48 ideas
| 6928 | Only that which can be an object of religion is an object of philosophy [Feuerbach] |
| Full Idea: Only that which can be an object of religion is an object of philosophy. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §35) | |
| A reaction: The temple of Pythagoras at Solon sounds like an embodiment of this idea. The obvious candidate would be truth, to which philosophers must show almost religious respect. Some what motivates the philosophy of a minimalist (Idea 3750)? |
| 6918 | Philosophy should not focus on names, but on the determined nature of things [Feuerbach] |
| Full Idea: Philosophy need not care about the conceptions that common usage or misuse attaches to a name; philosophy, however, has to bind itself to the determined nature of things, whose signs are names. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §23) | |
| A reaction: I like this attempt to nip ordinary language philosophy in the bud. Indeed I like the notion of philosophy binding itself to the 'determined nature of things' (which sound like essences to me), rather than to their names or descriptions. |
| 6904 | Modern philosophy begins with Descartes' abstraction from sensation and matter [Feuerbach] |
| Full Idea: The beginning of Descartes' philosophy, namely, the abstraction from sensation and matter, is the beginning of modern speculative philosophy. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §10) | |
| A reaction: In Britain it might be said that modern philosophy begins with a rebellion against Descartes' move. Feuerbach is charting the movement towards idealism. |
| 6931 | Empiricism is right about ideas, but forgets man himself as one of our objects [Feuerbach] |
| Full Idea: Empiricism rightly derives the origin of our ideas from the senses; only it forgets that the most important and essential object of man is man himself. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §41) | |
| A reaction: This seems to nicely pinpoint the objection of most 'continental' philosophy to British empiricism and analytic philosophy. It seems to point towards Husserl's phenomenology as the next step. It is true that empiricists divided person from world. |
| 6933 | The laws of reality are also the laws of thought [Feuerbach] |
| Full Idea: The laws of reality are also the laws of thought. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §45) | |
| A reaction: I like this a lot, though it runs contrary to a lot of conventionalist thinking in the twentieth century. Russell, though, agrees with Feuerbach (Idea 5405). There is not much point to thought if it doesn't plug into reality at the roots. |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv' |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7 | |
| A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is! |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb' | |
| A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective. |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1 | |
| A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology. |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too. |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5 |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661. |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243 | |
| A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial. |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII | |
| A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind. |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'. |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest? |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| Full Idea: A system S is said to be infinite when it is similar to a proper part of itself. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64) |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5 | |
| A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'. |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers. | |
| From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1 | |
| A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation. |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241 |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered | |
| A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects. |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6 | |
| A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis. |
| 6919 | Absolute thought remains in another world from being [Feuerbach] |
| Full Idea: Absolute thought never extricates itself from itself to become being. Being remains in another world. …If being is to be added to an object of thought, so must something distinct from thought be added to thought itself. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §24/5) | |
| A reaction: This sounds a bit like a child wishing for the moon. Is he saying he doesn't just want to think about reality - he wants his mental states to BE external reality? The distinction between a thought and its content or intentionality would help here. |
| 19457 | Being is what is undetermined, and hence indistinguishable [Feuerbach] |
| Full Idea: Being in the sense in which it is an object of speculative thought is that which is purely and simply unmediated, that is, undetermined; in other words, there is nothing to distinguish and nothing to think of in being. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], 26) | |
| A reaction: This sounds remarkably like the idea of 'prime matter' used in scholastic Aristotelian philosophy. Matter existing without form is somehow ungraspable, but presented from Hegel onwards as the ultimate mystery. |
| 6920 | Being posits essence, and my essence is my being [Feuerbach] |
| Full Idea: Being is the positing of essence. That which is my essence is my being. The fish exists in water; you cannot, however, separate its essence from this being. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §27) | |
| A reaction: This throws a different light on later (e.g. Heidegger) discussions of 'being', which may map onto Aristotelian discussions of essences. |
| 6921 | Particularity belongs to being, whereas generality belongs to thought [Feuerbach] |
| Full Idea: Particularity and individuality belong to being, whereas generality belongs to thought. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §29) | |
| A reaction: This agrees with Russell's view that every sentence (and proposition) must contain a universal (i.e a generality). The very notion of thinking 'about' a horse seems to require a move to the universal concept of a horse. |
| 6926 | The only true being is of the senses, perception, feeling and love [Feuerbach] |
| Full Idea: Being as an object of being - and only this being is being and deserves the name of being - is the being of the senses, perception, feeling, and love. …Only passion is the hallmark of existence. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §33) | |
| A reaction: This remark seems to make Feuerbach a romantic and anti-Enlightenment figure. I don't see why there shouldn't be just as much 'being' in doing maths as in admiring a landscape. The mention of love links him to Empedocles (Ideas 459 + 630). |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1) | |
| A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology. |
| 6908 | Consciousness is absolute reality, and everything exists through consciousness [Feuerbach] |
| Full Idea: Consciousness is the absolute reality, the measure of all existence; all that exists, exists only as being for consciousness, as comprehended in consciousness; for consciousness is first and foremost being. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §17) | |
| A reaction: This is Feuerbach declaring himself in favour of idealism even as he was trying to rebel against it, and move towards a more sensuous and human view of the world. I just see idealists as confusing ontology and epistemology. |
| 6932 | Ideas arise through communication, and reason is reached through community [Feuerbach] |
| Full Idea: Only through communication and conversation between man and man do ideas arise; not alone, but only with others, does one reach notions and reason in general. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §41) | |
| A reaction: This is a strikingly modern view of the solipsism problem, and is close in spirit to Wittgenstein's Private Language Argument (Ideas 4143 +4158). Feuerbach is interested in universals rather than rules. I prefer Feuerbach. |
| 6935 | In man the lowest senses of smell and taste elevate themselves to intellectual acts [Feuerbach] |
| Full Idea: Even the lowest senses, smell and taste, elevate themselves in man to intellectual and scientific acts. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §53) | |
| A reaction: Since Darwin we have, I am glad to say, lost this need to distinguish what is 'low' or 'high', and to try to show that even our 'lowest' functions are on the 'high' side. Personally, though, I still need the low/high distinction in moral thinking. |
| 6925 | The new philosophy thinks of the concrete in a concrete (not a abstract) manner [Feuerbach] |
| Full Idea: The new philosophy is the philosophy that thinks of the concrete not in an abstract, but in a concrete manner. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §31) | |
| A reaction: This leads to placing a high value on art, and on virtuous action through particulars rather than principles, and on empirical science. The only problem is that what he proposes is impossible. To think 'about' is to abstract from the particulars. |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics | |
| A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven? |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73) | |
| A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective. |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV | |
| A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic. |
| 6924 | Plotinus was ashamed to have a body [Feuerbach] |
| Full Idea: Plotinus, according to his biographers, was ashamed to have a body. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §29) | |
| A reaction: When Feuerbach draws our attention to this, we see what an astonishing state it is for a human being to have got into. Modern thought is appalled by it, but it also has something heroic about it, like swimming all the time because you want to be a fish. |
| 6927 | If you love nothing, it doesn't matter whether something exists or not [Feuerbach] |
| Full Idea: To him who loves nothing it is all the same whether something does or does not exist. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §33) | |
| A reaction: This seems to me to be quite a good motto for the aim of education - just get them to love something, no matter what (well, almost!). Loving something, even if it is train-spotting, seems a good route to human happiness. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 6934 | Man is not a particular being, like animals, but a universal being [Feuerbach] |
| Full Idea: Man is not a particular being, like the animals, but a universal being. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §53) | |
| A reaction: This sounds a bit extravagent. The capacity of man to use universals in thought seems crucial to Feuerbach (though he doesn't directly address the problem). 'We are particulars with access to universals' sounds better. |
| 6936 | The essence of man is in community, but with distinct individuals [Feuerbach] |
| Full Idea: The essence of man is contained only in the community and unity of man and man; it is a unity, however, which rests only on the reality of the distinction between I and thou. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §59) | |
| A reaction: In English provincial suburbs (where I live) it is astonishing how little interest in and need for their neighbours people seem to have. People seem to survive without community. Most of us, though, think full human happiness needs community. |
| 6913 | God's existence cannot be separated from essence and concept, which can only be thought as existing [Feuerbach] |
| Full Idea: God is the being in which existence cannot be separated from essence and concept and which cannot be thought except as existing. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §18) | |
| A reaction: This shows how faith in God endured through the Idealist movement by means of the Ontological Argument, despite the criticisms of Hume and Kant. To me this now appears as an odd abberation in the history of human thought. |
| 6903 | If God is only an object for man, then only the essence of man is revealed in God [Feuerbach] |
| Full Idea: If God is only an object of man, what is revealed to us in his essence? Nothing but the essence of man. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §07) | |
| A reaction: It is important to distinguish here between what we could know about God, and what we think God might actually be like. We may well only be able to read the essence of man into God, but we might speculate that God is more than that. |
| 6923 | God is what man would like to be [Feuerbach] |
| Full Idea: God is what man would like to be. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §29) | |
| A reaction: It is hard to see how even the most devout person could deny the truth of this. Perhaps the essential hallmark of humanity is a desire to be different from the way we are. |
| 6911 | God is for us a mere empty idea, which we fill with our own ego and essence [Feuerbach] |
| Full Idea: God exists, but he is for us a tabula rasa, an empty being, a mere idea; God, as we conceive and think of him, is our ego, our mind, and our essence. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §17) | |
| A reaction: He accepted God's existence because of the Ontological Argument. This is a little stronger than Hume's view (Idea 2185), because Hume seems to be talking about imagining God, but Feuerbach says this is our understanding of God. |
| 6902 | Catholicism concerns God in himself, Protestantism what God is for man [Feuerbach] |
| Full Idea: Protestantism is no longer concerned, as Catholicism is, about what God is in himself, but about what he is for man. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §02) | |
| A reaction: It is certainly true that the major religions in their origins seem to be almost exclusively concerned with God alone, and have little interest in human life (or morality). |
| 6905 | Absolute idealism is the realized divine mind of Leibnizian theism [Feuerbach] |
| Full Idea: Absolute idealism is nothing but the realized divine mind of Leibnizian theism. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §10) | |
| A reaction: In general it seems an accurate commentary that during the eighteenth century philosophers on the continent were designing a religion without God. Kantian duty tries to replace the authority of God with pure reason. |