16 | |
| A reaction: This comfortable notion was undermined by Russell's discovery of a concept which couldn't have an extension. Maybe we could defeat the Russell problem (and return to Frege's common sense) by denying that sets are objects. |
| 13878 | Concepts are, precisely, the references of predicates [Frege, by Wright,C] |
| Full Idea: For Frege concepts are, precisely, the Bedeutungen of predicates. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 1.iv | |
| A reaction: On p.17 Wright challenges Frege's right to make that assumption. |
| 7736 | A concept is a non-psychological one-place function asserting something of an object [Frege, by Weiner] |
| Full Idea: A concept is a one-place function - something that can be asserted of an object - as found in 'Earth is a planet' and 'Venus is a planet'. This notion of concept does not belong to psychology at all. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.4 | |
| A reaction: This doesn't seem to leave room for the concept of the object or substance of which the something is asserted. In 'x is a planet' we need a concept of what x is. But then Frege will reduce the reference to a set of descriptions (i.e. functions). |
| 17430 | Fregean concepts have precise boundaries and universal applicability [Frege, by Koslicki] |
| Full Idea: Both precise boundaries and universal applicability are built into the very notion of a Fregean concept from the outset, while isolation and non-arbitrary division are additional criteria imposed on concepts. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1 | |
| A reaction: The latter two criteria are for concepts which create counting units. |
| 8622 | Psychological accounts of concepts are subjective, and ultimately destroy truth [Frege] |
| Full Idea: Defining concepts psychologically, in terms of the nature of the human mind, makes everything subjective, and if we follow it through to the end, does away with truth. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro) | |
| A reaction: This is the reason for Frege's passionate opposition to psychological approaches to thought. The problem, though, is to give an account in which the fixity of truth connects to the fluctuations of mental life. How does it do that?? |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties. |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it. | |
| From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects | |
| A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status. |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable. |
| 18752 | 'The concept "horse"' denotes a concept, yet seems also to denote an object [Frege, by McGee] |
| Full Idea: The phrase 'the concept "horse"' can be the subject of a sentence, and ought to denote an object. But it clearly denotes the concept "horse". Yet Fregean concepts are said to be 'incomplete' objects, which led to confusion. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Vann McGee - Logical Consequence 4 | |
| A reaction: This is the notorious 'concept "horse"' problem, which was bad news for Frege's idea of a concept. |
| 9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
| Full Idea: Frege equated the concepts under which an object falls with its properties. | |
| From: report of Gottlob Frege (On Concept and Object [1892], p.201) by Michael Dummett - Frege philosophy of mathematics Ch.8 | |
| A reaction: I take this to be false, as objects can fall under far more concepts than they have properties. I don't even think 'being a pencil' is a property of pencils, never mind 'being my favourite pencil', or 'not being Alexander the Great'. |
| 9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
| Full Idea: In later Frege, a concept could be taken as a particular case of a function, mapping every object on to one of the truth-values (T or F), according as to whether, as we should ordinarily say, that object fell under the concept or not. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Michael Dummett - The Philosophy of Mathematics 3.5 | |
| A reaction: As so often in these attempts at explanation, this sounds circular. You can't decide whether an object truly falls under a concept, if you haven't already got the concept. His troubles all arise (I say) because he scorns abstractionist accounts. |
| 13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |
| Full Idea: Frege took the study of concepts and their extensions to be within logic. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Stewart Shapiro - Foundations without Foundationalism 7.1 | |
| A reaction: This is part of the plan to make logic a universal language (see Idea 13664). I disagree with this, and with the general logicist view of the position of logic. The logical approach thins concepts out. See Deleuze/Guattari's horror at this. |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity. |
| 8651 | A concept is a possible predicate of a singular judgement [Frege] |
| Full Idea: A concept is for me that which can be predicate of a singular judgement-content. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §66 n) | |
| A reaction: This seems intuitively odd, given that a predicate could (in principle) be of almost infinite complexity, whereas I would be reluctant to call anything a 'concept' if it couldn't be grasped by a single action of a normal conscious mind. |
| 4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
| Full Idea: As I understand it, a concept is the meaning of a grammatical predicate. | |
| From: Gottlob Frege (On Concept and Object [1892], p.193) | |
| A reaction: All the ills of twentieth century philosophy reside here, because it makes a concept an entirely linguistic thing, so that animals can't have concepts, and language is cut off from reality, leading to relativism, pragmatism, and other nonsense. |
| 9846 | Defining 'direction' by parallelism doesn't tell you whether direction is a line [Dummett on Frege] |
| Full Idea: The stipulation that the direction of a line a is to be the same as that of a line b just in case a is parallel to b does not determine whether the direction of a line is itself a line or something quite different. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §60) by Michael Dummett - Frege philosophy of mathematics Ch.11 | |
| A reaction: Nice point. Maybe not being able to say exactly what something is is either a symptom of nonsense, and simply a symptom that we are dealing with an abstract concept. If abstractions don't exist, they don't need individuation criteria. |
| 9976 | Frege accepts abstraction to the concept of all sets equipollent to a given one [Tait on Frege] |
| Full Idea: Frege's own conception of abstraction (although he disapproves of the term) is in agreement with the view that abstracting from the particular nature of the elements of M would yield the concept under which fall all sets equipollent to M. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by William W. Tait - Frege versus Cantor and Dedekind III | |
| A reaction: Nice! This shows how difficult it is to slough off the concept of abstractionism and live with purely logical concepts of it. If we 'construct' a set, then there is a process of creation to be explained; we can't just think of platonic givens. |
| 10803 | Frege himself abstracts away from tone and color [Yablo on Frege] |
| Full Idea: Frege himself abstracts away from tone and color. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stephen Yablo - Carving Content at the Joints §3 | |
| A reaction: Gotcha! I have been searching for instances where Frege perpetrates psychological abstraction right in the heart of his theory. No one can avoid it, if they are in the business of trying to formulate new concepts. Reference ignores sense, and vice versa. |
| 9988 | If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege] |
| Full Idea: When from a set of two cats, one black and one white, we 'abstract' the number two as a set of pure units, the units are not black and white, respectively, and they are not cats. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §34) by William W. Tait - Frege versus Cantor and Dedekind XI | |
| A reaction: Well said. Frege is contemptuous of this approach, as if we were incapable of thinking of a black cat as anything other than as black or cat, when we can catch cats as 'food', or 'objects', or just plain 'countables'. |
| 9579 | Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege] |
| Full Idea: If from a black cat and a white cat we disregard colour, then posture, then location, ..we finally derive something which is completely without restrictions on content; but what is derived from the objects does differ, although it is not easy to say how. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: This is a key objection to abstractionism for Frege - we are counting two cats, not two substrata of essential catness, or whatever. But what makes a cat countable? (Key question!) It isn't its colour, or posture or location. |
| 9587 | How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege] |
| Full Idea: Inattention is a very strong lye which must not be too concentrated, or it dissolves everything (such as the connection between the objects), but must not be too weak, to produce sufficient change. Personally I cannot find the proper dilution. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.330) | |
| A reaction: We may sympathise with the lack of precision here (frustrating for a logician), but it is not difficult to say of a baseball defence 'just concentrate on the relations, and ignore the individuals who implement it'. You retain basic baseball skills. |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid. |
| 9855 | Frege's logical abstaction identifies a common feature as the maximal set of equivalent objects [Frege, by Dummett] |
| Full Idea: Like psychological abstractionism, Frege's method (which we can call 'logical abstraction') aims at isolating what is in common between the members of any equivalent sets of objects, by identifying the feature with the maximal set of such objects. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.14 | |
| A reaction: [compressed] So Frege's approach to abstraction is a branch of the view that properties are sets. This view, in addition to being vulnerable to Russell's paradox, ignores the causal role of properties, making them all categorical (which is daft). |
| 10802 | Frege's 'parallel' and 'direction' don't have the same content, as we grasp 'parallel' first [Yablo on Frege] |
| Full Idea: Frege's discussion of 'direction' borders on incoherent. He claims that the equivalence of lines a and b and their directions being equal have the same content, which leads to the concept of direction, but we grasp the equivalence before the equality. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stephen Yablo - Carving Content at the Joints § 1 | |
| A reaction: [The Frege is in Grundlagen §64] Well said. The notion that we get the full concept of 'direction' from such paltry resources seems very weak. For a start, parallel lines exhibit two directions, not one. |
| 10525 | Frege put the idea of abstraction on a rigorous footing [Frege, by Fine,K] |
| Full Idea: It was Frege who first showed how the idea of abstraction could be put on a rigorous footing. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kit Fine - Precis of 'Limits of Abstraction' p.305 | |
| A reaction: This refers to the crucial landmark in philosophical thought about abstraction. The question is whether Frege had to narrow the concept of abstraction and abstract entities too severely, in order to achieve his rigour. |
| 10526 | Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K] |
| Full Idea: Fregean abstraction rests on initial items, taken to be related by an equivalence relation (e.g. parallelism, or equinumerosity), and then an operation for forming abstraction (e.g. direction or number), with identity related to their equivalence. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kit Fine - Precis of 'Limits of Abstraction' p.305 | |
| A reaction: [compressed] This is the best summary I have found of the modern theory of abstraction, as opposed to the nature of the abstracta themselves. A minimum of two items is needed to implement the process. |
| 10556 | We create new abstract concepts by carving up the content in a different way [Frege] |
| Full Idea: (In creating the concept of direction..) We carve up the content in a way different from the original way, and this yields us a new concept. ...It is a matter of drawing boundary lines that were not previously given. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64) | |
| A reaction: [second half in §88] 'Recarving' is now the useful shorthand for Frege's way of creating abstract concepts (rather than the old psychological way of ignoring some features of an object). |
| 9882 | You can't simultaneously fix the truth-conditions of a sentence and the domain of its variables [Dummett on Frege] |
| Full Idea: Frege's root confusion (over abstraction by identity, and other things) was to believe that he could simultaneously fix the truth-conditions of such statements and the domain over which the individual variables were to range. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64-68) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: This strikes me as a wonderfully penetrating criticism, but it also seems to me to threaten Dummett's whole programme of doing ontology through language. If a quantified sentences needs a domain, how do you first decide your domain? |
| 9881 | From basing 'parallel' on identity of direction, Frege got all abstractions from identity statements [Frege, by Dummett] |
| Full Idea: Having rightly perceived that the fundamental class here was statements of identity between directions, Frege leapt to the conclusion that the basis for introducing new abstract terms consisted of determining the truth-conditions of identity-statements. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64-68) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: This seems to be the modern view - that abstraction consists of the assertion of an equivalence principle. Dummett criticises Frege here (see Idea 9882). There always seems to be a chicken/egg problem. Why would the identity be asserted? |
| 5816 | Frege said concepts were abstract entities, not mental entities [Frege, by Putnam] |
| Full Idea: Frege, rebelling against 'psychologism', identified concepts (and hence 'intensions' or meanings) with abstract entities rather than mental entities. | |
| From: report of Gottlob Frege (works [1890]) by Hilary Putnam - Meaning and Reference p.119 | |
| A reaction: This, of course, assumes that 'abstract' entities and 'mental' entities are quite distinct things. A concept is presumably a mental item which has content, and the word 'concept' is simply ambiguous, between the container and the contents. |
| 9588 | Number-abstraction somehow makes things identical without changing them! [Frege] |
| Full Idea: Number-abstraction simply has the wonderful and very fruitful property of making things absolutely the same as one another without altering them. Something like this is possible only in the psychological wash-tub. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.332) | |
| A reaction: Frege can be awfully sarcastic. I don't really see his difficulty. For mathematics we only need to know what is countable about an object - we don't need to know how many hairs there are on the cat, only that it has identity. |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction... | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99) | |
| A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it. |
| 9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
| Full Idea: Frege felt that meanings are public property, and identified concepts (and hence 'intensions' or meanings) with abstract entities rather than mental entities. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by Hilary Putnam - Meaning and Reference p.150 | |
| A reaction: This is the germ of Wittgenstein's private language argument. I am inclined to feel that Frege approached language strictly as a logician, and didn't really care that he got himself into implausible platonist ontological commitments. |
| 9583 | Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege] |
| Full Idea: The psychological logicians are concerned with the sense of the words and with the presentations, which they do not distinguish from the sense; but the mathematicians are concerned with the matter itself, with the reference of the words. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326) | |
| A reaction: This is helpful for showing the point of his sense/reference distinction; it is part of his campaign against psychologism, by showing that there is a non-psychological component to language - the reference, where it meets the public world. |
| 9584 | Identity baffles psychologists, since A and B must be presented differently to identify them [Frege] |
| Full Idea: The relation of sameness remains puzzling to a psychological logician. They cannot say 'A is the same as B', because that requires distinguishing A from B, so that these would have to be different presentations. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327) | |
| A reaction: This is why Frege needed the concept of reference, so that identity could be outside the mind (as in Hesperus = Phosophorus). Think about an electron; now think about a different electron. |
| 22318 | Frege failed to show when two sets of truth-conditions are equivalent [Frege, by Potter] |
| Full Idea: Frege's account suffered from a lack of precision about when two sets of truth-conditions should count as equivalent. (Wittgenstein aimed to rectify this defect). | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 50 Intro |
| 7307 | A thought is not psychological, but a condition of the world that makes a sentence true [Frege, by Miller,A] |
| Full Idea: For Frege, a thought is not something psychological or subjective; rather, it is objective in the sense that it specifies some condition in the world the obtaining of which is necessary and sufficient for the truth of the sentence that expresses it. | |
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.2 | |
| A reaction: It is worth emphasising Russell's anti-Berkeley point about 'ideas', that the idea is in the mind, but its contents are in the world. Since the contents are what matter, this endorses Frege, and also points towards modern externalism. |
| 4980 | The meaning (reference) of a sentence is its truth value - the circumstance of it being true or false [Frege] |
| Full Idea: We are driven into accepting the truth-value of a sentence as constituting what it means (refers to). By the truth-value I understand the circumstance that it is true or false. | |
| From: Gottlob Frege (On Sense and Reference [1892], p.34) | |
| A reaction: Sounds bizarre, but Black's translation doesn't help. The notion of what the whole sentence refers to (rather than its sense) is a very theoretical notion. 'All true sentences refer to the truth' sounds harmless enough. |
| 16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
| Full Idea: No sense accrues to a sign by the mere fact that it is used in one or more sentences, the other constituents of which are known. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.213) | |
| A reaction: Music to my ears. I've never grasped how meaning could be grasped entirely through use. |
| 8646 | Words in isolation seem to have ideas as meanings, but words have meaning in propositions [Frege] |
| Full Idea: We consider the meanings of words in isolation, which leads us to accept an idea as the meaning, and words with no mental picture appear to have no mental content. But only in a proposition have the words really a meaning. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §60) | |
| A reaction: Frege (later) sees concepts as functions, which need input and output to be understood. It points to the idea that meaning is nothing more than usage. Something, though, is missing. As ever, WHY does something have a particular function? |
| 7732 | Never ask for the meaning of a word in isolation, but only in the context of a proposition [Frege] |
| Full Idea: Never ask for the meaning of a word in isolation, but only in the context of a proposition. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], p.x) | |
| A reaction: [Called the 'Contextual Principle']. But surely the word 'pig' has a known meaning, even if I don't give it a context? A word like 'the' seems to need a context, though. One might demand the context of the proposition as well. |
| 8446 | We understand new propositions by constructing their sense from the words [Frege] |
| Full Idea: The possibility of our understanding propositions which we have never heard before rests on the fact that we construct the sense of a proposition out of parts that correspond to words. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.43) | |
| A reaction: This is the classic statement of the principle of compositionality, which seems to me so obviously correct that I cannot understand anyone opposing it. Which comes first, the thought or the word, may be a futile debate. |
| 9180 | Holism says all language use is also a change in the rules of language [Frege, by Dummett] |
| Full Idea: Frege thought of a language as a game played with fixed rules, there being all the difference in the world between a move in the game and an alteration of the rules; but, if holism is correct, every move in the game changes the rules. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Frege's Distinction of Sense and Reference p.248 | |
| A reaction: Rules do shift over time, so there must be some mechanism for that - the rules can't sit in sacrosanct isolation. People play games with the language itself, as well as using it to play other games. |
| 4981 | The reference of a word should be understood as part of the reference of the sentence [Frege] |
| Full Idea: I have transferred the relation between the parts and the whole of the sentence to its reference, by calling the reference of the word part of the reference of the sentence, if the word itself is part of the sentence. | |
| From: Gottlob Frege (On Sense and Reference [1892], p.35) | |
| A reaction: Since Frege says the reference of a true sentence is simply to truth, words have reference insofar as they make contributions to attempts at stating truths. |
| 15597 | Frege's Puzzle: from different semantics we infer different reference for two names with the same reference [Frege, by Fine,K] |
| Full Idea: Frege's Puzzle: If two sentences convey different information, they have different semantic roles, so the names 'Cicero' and 'Tully' are semantically different, in which case they are referentially different - but they are not referentially different. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Kit Fine - Semantic Relationism 2.A | |
| A reaction: [this is my summary of Fine's summary] Given the paradox, the question is which of these premisses should be challenged. Fregeans reject their being referentially different. Referentialists reject the different semantic roles. |
| 17002 | Frege's 'sense' is ambiguous, between the meaning of a designator, and how it fixes reference [Kripke on Frege] |
| Full Idea: Frege should be criticised for using the term 'sense' in two senses. He takes the sense of a designator to be its meaning; and he also takes it to be the way its reference is determined. …They correspond to two ordinary uses of 'definition'. | |
| From: comment on Gottlob Frege (On Sense and Reference [1892]) by Saul A. Kripke - Naming and Necessity lectures Lecture 1 | |
| A reaction: Stalnaker quotes this, but seems unconvinced that Frege is guilty. If the 'meaning' largely consists of a way of determining a reference, Frege would be in the clear. |
| 18778 | Every descriptive name has a sense, but may not have a reference [Frege] |
| Full Idea: It may perhaps be granted that every grammatically well-formed expression representing a proper name always has a sense. But this is not to say that to this sense there also corresponds a reference. | |
| From: Gottlob Frege (On Sense and Reference [1892]), quoted by Bernard Linsky - Quantification and Descriptions 3.1 | |
| A reaction: Presumably this concerns fictional names such as 'Pegasus'. It seems to be good simple evidence for the distinction between sense and reference. |
| 7805 | Frege started as anti-realist, but the sense/reference distinction led him to realism [Frege, by Benardete,JA] |
| Full Idea: In the Grundlagen of 1884 Frege was an anti-realist, but in Grundgesetze of 1893 he is a realist, who has profited by his interim discovery of the sense/reference distinction. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by José A. Benardete - Logic and Ontology | |
| A reaction: This is the germ of the new realist philosophy which seems to be growing out of Kripke and co's causal theory of reference. The very notion of reference is realist (hence Russell's realism). |
| 4976 | The meaning (reference) of 'evening star' is the same as that of 'morning star', but not the sense [Frege] |
| Full Idea: The meaning (reference) of 'evening star' is the same as that of 'morning star', but not the sense. | |
| From: Gottlob Frege (On Sense and Reference [1892], p.27) | |
| A reaction: Max Black translates 'bedeutung' as 'meaning', but nowadays everyone calls it 'reference'. This is Frege's crucial distinction, which greatly clarified analytical philosophy. Nevertheless, is it a sharp distinction? E.g. referring to a fictional name? |
| 4977 | In maths, there are phrases with a clear sense, but no actual reference [Frege] |
| Full Idea: The expression 'the least rapidly convergent series' has a sense but demonstrably there is no reference, since a less rapidly convergent series (for any given series) can always be found. | |
| From: Gottlob Frege (On Sense and Reference [1892], p.28) | |
| A reaction: A nice example. 'The second Kennedy assassin' has a clear meaning, but does it have a reference? The meaning 'points at' a possible reference. We yet discover an identity. |
| 4979 | We are driven from sense to reference by our desire for truth [Frege] |
| Full Idea: The striving for truth drives us always to advance from the sense to the thing meant (the reference). | |
| From: Gottlob Frege (On Sense and Reference [1892], p.33) | |
| A reaction: As in, we want to know the reference of 'the person who shot Kennedy'. I always perk up if truth is mentioned in a discussion of language, because it reminds us of the point of the whole thing. In 'Is he the best man?' I have the reference, not the truth. |
| 8449 | Senses can't be subjective, because propositions would be private, and disagreement impossible [Frege] |
| Full Idea: If the sense of a name was subjective, then the proposition and the thought would be subjective; the thought one man connects with this proposition would be different from that of another man. One man could not then contradict another. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.44) | |
| A reaction: This is an implicit argument for the identity of 'proposition' and 'thought'. This argument resembles Plato's argument for universals (Idea 223). See also Kant on existence as a predicate (Idea 4475). But people do misunderstand one another. |
| 15155 | Expressions always give ways of thinking of referents, rather than the referents themselves [Frege, by Soames] |
| Full Idea: For Frege, expressions always contribute ways of thinking of their referents, rather than the referents themselves, to the thoughts expressed by sentences. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Scott Soames - Philosophy of Language 1.16 | |
| A reaction: I have some sympathy for Frege. It always strikes me as daft to think that if I say 'my dustbin is empty', the dustbin becomes 'part' of my sentence. Sentences don't contain large plastic objects. |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false. | |
| From: Gottlob Frege (Function and Concept [1891], p.14) | |
| A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?' |
| 22280 | Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter] |
| Full Idea: Frege's account was top-down, not bottom-up: he aimed to decompose and discern function-argument structure in already existing sentences, not to explain how those sentences acquired their meanings in the first place. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'Func' | |
| A reaction: This goes with the holistic account of meaning, which leads to Quine's gavagai and Kuhn's obfuscation of science. I recommend compositionality for everthing. |
| 7309 | Frege's 'sense' is the strict and literal meaning, stripped of tone [Frege, by Miller,A] |
| Full Idea: Frege held that "and" and "but" have the same 'sense' but different 'tones' (note: they have the same truth tables); the sense of an expression is what a sentence strictly and literally means, stripped of its tone. | |
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.6 | |
| A reaction: It seems important when studying Frege to remember what has been stripped out. In "he is a genius and he plays football", if you substitute 'but' for 'and', the new version says (literally?) something very distinctive about football. |
| 7312 | 'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Frege, by Miller,A] |
| Full Idea: Frege's introduction of 'sense' was motivated by the desire to solve three problems: the problem of bearerless names, the problem of substitution in belief contexts, and the problem of informativeness. | |
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.9 | |
| A reaction: A proposal which solves three problems sounds pretty good! These three problems can be used to test the counter-proposals of Russell and Kripke. |
| 11126 | 'Sense' gives meaning to non-referring names, and to two expressions for one referent [Frege, by Margolis/Laurence] |
| Full Idea: Frege notes that an expression without a referent ('Pegasus') needn't lack a meaning, since it still has a sense, and the same referent (Eric Blair) can be associated with different expressions (George Orwell) because they convey different senses. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by E Margolis/S Laurence - Concepts 1.3 | |
| A reaction: A nice neat summary of the value of Frege's introduction of the sense/reference distinction, which seems to me to be virtually undeniable (a rare event in modern philosophy). |
| 8164 | Frege was the first to construct a plausible theory of meaning [Frege, by Dummett] |
| Full Idea: Frege was the first to construct a plausible theory of meaning, that is, a theory of how a human language functions. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Thought and Reality 1 | |
| A reaction: Presumably Frege had an advantage because he was the first to distinguish sense from reference, and hence to identify the subject-matter of the theory. Essentially Frege's theory is that of truth-conditions. |
| 9817 | Earlier Frege focuses on content itself; later he became interested in understanding content [Frege, by Dummett] |
| Full Idea: Earlier Frege was interested solely in the content of our statements, not in our grasp of that content. His notion of 'sense' from 1891 onwards, has to do with understanding; the sense of an expression is something we grasp. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Frege philosophy of mathematics Ch.2 | |
| A reaction: The important point must be that the later theory depends on the earlier, so we can hardly give theories of understanding, if we don't have a view about what it is that is understood. |
| 8171 | Frege divided the meaning of a sentence into sense, force and tone [Frege, by Dummett] |
| Full Idea: Frege distinguished three components of the meaning of a sentence: sense, force and tone; he used no single term for 'linguistic meaning' in general. ...The sense is only what bears on the truth or falsity of what the sentence expresses. | |
| From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Thought and Reality 3 | |
| A reaction: Modern theories of meaning seem to assume that there is one item called 'meaning' which needs to be explained, but presumably this is 'strict and literal meaning', leaving the rest to pragmatics. |
| 4954 | Frege uses 'sense' to mean both a designator's meaning, and the way its reference is determined [Kripke on Frege] |
| Full Idea: Frege should be criticised for using the term 'sense' in two senses. For he takes the sense of a designator to be its meaning; and he also takes it to be the way its reference is determined. | |
| From: comment on Gottlob Frege (On Sense and Reference [1892]) by Saul A. Kripke - Naming and Necessity lectures Lecture 1 | |
| A reaction: This criticism doesn't surprise me, as heroic pioneers like Frege seem to have been extremely unclear about what they were claiming. Kripke has helped, but we still need some great mind to step in and sort out the mess. |
| 7304 | Frege explained meaning as sense, semantic value, reference, force and tone [Frege, by Miller,A] |
| Full Idea: Frege analysed the intuitive notion of meaning in terms of the notions of sense, semantic value, reference, force and tone. | |
| From: report of Gottlob Frege (On Sense and Reference [1892], Pref) by Alexander Miller - Philosophy of Language Pref | |
| A reaction: This suggests that there are two approaches to the explanation of meaning: either a simple identity with some other mental fact, or an analysis (as here) into a range of components. I remain open-minded on that. |
| 4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |
| Full Idea: For all the multiplicity of languages, mankind has a common stock of thoughts. | |
| From: Gottlob Frege (On Concept and Object [1892], p.196n) | |
| A reaction: Given the acknowledgement here that two very different sentences in different languages can express the same thought, he should recognise that at least some aspects of a thought are non-linguistic. |
| 16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
| Full Idea: A thought is not something subjective, is not the product of any form of mental activity; for the thought that we have in Pythagoras's theorem is the same for everybody. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: When such thoughts are treated as if the have objective (platonic) existence, I become bewildered. I take a thought (or proposition) to be entirely psychological, but that doesn't stop two people from having the same thought. |
| 16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
| Full Idea: The sentence is of value to us because of the sense that we grasp in it, which is recognisably the same in a translation. I call this sense the thought. What we prove is not a sentence, but a thought. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: The 'sense' is presumably the German 'sinn', and a 'thought' in Frege is what we normally call a 'proposition'. So the sense of a sentence is a proposition, and logic proves propositions. I'm happy with that. |
| 19467 | A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege] |
| Full Idea: I call a 'thought' something for which the question of truth can arise at all. ...So I can say: thoughts are senses of sentences, without wishing to assert that the sense of every sentence is a thought. | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.327-8 (61)) | |
| A reaction: This builds on his distinction between sense and reference. The reference of every truth sentence is just 'the true', and the sense is the proposition. The concept of a proposition seems indispensable to logic, I would say. |
| 16874 | The parts of a thought map onto the parts of a sentence [Frege] |
| Full Idea: A sentence is generally a complex sign, so the thought expressed by it is complex too: in fact it is put together in such a way that parts of a thought correspond to parts of the sentence. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.207) | |
| A reaction: This is the compositional view of propositions, as opposed to the holistic view. |
| 19472 | A sentence is only a thought if it is complete, and has a time-specification [Frege] |
| Full Idea: Only a sentence with the time-specification filled out, a sentence complete in every respect, expresses a thought. | |
| From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.343(76)) | |
| A reaction: I take the 'every respect' to include the avoidance of ambiguity, and some sort of perspicacious reference for the terms. I wish philosophers would focus on the thoughts in their subject, and not nit-pick about the sentences. Does he mean 'utterances'? |
| 9370 | A statement is analytic if substitution of synonyms can make it a logical truth [Frege, by Boghossian] |
| Full Idea: According to Frege, a statement's analyticity (in my epistemological sense) is to be explained by the fact that it is transformable into a logical truth by the substitution of synonyms for synonyms. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03) by Paul Boghossian - Analyticity Reconsidered §I | |
| A reaction: [He says this interpretation of Frege's semantical notion of analyticity may be controversial] Presumably we see that 'bachelors are unmarried men' is analytic when we start substituting for 'bachelor'. Sounds reasonable. |
| 8743 | Frege considered analyticity to be an epistemic concept [Frege, by Shapiro] |
| Full Idea: Frege held that analyticity is like a priority in being an epistemic concept. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03) by Stewart Shapiro - Thinking About Mathematics 5.1 | |
| A reaction: Kripke very firmly says that this is not so. While a priori is an epistemic concept, analyticity is a semantic concept. I cling on to Kripke's framework, but probably more because it is neat and comfortable than because it is true. |
| 7725 | 'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Frege, by Weiner] |
| Full Idea: 'It is raining or it is not raining' appears to true because of the general principle 'p or not-p', so it is analytic; but this does not fit Kant's idea of an analytic truth, because it is not obvious that it has a subject concept or a predicate concept. | |
| From: report of Gottlob Frege (works [1890]) by Joan Weiner - Frege Ch.2 | |
| A reaction: The general progress of logic seems to be a widening out to embrace problem sentences. However, see Idea 7315 for the next problem that arises with analyticity. All this culminates in Quine's attack (e.g. Idea 1624). |
| 20295 | All analytic truths can become logical truths, by substituting definitions or synonyms [Frege, by Rey] |
| Full Idea: Frege appealed to definition, or (if 'meaning' is preserved) synonymy: the non-logical analytic truths can be converted to logical truths by substitution of definitions for defined terms, or synonyms for synonyms. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §005, 88) by Georges Rey - The Analytic/Synthetic Distinction 1.2 | |
| A reaction: This is a 'dogma of empiricism' attacked by Quine. It seems rather obvious (with hindsight?) that you can smuggle whatever is required to do the job into your definition. Or assert some slightly dubious synonymy. |
| 7316 | Analytic truths are those that can be demonstrated using only logic and definitions [Frege, by Miller,A] |
| Full Idea: Frege (according to Quine) characterises analytic truths as those that can be demonstrated or proved using only logical laws and definitions as premises. | |
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 4.2 | |
| A reaction: This is the big shift away from the Kantian version (predicate contained in the subject) towards a modern version, perhaps fixed by a truth table giving true for all values. |
| 21763 | When we explicate the category of being, we watch a new category emerge [Hegel, by Houlgate] |
| Full Idea: For Hegel, by explicating the indeterminate category of being, we do not merely restate in different words what is obviously 'contained' in it; we watch a new category emerge. | |
| From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'The Method' | |
| A reaction: This is obviously a response to Kant's view of analyticity, as merely explicating the contents of the subject of the sentence, without advancing knowledge or conceptual resources. A key idea of Hegel's, which I find unconvincing. |
| 2515 | Frege fails to give a concept of analyticity, so he fails to explain synthetic a priori truth that way [Katz on Frege] |
| Full Idea: Frege's approach provides no concept of analyticity (hence Quine's attack), so there is no notion of the analytic a priori under which to bring the metaphysician's synthetic a priori propositions. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Jerrold J. Katz - Realistic Rationalism Int.xxi | |
| A reaction: So Frege might have been a logical positivist, if only he had given himself the right tools for the job? |
| 22769 | The concept of the will is the free will which wills its freedom [Hegel] |
| Full Idea: The abstract concept of the Idea of the will is in general the free will which wills the free will. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 027) | |
| A reaction: Since Hegel thinks we only have free will because we will to have it, it makes sense that that will precedes the free will. But I don't understand how the will which wills that freedom is itself free. No doubt Hegelians understand this. |
| 21787 | Evil enters a good will when we believe we are doing right, but allow no criticism of our choice [Hegel, by Houlgate] |
| Full Idea: The evil Hegel finds at the heart of the good will is not simply the criminal violation of rights, but the evil which lies in believing oneself to be doing what is truly good, while allowing no one but oneself to determine what the good actually is. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821]) by Stephen Houlgate - An Introduction to Hegel 08 'The Problem' | |
| A reaction: That is not intellectualism, but the implication that intellectualism is a potential source of evil. The interesting thought is that Hegel is contributing a social dimension to the weakness of will problem. |
| 18549 | Nineteenth century aesthetics focused on art rather than nature (thanks to Hegel) [Hegel, by Scruton] |
| Full Idea: Only In the course of the nineteenth century, and in the wake of Hegel's posthumously published lectures on aesthetics, did the topic of art come to replace that of natural beauty as the core subject-matter of aesthetics. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826], 5) by Roger Scruton - Beauty: a very short introduction |
| 22043 | Hegel largely ignores aesthetic pleasure, taste and beauty, and focuses on the meaning of artworks [Hegel, by Pinkard] |
| Full Idea: Unlike his predecessors (including Kant), Hegel does not focus on aesthetic pleasure, nor on good taste, nor even on the nature and criteria for beauty. Instead he focuses on the meaning of artworks and their role in forming mankind's self-consciousness. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Personally I dislike over-intellectualising art. The aim of a work of art is to give a certain experience, not to generate an ensuing sequence of theorising. I doubt whether Vermeer had any 'meaning' in mind in his obsessive work. |
| 22042 | Natural beauty is unimportant, because it doesn't show human freedom [Hegel, by Pinkard] |
| Full Idea: Hegel thinks that natural beauty is of no real significance since it cannot display our freedom to us; nature per se is meaningless. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Presumably freedom is in the creation, and so creativity is what matters in aesthetics. But what are the criteria of good creativity? |
| 20413 | For Hegel the importance of art concerns the culture, not the individual [Hegel, by Eldridge] |
| Full Idea: Hegel locates the significance of art in its role in cultural life in general, not in relation to the psychological needs of individuals. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Richard Eldridge - G.W.F. Hegel (aesthetics) 1 | |
| A reaction: I'm beginning to see that art is a wonderful focus and test case for political attitudes. Roughly, liberalism focuses on individual responses, but more societal views (from right and left) see it in terms of role in the community. Which are you? |
| 20394 | The purpose of art is to reveal to Spirit its own nature [Hegel, by Davies,S] |
| Full Idea: According to Hegel, the goal of art was to serve as a phase in a process by which Spirit would come to understand its own nature. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Stephen Davies - The Philosophy of Art (2nd ed) 2.7 | |
| A reaction: I try very hard to understand ideas like this. Really really hard. However, since I see little sign of 'Spirit' really understanding its own nature, I'm guessing that the project is not going well. |
| 21794 | The main purpose of art is to express the unity of human life [Hegel] |
| Full Idea: Art's primary function, for Hegel, is to give expression to the unity and wholeness of life - especially human life - that the contingencies of everyday existence frequently conceal. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826]), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Beauty' | |
| A reaction: I don't find the view that human life is 'unified' and 'whole' vary illuminating, and I have no objection to art which reflects the fragmentary and unstable aspects of life. I suspect Hegel would just prefer it if life were a unity. |
| 20415 | Art forms a bridge between the sensuous world and the world of pure thought [Hegel] |
| Full Idea: Spirit generates out of itself works of fine art as the first reconciling middle term between pure thought and what is merely external, sensuous and transient - between finite natural reality and the infinite freedom of conceptual thinking. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], p.8), quoted by Richard Eldridge - G.W.F. Hegel (aesthetics) | |
| A reaction: This apparently says that there is necessarily an intellectual and conceptual component in art. This means little to me. Does he include portraits? Dutch domestic scenes? Would photography qualify? |
| 21786 | Conscience is the right of the self to know what is right and obligatory, and thus make them true [Hegel] |
| Full Idea: Conscience is the expression of the absolute title of subjective self-consciousness to know in itself and from within itself what is right and obligatory, to recognise only what it knows as good, and that what is thus known is right and obligatory. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 137), quoted by Stephen Houlgate - An Introduction to Hegel 08 'The Problem' | |
| A reaction: [compressed] This is the sort of rabbit-out-of-the-hat move that Hegel loves, and I find implausible. Mill made the key point about conscience. |
| 21796 | Man is God if he raises himself, by denying his nature and finitude [Hegel] |
| Full Idea: Man is only God in so far as he negates the natural existence and finitude of his spirit and raises himself to God. | |
| From: Georg W.F.Hegel (The Philosophy of History [1840], p.324), quoted by Stephen Houlgate - An Introduction to Hegel 10 'God' | |
| A reaction: I suspect that it was ideas like this which motivated Nietzsche - denial of what we are, in the name of some idle daydream. I personally have no idea how to negate my natural existence or my finitude. |
| 22784 | Love is ethical life in its natural form [Hegel] |
| Full Idea: Love is a feeling, that is, ethical life in its natural form. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 158 add) | |
| A reaction: For Hegel the less natural forms are more abstract - such as the categorical imperative. Does this imply that intellectual beings should extend the feeling of love into more abstract forms, such as virtues or principles or ideals? |
| 23274 | World history has no room for happiness [Hegel] |
| Full Idea: World history is not the place for happiness. Periods of happiness are empty pages in history. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: Clearly, Hegel thinks the progress of world history is much more important than happiness. This idea gives backing to those who don't care much about the casualties on either side in a major war. |
| 8029 | You can't have a morality which is supplied by the individual, but is also genuinely universal [Hegel, by MacIntyre] |
| Full Idea: Hegel attacks doctrines which are attempts by the individual to supply his own morality, and at one and the same time, to claim for it a genuine universality. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821]) by Alasdair MacIntyre - A Short History of Ethics Ch.15 | |
| A reaction: Hegel clearly has Kant in mind. It is a penetrating criticism. Of course, there is no reason why a universal mathematical proof shouldn't be 'provided' by the individual. The Kantian seeks agreement. See Contractualism. |
| 22771 | Be a person, and respect other persons [Hegel] |
| Full Idea: The commandment of right is: be a person, and respect other persons | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 036) | |
| A reaction: This seems to be presented as a categorical imperative. He implies that you can choose whether to be a person, which seems wrong. I love making 'respect other persons' the supreme command - but I prefer 'respect everything'. |
| 22051 | The categorical imperative lacks roots in a historical culture [Hegel, by Bowie] |
| Full Idea: Hegel criticised the categorical imperative for lacking any roots in the moral habits and practices which develop in actual historical communities. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821]) by Andrew Bowie - German Philosophy: a very short introduction 1 | |
| A reaction: This is the gist of Alasdair MacIntyre's defence of virtue theory, against rational Enlightenment ethics. Charles Taylor made the link to Hegel. |
| 22781 | The categorical imperative is fine if you already have a set of moral principles [Hegel] |
| Full Idea: The proposition 'Consider whether your maxim can be asserted as a universal principle' would be all very well if we already had determinate principles concerning how to act. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 135 add) | |
| A reaction: Excellent! I have always taken this to be the overwhelming problem with Kant's theory. Kant's examples always presume a set of unquestioned conventional values. Kant offers a framework for moral thought, but values are what matter. |
| 22779 | The good is realised freedom [Hegel] |
| Full Idea: The good is realised freedom, the absolute and ultimate end of the world. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 129) | |
| A reaction: This remark could have been made by Sartre. On its own I find it baffling, and can make no sense of an account of ethics that gives no guidance on behaviour at all, other than that freedom should be asserted. |
| 21758 | Humans have no fixed identity, but produce and reveal their shifting identity in history [Hegel, by Houlgate] |
| Full Idea: For Hegel, the absolute truth of humanity is that human beings have no fixed, given identity, but rather determine and produce their own identity and their world in history, and that they gradually come to the recognition of this fact in history. | |
| From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01 | |
| A reaction: This quintessentially existentialist idea, most obvious in Sartre, seems to have originated with this view of Hegel's. |
| 8930 | The in-itself must become for-itself, which requires self-consciousness [Hegel] |
| Full Idea: The in-itself has to express itself outwardly and become for itself, and this means simply that it has to posit self-consciousness as one with itself. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 26) | |
| A reaction: This famous distinction seems to be at the core of idealism, but also to be the germ of existentialism (prior to Kierkegaard), which builds on this view of what it means to exist as an individual. Self-consciousness in nature is inevitable? |
| 23275 | The state of nature is one of untamed brutality [Hegel] |
| Full Idea: The 'state of nature' is not an ideal condition, but a condition of injustice, of violence, of untamed natural drives, inhuman acts and emotions. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: He agrees with Hobbes, and disagrees with Rousseau. Hobbes's solution is authoritarian monarchy, but Hegel's solution is the unified and focused state, in which freedom can be realised. |
| 20414 | Hegel's Absolute Spirit is the union of human rational activity at a moment, and whatever that sustains [Hegel, by Eldridge] |
| Full Idea: We may take Hegel's Absolute Spirit to be the union of collective, human rational activity at a historical moment with its proper object, the forms of social and individual life that the rational activity is devoted to understanding and sustaining. | |
| From: report of Georg W.F.Hegel (works [1812]) by Richard Eldridge - G.W.F. Hegel (aesthetics) 1 | |
| A reaction: From this formulation it sounds as if the whole human race might have momentary union, but presumably it is more local 'peoples' that can exhibit this. |
| 22787 | The family is the first basis of the state, but estates are a necessary second [Hegel] |
| Full Idea: While the family is the primary basis of the state, the estates are second. The latter are of special importance, because private persons, despite their selfishness, must have recourse to others. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 201 add) | |
| A reaction: He mentions agriculture as an estate. The implication is that interactions between families requires state institutions, but in simpler societies families can obviously interact and help one another directly. He wants the state to be indispensable. |
| 23276 | The soul of the people is an organisation of its members which produces an essential unity [Hegel] |
| Full Idea: The soul [of the people] exists only insofar as it is an organisation of its members, which - by taking itself together in its simple unity - produce the soul. Thus the people is one individuality in its essence. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: Hegel is seen (e.g. by Charles Taylor) as the ancestor of a rather attractive communitarianism, but I think Popper is more accurate in seeing him as the first stage of modern totalitarianism. The people seen as one individual terrifies me. |
| 22790 | We cannot assert rights which are unnatural [Hegel] |
| Full Idea: No one can assert a right against nature. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 244 add) | |
| A reaction: Although the existence of natural rights is dubious (or nonsense, for Bentham), this is a vague but sensible constraint on what can plausibly be asserted as a right. The rights we create in society must respond to natural needs. |
| 21785 | We are only free, with rights, if we claim our freedom, and there are no natural rights [Hegel, by Houlgate] |
| Full Idea: Hegel says we are only truly free, and so bearers of rights, in so far as we claim our freedom. ...So there are no merely natural rights, and animal's have no rights. | |
| From: report of Georg W.F.Hegel (Lectures on the Philosophy of Right [1819], p.78) by Stephen Houlgate - An Introduction to Hegel 08 'Rights' | |
| A reaction: If there are no natural rights, then it is hard to see how claiming a right will create it. I can't create a right to drink the best champagne. It seems particularly unjust to deny rights to people so enslaved that freedom has never occurred to them. |
| 22767 | I aim to portray the state as a rational entity [Hegel] |
| Full Idea: This treatise is an attempt to comprehend and portray the state as an inherently rational entity. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], Pref) | |
| A reaction: Right now I see very little sign of that being the case. States contain many institutions which are fairly rational, because they focus efficiently on a clear object, but a state can only be rational if there is a wide consensus on its objective. |
| 22789 | Society draws people, and requires their work, making them wholly dependent on it [Hegel] |
| Full Idea: Civil society is the immense power which draws people to itself and requires them to work for it, to owe everything to it, and to do everything by its means. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 238 add) | |
| A reaction: This is the disturbing side of Hegel's quite attractive communitarian thinking. His general picture is of the state prescribing what is required of its citizens, with little scope for citizens to prescribe what they need from the state. See Popper. |
| 22791 | The state is the march of God in the world [Hegel] |
| Full Idea: The state consists of the march of God in the world, and its basis is the power of reason actualising itself as will. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 258) | |
| A reaction: The most notorious sentence in the whole book. See Wiki article on it. The hair-raising aspect of it is that God won't tell us where the state is going, so those in charge will decide that for us. God gives their preferences maximum authority. |
| 3909 | Society isn’t founded on a contract, since contracts presuppose a society [Hegel, by Scruton] |
| Full Idea: For Hegel, society cannot be founded on a contract, since contracts have no reality until society is in place. | |
| From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Modern Philosophy:introduction and survey 28.2 | |
| A reaction: Interesting, and reminiscent of the private language argument, but contracts surely start as deals between individuals (on a desert island?). |
| 22778 | Individuals can't leave the state, because they are natural citizens, and humans require a state [Hegel] |
| Full Idea: The arbitrary will of individuals cannot break away from the state, because the individual is already by nature a citizen of it. It is the rational destiny of humans to live within a state, and if there is no state reason requires it to be established. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 075 add) | |
| A reaction: The Aristotelian view, in opposition to the social contract idea that individuals must choose to have a state. I agree with Hegel, but find his authoritarian tone disturbing. What else will I be told is my 'rational destiny'? We want liberal communiity. |
| 22794 | A fully developed state is conscious and knows what it wills [Hegel] |
| Full Idea: An essential part of the fully developed state is consciousness or thought; the state accordingly knows what it wills and knows this an a object of thought. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 270 add) | |
| A reaction: The silliest idea by a famous philosopher anywhere in this database. I bet the criterion for being fully developed is being conscious, and the criterion for being conscious is being fully developed, whatever that means. General will run riot. |
| 22799 | The people do not have the ability to know the general will [Hegel] |
| Full Idea: To know what one wills, and even more to know what reason wills, is the fruit of profound cognition and insight, and this the very thing which 'the people' lack. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 301) | |
| A reaction: This is obviously directed at Rousseau, and seems to be specifically anti-democratic. Hegel sees the general will as a mystical fact, only knowable to some elite intellectual priesthood. |
| 22801 | The great man of the ages is the one who reveals and accomplishes the will of his time [Hegel] |
| Full Idea: He who expresses the will of his age, tells it what its will is, and accomplishes this will, is the great man of the age. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 318 add) | |
| A reaction: The great man of Hegel's age had obviously been Napoleon, who may have accomplished the will of part of the French people, but went massively against the will of the rest of Europe. For Hegel this seems to be the reality of the General Will. |
| 22796 | A constitution embodies a nation's rights and condition [Hegel] |
| Full Idea: The constitution of a nation must embody the nation's feeling for its rights and present condition. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 274 add) | |
| A reaction: Most constitutions also specify the institutions needed to maintain its principles and values. If it specifies its 'present' condition, that is a licence to change it from time to time. Hegel endorses such flexibility. |
| 22777 | Individuals must dedicate themselves to the ethical whole, and give their lives when asked [Hegel] |
| Full Idea: The individual person is a subordinate entity who must dedicate himself to the ethical whole. Consequently, if the state demands his life, the individual must surrender it. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 070 add) | |
| A reaction: The obvious problem is a war which is perceived to be unjust. Vietnam draft dodgers. We should always consider the common good, but 'dedicate himself to the ethical whole'? It depends whether the ethical whole is dedicated to us. |
| 21791 | Social groups must focus on the state, which must in turn respect their inclusion and their will [Hegel] |
| Full Idea: The interests of family and civil society must concentrate themselves on the state, although the universal end cannot be advanced without the personal knowledge and will of its particular members, whose own rights must be maintained. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 260), quoted by Stephen Houlgate - An Introduction to Hegel 08 'Freedom' | |
| A reaction: Hegel's emphasis on the state has sometimes allowed him to be presented as a proto-fascist, so the second half of this is important - especially the remark about citizens having 'knowledge' of what is going on. Is citizen commitment conditional on this? |
| 22795 | People can achieve respect for their state by insight into its essence [Hegel] |
| Full Idea: The best way for humans to achieve respect for the state as that whole of which they are branches is through philosophical insight into its essence. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 270 add) | |
| A reaction: Although Hegel on the state can be quite alarming, I rather approve of this Aristotelian thought. States do not, of course, have ready made essences awaiting the insights of philosophers, but discussion can converge on a concept of what the state is. |
| 21756 | All revolutions result from spirit changing its categories, to achieve a deeper understanding [Hegel] |
| Full Idea: All revolutions ...originate solely from the fact that spirit, in order to understand and comprehend itself with a view to possessing itself, has changed its categories, comprehending itself more truly, more deeply, more intimately in unity with itself. | |
| From: Georg W.F.Hegel (Philosophy of Nature (Encylopedia II) [1817], §246), quoted by Stephen Houlgate - An Introduction to Hegel 01 | |
| A reaction: Some Hegelian waffle here, but it focuses on what seems important, which is how societal thinking has shifted, so that what was previously tolerated now triggers a revolution. |
| 21988 | In the 1840s Hegel seemed to defend society being right as it is, as a manifestation of Mind [Hegel, by Singer] |
| Full Idea: In the 1840s the orthodox interpretation of Hegel was that since human society is the manifestation of Mind [Geist] in the world, everything is right and rational as it is. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821]) by Peter Singer - Marx 2 | |
| A reaction: This orthodoxy provoked the rebellion of Marx and the Young Hegelians. Modern Communitarians like Hegel, but that view seems to hover between right-wing authoritarianism and left-wing egalitarianism. |
| 22800 | Majority rule means obligations can be imposed on me [Hegel] |
| Full Idea: Majority decisions are at variance with the principle that I should be personally present in anything which imposes an obligation on me. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 309 add) | |
| A reaction: The big democratic problem of my time is sharp binary decisions made by a democracy, such as UK leaving the EU, or Scotland leaving the UK. A very large minority in such cases has their will entirely thwarted, whichever way it goes. |
| 21792 | The state should reflect all interests, and not just popular will, or a popular party [Hegel, by Houlgate] |
| Full Idea: The best guarantee of freedom is for the state to be organised in such a way that the legislature reflects all the substantial interests within civil society, and not just the 'will of the majority', or the parties which happen to find popular support. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 311) by Stephen Houlgate - An Introduction to Hegel 08 'Freedom' | |
| A reaction: In our first-past-the-post system innumerable interests fail to be represented, and parliament is crushed by dull plodders with ossified views who smugly hang on to safe seats. IMHO. |
| 22041 | Representatives by region ignores whether they care about the national interest [Hegel, by Pinkard] |
| Full Idea: Selecting representatives on the basis of geography means selecting people without any regard to whether they represent the basic and important interests of the 'whole' of society. | |
| From: report of Georg W.F.Hegel (Lectures on the Philosophy of Right [1819]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Proportional representation seems to get away from this, but that can still be arranged according to large regions. Some means is needed to prevent the whole nation from exploitation a regional minority (such as Welsh speakers). |
| 22797 | In modern states an individual's actions should be their choice [Hegel] |
| Full Idea: It is inherent in the principle of the modern state that all of an individual's actions should be mediated by his will. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 299 add) | |
| A reaction: This is the liberal side of Hegel's thinking. It is a corrective to his reverential attitude to the state. He criticise Plato for assigning citizens their jobs. |
| 23272 | The human race matters, and individuals have little importance [Hegel] |
| Full Idea: Individuals are of slight importance compared to the mass of the human race. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: A perfect statement of the anti-liberal viewpoint. Hegel is complex, but this is the strand that leads to ridiculous totalitarianism, where the highest ideal is to die for the glory of your nation. Importance can only start from individuals. |
| 22034 | Modern life needs individuality, but must recognise that human agency is social [Hegel, by Pinkard] |
| Full Idea: Hegel argued that the modern world necessarily had to make space for individuals and their inviolable conscience, while not becoming so individualistic that it failed to acknowledge the deep sociality of human agency. ...Subjectivity became a right. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Terry Pinkard - German Philosophy 1760-1860 09 | |
| A reaction: [at the end of the chapter on the history of Geist in the Phenomenology] Conservatives, revolutionaries and communitarians all claim Hegel as their own. The sociality is a matter of mutual law-giving, as in the Master/Slave. |
| 21790 | Moral individuals become ethical when they see the social aspect of a matter [Hegel, by Houlgate] |
| Full Idea: The moral individual becomes an ethical individual when he recognises that his own voice need not always utter the last word on a given matter, but should be understood as participating in ongoing social and political practices. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821]) by Stephen Houlgate - An Introduction to Hegel 08 'Freedom' | |
| A reaction: This is a key idea in Hegel, and is seen (by Charles Taylor etc) as the foundations of modern communitarianism. |
| 8030 | For Hegel, the moral life can only be led within a certain type of community [Hegel, by MacIntyre] |
| Full Idea: Hegel's final standpoint is that the moral life can only be led within a certain type of community. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821]) by Alasdair MacIntyre - A Short History of Ethics Ch.15 | |
| A reaction: This (together with Aristotle) is the basis of modern communitarianism. There is the problem of saintly people who kept their integrity through the Nazi period. I agree with the proposal, in a loose sort of way. |
| 8936 | Human nature only really exists in an achieved community of minds [Hegel] |
| Full Idea: Human nature only really exists in an achieved community of minds. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 69) | |
| A reaction: A lovely slogan, that makes Hegel the father of the communitarian movement. The politics of Hegel can, of course, be sinister, so one must proceed with care, and study history to see where it can all go wrong. |
| 22785 | Even educated women are unsuited to science, philosophy, art and government [Hegel] |
| Full Idea: Women may well be educated, but they are not made for the higher sciences, for philosophy and certain artistic productions which require a universal element. …When women are in charge of government the state is in danger. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 166 add) | |
| A reaction: This makes unpleasant reading. Women have recently played a leading role in creating the Covid vaccines which may well have saved millions of lives. There were plenty of good women novelists around in Hegel's time. |
| 23273 | In a good state the goal of the citizens and of the whole state are united [Hegel] |
| Full Idea: A state is well constituted and internally strong if the private interest of the citizens is united in the universal goal of the state. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: The obvious question is who decides on the goals, and what to do with the citizens who don't accept them. |
| 21789 | Slaves have no duties because they have no rights [Hegel] |
| Full Idea: Slaves have no duties because they have no rights. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 261), quoted by Stephen Houlgate - An Introduction to Hegel 08 'Freedom' | |
| A reaction: Does this correlation go all the way up society? Do I only have duties insofar as I have correlative rights? Monarchs seem to have maximum duties and maximum rights. Democratic leaders seem thereby to get a raw deal. |
| 22776 | Slaves are partly responsible for their own condition [Hegel] |
| Full Idea: If someone is a slave, his own will is responsible. The wrong of slavery is not only the fault of those who enslave people, but of the slaves themselves. …[66 add: The slave has an absolute right to free himself] | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 057 add) | |
| A reaction: He accepts that enslaving people is wrong. Are the slaves at fault for losing their struggle? Would Hegel approve of someone giving modern weapons to the slaves? |
| 21783 | State slavery is a phase of education, moving towards a full culture [Hegel] |
| Full Idea: Because slavery exists in states, it is a phase of advance from the merely isolated sensual existence - a phase of education - a mode of becoming participant in a higher morality and the culture connected with it. | |
| From: Georg W.F.Hegel (The Philosophy of History [1840], p.98), quoted by Stephen Houlgate - An Introduction to Hegel 08 'Rights' | |
| A reaction: [He adds that slavery should be removed slowly, not suddenly] A nicely provocative thought. Is it better to participate in something grand (like pyramid building) as a slave, or drift in dull isolation? How long should this 'phase' last? |
| 21784 | Slavery is unjust, because humanity is essentially free [Hegel] |
| Full Idea: Slavery is in and for itself an injustice, for the essence of humanity is freedom. | |
| From: Georg W.F.Hegel (The Philosophy of History [1840], p.99), quoted by Stephen Houlgate - An Introduction to Hegel 08 'Rights' | |
| A reaction: This is a corrective to Idea 12783, which offers a defence of the reality of historical slavery. That seemed to depend on some notion that each phase of history is necessary, which is implausible. |
| 21778 | True liberal freedom is to pursue something, while being free to cease the pursuit [Hegel, by Houlgate] |
| Full Idea: The third moment of liberal freedom for Hegel is the unity of the first two - the freedom to engage in some specific pursuit, but in so doing to preserve the sense that one is not irrevocably committed to that pursuit. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 005) by Stephen Houlgate - An Introduction to Hegel 08 'The Limits' | |
| A reaction: Not too surprising, but Hegel is interesting for thinking that we shouldn't just rabbit on about having 'freedom', but should investigate more closely what this is exactly supposed to mean. |
| 21779 | People assume they are free, but the options available are not under their control [Hegel] |
| Full Idea: The ordinary man believes himself to be free ...to act as he wants, but this arbitrariness entails that he is not free, because what it is that he wills is not intrinsic to self-determining activity, ...and depends on a given content and material. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 015), quoted by Stephen Houlgate - An Introduction to Hegel 08 'The Limits' | |
| A reaction: [a bit compressed] I take this to be an extraordinarily influential idea (especially for Marx). Hitherto philosophers just wanted some vague metaphysical 'free will', making moral responsibility and pure reason possible. But who controls the options? |
| 23271 | The goal of the world is Spirit's consciousness and enactment of freedom [Hegel] |
| Full Idea: The final goal of the world is Spirit's consciousness of its freedom, and hence also the actualisation of that very freedom. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: I have the impression that this ridiculous idea has been very influential in modern French philosophy, since they all seem to be dreaming of some perfect freedom at the end of the rainbow. Freedom is good, but this gives it a bad name. |
| 22085 | Freedom requires us to submit to a family, or a corporation, or a state [Hegel, by Houlgate] |
| Full Idea: Hegel thinks that political and social freedom involves letting one's actions be guided by those institutional structures (such as the family, corporations and the state) which secure rights, welfare, and mutual respect. | |
| From: report of Georg W.F.Hegel (Elements of the Philosophy of Right [1821]) by Stephen Houlgate - Hegel 102 | |
| A reaction: Since there are some hideous families, corporations and states, we will need more than that. He may have a point, though, that the rights we desire can only exist in healthy examples of such institutions. Popper loved institutions. |
| 22798 | Money is the best way to achieve just equality [Hegel] |
| Full Idea: The justice of equality can be achieved most effectively by money. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 299) | |
| A reaction: There are also important equalities such as access to education and to superior jobs. Money is more tangible, but you can fob poor people off with quite small sums of money. |
| 22783 | Rights imply duties, and duties imply rights [Hegel] |
| Full Idea: A human being has rights in so far as he has duties, and duties in so far as he has rights. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 155) | |
| A reaction: I would express this as 'why we should we be loyal to the state if the state is not loyal to us'. The state must not only provide us with nominal rights, but must also enforce them. Without that the citizens are alienated, and the sense of duty fades. |
| 21781 | The absolute right is the right to have rights [Hegel] |
| Full Idea: The absolute right is the right to have rights. | |
| From: Georg W.F.Hegel (Lectures on the Philosophy of Right [1819], p.127), quoted by Stephen Houlgate - An Introduction to Hegel 08 'Rights' | |
| A reaction: What a beautifully succinct and important idea! Does a foetus, or a dog, or a person in a vegetative state, or a slave, qualify? |
| 21782 | Man has an absolute right to appropriate things [Hegel] |
| Full Idea: A person has as his substantive end the right of putting his will into any and every thing and thereby making it his ...This is the absolute right of appropriation which man has over all things. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 044), quoted by Stephen Houlgate - An Introduction to Hegel 08 'Rights' | |
| A reaction: Houlgate shows this is not a defence of theft. Hegel thinks the right to property stems from our freedom, not from our natural needs. Did Hegel know Locke? It is not obvious that if I pocket a stone I thereby 'own' it. Do birds own their nests? |
| 22773 | Because only human beings can own property, everything else can become our property [Hegel] |
| Full Idea: All things can become the property of human beings, because the human being is free will, and exists in and for himself, whereas that which confronts him does not have this quality. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 044 add) | |
| A reaction: Note that the human 'is' free will, rather than 'has' free will. He explicitly includes animals. From a modern ecological view this is a sinister idea. The default position is that if you own something you can do whatever you like with it. |
| 22774 | A community does not have the property-owning rights that a person has [Hegel] |
| Full Idea: Many states have rightly dissolved the monasteries, because a community does not ultimately have the same right to property as a person does. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 046) | |
| A reaction: Trinity College, Cambridge, owns vast amounts of land. A lot of property seems to be owned by legal trusts. Hegel sees the basis of property ownership in a person's will. He allows some exceptions. |
| 22775 | The owner of a thing is obviously the first person to freely take possession of it [Hegel] |
| Full Idea: That a thing belongs to a person who happens to be the first to take possession of it is immediately self-evident. …This is not because he is the first, but because he is a free will. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 050) | |
| A reaction: At this time they were very conscious of the native Americans. They seem to have lost their lands because they had no institution of private property, and had not asserted their ownership. I suspect Hegel of endorsing this. |
| 22802 | Wars add strength to a nation, and cure internal dissension [Hegel] |
| Full Idea: Not only do peoples emerge from wars with added strength, but nations troubled by civil dissension gain internal peace as a result of wars with their external enemies. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 324 add) | |
| A reaction: I suspect that Hegel quite likes wars because they accelerate the development of history. I don't think he would have written nonsense like this after WW1 and WW2. Leaders facing internal dissent like small external wars. |
| 22786 | Children need discipline, to break their self-will and eradicate sensuousness [Hegel] |
| Full Idea: One of the chief moments in a child's upbringing is discipline, the purpose of which is to break the child's self-will in order to eradicate the merely sensuous and natural. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 174 add) | |
| A reaction: A standard view for his time, no doubt. No sensible parent doubts that children need to be civilised, and taught to recognise the needs of others. I hope the general aspiration in our society to 'break' a child's self-will has now faded away. |
| 8619 | To learn something, you must know that you don't know [Frege] |
| Full Idea: The first prerequisite for knowing anything is the knowledge that we do not know. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro) | |
| A reaction: This is serious practical advice for teachers. Intelligent people are aware of most philosophical problems, but tongue-tied when asked to discuss them. |
| 21987 | History is the progress of the consciousness of freedom [Hegel] |
| Full Idea: The History of the World is none other than than the progress of the consciousness of freedom. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807]), quoted by Peter Singer - Marx 2 | |
| A reaction: [no ref given] Presumably there is an evolutionary view implicit in this. Presumably also later generations are hereby superior to previous generations. Since no one still has this view of history, does that invalidate Hegel? |
| 23270 | We should all agree that there is reason in history [Hegel] |
| Full Idea: We ought to have the firm and unconquerable belief that there is reason in history. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 2) | |
| A reaction: This is a ridiculous but hugely influential idea, and I have no idea what makes Hegel believe it. It is the Stoic idea that nature is intrinsically rational, but extending it to human history is absurd. Human exceptionalism. Needs a dose of Darwin. |
| 4347 | When man wills the natural, it is no longer natural [Hegel] |
| Full Idea: When man wills the natural, it is no longer natural. | |
| From: Georg W.F.Hegel (works [1812]), quoted by Rosalind Hursthouse - On Virtue Ethics Ch.4 | |
| A reaction: Sounds good, though I'm not sure what it means. The application of the word 'natural' seems a bit arbitrary to me. No objective joint exists between the natural and unnatural. The default position has to be that everything is natural. |
| 15614 | Old metaphysics tried to grasp eternal truths through causal events, which is impossible [Hegel] |
| Full Idea: When finite things are grasped according to the determinations of cause and effect they are known in their finitude. But objects of reason cannot be determined through such finite predicates, and the attempt to do this was the defect of older metaphysics. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §28 Add) | |
| A reaction: This sounds the launching point for a grand philosophical system which makes scientifically inclined philosophers feel very nervous indeed. I think I prefer the old (pre-Kantian) metaphysics. |
| 8656 | The laws of number are not laws of nature, but are laws of the laws of nature [Frege] |
| Full Idea: The laws of number are not applicable to external things, and are not laws of nature, but they are applicable to judgements of external things: they are laws of the laws of nature. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §87) | |
| A reaction: We seem to be somewhere between pythagoreanism and 'the mind of God'. I feel fairly strongly that we are looking through the wrong end of the telescope here. The laws of nature 'emerge' from nature, and high-level abstractions emerge with them. |
| 8931 | The movement of pure essences constitutes the nature of scientific method [Hegel] |
| Full Idea: The movement of pure essences constitutes the nature of scientific method in general. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 34) | |
| A reaction: This would appear to be precisely the idea of scientific essentialism - if he is saying that science seeks to understand the movement (or power) of essences as they occur in nature. |
| 8933 | Science confronts the inner necessities of objects [Hegel] |
| Full Idea: Scientific cognition demands surrender to the life of the object, or, what amounts to the same thing, confronting and expressing its inner necessity. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 53) | |
| A reaction: This strikes me as being a much better account of what science tries to do than all the modern talk about laws and theories. |
| 15635 | The older conception of God was emptied of human features, to make it worthy of the Infinite [Hegel] |
| Full Idea: In earlier times, every type of so-called anthropomorphic representation was banished from God as finite, and hence unworthy of the Infinite; and as a result he had already grown into something remarkably empty. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §62 Rem) | |
| A reaction: Hegel favoured Christianity, because of its human aspect. His description fits Islam, where indeed the concept of God seems so drain of particularity that there is little in it to doubt, which might explain the durability of that religion. |
| 21980 | God is the absolute thing, and also the absolute person [Hegel] |
| Full Idea: It is true that God ...is the absolute thing: he is however no less the absolute person. That he is the absolute person however is a point which the philosophy of Spinoza never reached. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], I §151Z p.214), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.6 | |
| A reaction: Moore says Hegel was a Spinozist, in his commitment to a single substance, but his idea of God is very different, presumably because consciousness and concepts are so important to Hegel. Hegel needs a Lockean abstract notion of 'person' here. |
| 15618 | If God is the abstract of Supremely Real Essence, then God is a mere Beyond, and unknowable [Hegel] |
| Full Idea: When the concept of God is apprehended merely as that of the abstract of Supremely Real Essence, then God becomes for us a mere Beyond, and there can be no further talk of the cognition of God. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §36 Add) |
| 21775 | The God of revealed religion can only be understood through pure speculative knowledge [Hegel] |
| Full Idea: God is attainable in pure speculative knowledge alone and is only in that knowledge, and is only that knowledge itself, for He is Spirit; and this speculative knowledge is the knowledge of revealed religion. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], p.461), quoted by Stephen Houlgate - An Introduction to Hegel 04 'Absolute' | |
| A reaction: If you were hoping to find out why Hegel believed in God, I fear this is the best evidence available. He is evidently opposed to natural theology. Hegel's language makes it very hard to grasp how we sees the nature of God. |
| 15633 | We establish unification of the Ideal by the ontological proof, deriving being from abstraction of thinking [Hegel] |
| Full Idea: One unification through which the Ideal is to be established starts from the abstraction of thinking and goes on to the determination for which being alone remains; this is the ontological proof that God is there. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §51) | |
| A reaction: It should come as no surprise that a philosopher who so passionately endorses pure thinking, in opposition to empiricism, should end up endorsing the highly implausible ontological argument for God's existence. Jacquette gets existence from reason. |
| 3307 | Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA] |
| Full Idea: Frege put forward an ontological argument for the existence of numbers. | |
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.4 |
| 4188 | Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof [Schopenhauer on Hegel] |
| Full Idea: Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof. | |
| From: comment on Georg W.F.Hegel (works [1812]) by Arthur Schopenhauer - Abstract of 'The Fourfold Root' Ch.II | |
| A reaction: All massive a priori metaphysics is summed up in this argument, which is right at the core of philosophy. |
| 7741 | The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner] |
| Full Idea: On Frege's logical analysis, the predicate 'exists' is actually a natural language expression for a quantifier. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege Ch.8 | |
| A reaction: However see Idea 6067, for McGinn's alternative view of quantifiers. In the normal conventions of predicate logic it may be that existence is treated as a quantifier, but that is not the same as saying that existence just IS a quantifier. |
| 22286 | Existence is not a first-level concept (of God), but a second-level property of concepts [Frege, by Potter] |
| Full Idea: For Frege (unlike Kant) existence is a genuine concept, but of the second level, not the first. Since God's perfections are of the first level, existence is not a candidate to be one of them. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §053) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 09 'App' | |
| A reaction: That is, God's perfections are of God, but existence is a concept of concepts (that they are instantiated). So existence is a metaconcept. I'm not convinced. If I bake a successful cake, its existence is its most wonderful feature. |
| 8644 | Because existence is a property of concepts the ontological argument for God fails [Frege] |
| Full Idea: Because existence is a property of concepts the ontological argument for the existence of God breaks down. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §53) | |
| A reaction: The point being that existence (like number) is not a property of actual things. His proposition sounds rather dubious. The concept of unicorns exists quite entertainingly; it is the failure of actual unicorns to exist that is so heartbreaking. |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
| Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept. | |
| From: Gottlob Frege (Function and Concept [1891], p.38 n) | |
| A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate. |
| 6917 | God is the essence of thought, abstracted from the thinker [Hegel, by Feuerbach] |
| Full Idea: In Hegel the essence of God is actually nothing other than the essence of thought, or thought abstracted from the ego, that is, from the one who thinks. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Ludwig Feuerbach - Principles of Philosophy of the Future §23 | |
| A reaction: Presumably Descartes' Cogito is the origin for this train of thought. This is Feuerbach's reading of Hegel, but the former was keen on the idea of God as idealised humanity. |
| 6915 | Hegel made the last attempt to restore Christianity, which philosophy had destroyed [Hegel, by Feuerbach] |
| Full Idea: The Hegelian philosophy is the last magnificent attempt to restore Christianity, which was lost and wrecked, through philosophy, and to restore Christianity (as usual in the modern era) by identifying it with the negation of Christianity. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Ludwig Feuerbach - Principles of Philosophy of the Future §21 | |
| A reaction: What is meant by the 'negation' of Christianity needs some untangling, but I suspect that a lot of 'continental' philosophy 1750-1950 is to do with Christianity, unlike British empiricism, which is intrinsically atheistic. |
| 6686 | Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham] |
| Full Idea: Hegel claimed that his philosophy was nothing less than an encyclopaedic rationalisation of the Christian religion. | |
| From: report of Georg W.F.Hegel (works [1812]) by Gordon Graham - Eight Theories of Ethics Ch.5 | |
| A reaction: Why did he pick Christianity to rationalise? How can you reason properly if you start with a dogma? |
| 21798 | To universalise 'give everything to the poor' leads to absurdity [Hegel] |
| Full Idea: If everyone gave everything to the poor, then soon there would be no more poor to give anything to, or no more persons who would have anything to give. | |
| From: Georg W.F.Hegel (Lectures on the Philosophy of Religion [1827], III: 152), quoted by Stephen Houlgate - An Introduction to Hegel 10 'Faith' | |
| A reaction: Matthew 5:8, 19:21. Beautifully clear. [I always believed that I had thought of this idea - but not so]. If the logic is that it is better to be poor than to be rich, then the implication is that all excess wealth should be thrown into the sea. |
| 22782 | To have pagan beliefs and be a pagan are quite different [Hegel] |
| Full Idea: To believe in pagan religion and to be a pagan are two different things. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 147) | |
| A reaction: A nice general truth about all religions, and one not often understood by atheists. |
| 22793 | Some religions lead to harsh servitude and the debasement of human beings [Hegel] |
| Full Idea: It should not be a forgotten that can take on a from which leads to the harshest servitude within the fetters of superstition, and to the debasement of human beings to a level below that of animals. | |
| From: Georg W.F.Hegel (Elements of the Philosophy of Right [1821], 270) | |
| A reaction: Hegel was a Christian, though a very unorthodox one. He cities ancient Egypt and India as examples. If you want to assess a religion, see how it behaves when it has political power. |
| 21797 | Immortality does not come at a later time, but when pure knowing Spirit fully grasps the universal [Hegel] |
| Full Idea: The immortality of the soul must not be imagined as though it first emerges into actuality at some later time; rather it is a present quality. ...As pure knowing or as thinking, Spirit has the universal for its object - this is eternity. | |
| From: Georg W.F.Hegel (Lectures on the Philosophy of Religion [1827], III: 208), quoted by Stephen Houlgate - An Introduction to Hegel 10 'Death' | |
| A reaction: An unusual view of immortality, which challenges orthodoxy. The idea seems to be that 'pure knowing' is a grasping of the pure reason which embodies nature, which in turn is the nature of God. You enter eternity, rather than reside in it? |