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All the ideas for 'works', 'Regressive Method for Premises in Mathematics' and 'The Essence of Reference'

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43 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb]
     Full Idea: Aristotle takes wisdom to come in two forms, the practical and the theoretical, the former of which is good judgement about how to act, and the latter of which is deep knowledge or understanding.
     From: report of Aristotle (works [c.330 BCE]) by Dennis Whitcomb - Wisdom Intro
     A reaction: The interesting question is then whether the two are connected. One might be thoroughly 'sensible' about action, without counting as 'wise', which seems to require a broader view of what is being done. Whitcomb endorses Aristotle on this idea.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell]
     Full Idea: Any new discovery as to mathematical method and principles is likely to upset a great deal of otherwise plausible philosophising, as well as to suggest a new philosophy which will be solid in proportion as its foundations in mathematics are securely laid.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.283)
     A reaction: This is a manifesto for modern analytic philosophy. I'm not convinced, especially if a fictionalist view of maths is plausible. What Russell wants is rigour, but there are other ways of getting that. Currently I favour artificial intelligence.
2. Reason / A. Nature of Reason / 2. Logos
For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle]
     Full Idea: For Aristotle logos is the ability to speak rationally about, with the hope of attaining knowledge, questions of value.
     From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.26
2. Reason / A. Nature of Reason / 4. Aims of Reason
Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle]
     Full Idea: Aristotle is the great theoretician who articulates a vision of a world in which natural and stable structures can be rationally discovered. His is the most optimistic and richest view of the possibilities of logos
     From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.95
2. Reason / A. Nature of Reason / 6. Coherence
If one proposition is deduced from another, they are more certain together than alone [Russell]
     Full Idea: Two obvious propositions of which one can be deduced from the other both become more certain than either in isolation; thus in a complicated deductive system, many parts of which are obvious, the total probability may become all but absolute certainty.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279)
     A reaction: Thagard picked this remark out, in support of his work on coherence.
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Non-contradiction was learned from instances, and then found to be indubitable [Russell]
     Full Idea: The law of contradiction must have been originally discovered by generalising from instances, though, once discovered, it was found to be quite as indubitable as the instances.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274)
2. Reason / D. Definition / 4. Real Definition
Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine]
     Full Idea: A real definition, according to the Aristotelian tradition, gives the essence of the kind of thing defined. Man is defined as a rational animal, and thus rationality and animality are of the essence of each of us.
     From: report of Aristotle (works [c.330 BCE]) by Willard Quine - Vagaries of Definition p.51
     A reaction: Compare Idea 4385. Personally I prefer the Aristotelian approach, but we may have to say 'We cannot identify the essence of x, and so x cannot be defined'. Compare 'his mood was hard to define' with 'his mood was hostile'.
2. Reason / D. Definition / 5. Genus and Differentia
Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson]
     Full Idea: For Aristotle, to give a definition one must first state the genus and then the differentia of the kind of thing to be defined.
     From: report of Aristotle (works [c.330 BCE]) by J.O. Urmson - Aristotle's Doctrine of the Mean p.157
     A reaction: Presumably a modern definition would just be a list of properties, but Aristotle seeks the substance. How does he define a genus? - by placing it in a further genus?
4. Formal Logic / G. Formal Mereology / 1. Mereology
Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki]
     Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity.
     From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12
     A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit.
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
     Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality.
     From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4
     A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional.
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
It is best to say that a name designates iff there is something for it to designate [Sainsbury]
     Full Idea: It is better to say that 'For all x ("Hesperus" stands for x iff x = Hesperus)', than to say '"Hesperus" stands for Hesperus', since then the expression can be a name with no bearer (e.g. "Vulcan").
     From: Mark Sainsbury (The Essence of Reference [2006], 18.2)
     A reaction: In cases where it is unclear whether the name actually designates something, it seems desirable that the name is at least allowed to function semantically.
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury]
     Full Idea: Almost everyone agrees that intelligible definite descriptions may lack a referent; this has historically been a reason for not counting them among referring expressions.
     From: Mark Sainsbury (The Essence of Reference [2006], 18.2)
     A reaction: One might compare indexicals such as 'I', which may be incapable of failing to refer when spoken. However 'look at that!' frequently fails to communicate reference.
Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury]
     Full Idea: Definite descriptions used with referential intentions (usually in subject position) are normally rigid, ..but in predicate position they are normally not rigid, because there is no referential intention.
     From: Mark Sainsbury (The Essence of Reference [2006], 18.5)
     A reaction: 'The man in the blue suit is the President' seems to fit, but 'The President is the head of state' doesn't. Seems roughly right, but language is always too complex for philosophers.
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Which premises are ultimate varies with context [Russell]
     Full Idea: Premises which are ultimate in one investigation may cease to be so in another.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273)
The sources of a proof are the reasons why we believe its conclusion [Russell]
     Full Idea: In mathematics, except in the earliest parts, the propositions from which a given proposition is deduced generally give the reason why we believe the given proposition.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273)
Finding the axioms may be the only route to some new results [Russell]
     Full Idea: The premises [of a science] ...are pretty certain to lead to a number of new results which could not otherwise have been known.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.282)
     A reaction: I identify this as the 'fruitfulness' that results when the essence of something is discovered.
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
     Full Idea: It is an apparent absurdity in proceeding ...through many rather recondite propositions of symbolic logic, to the 'proof' of such truisms as 2+2=4: for it is plain that the conclusion is more certain than the premises, and the supposed proof seems futile.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272)
     A reaction: Famously, 'Principia Mathematica' proved this fact at enormous length. I wonder if this thought led Moore to his common sense view of his own hand - the conclusion being better than the sceptical arguments?
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Arithmetic was probably inferred from relationships between physical objects [Russell]
     Full Idea: When 2 + 2 =4 was first discovered, it was probably inferred from the case of sheep and other concrete cases.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272)
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki]
     Full Idea: Aristotle's discussion of the unmoved mover and of the soul confirms the suspicion that form, when it is not thought of as the object represented in a definition, plays the role of the ultimate mereological atom within his system.
     From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 6.6
     A reaction: Aristotle is concerned with which things are 'divisible', and he cites these two examples as indivisible, but they may be too unusual to offer an actual theory of how Aristotle builds up wholes from atoms. He denies atoms in matter.
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki]
     Full Idea: Thus in Aristotle we may think of an object's formal components as a sort of recipe for how to build wholes of that particular kind.
     From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.5
     A reaction: In the elusive business of pinning down what Aristotle means by the crucial idea of 'form', this analogy strikes me as being quite illuminating. It would fit DNA in living things, and the design of an artifact.
11. Knowledge Aims / A. Knowledge / 1. Knowledge
For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code]
     Full Idea: Aristotle thinks that in general we have knowledge or understanding when we grasp causes, and he distinguishes three fundamental types of knowledge - theoretical, practical and productive.
     From: report of Aristotle (works [c.330 BCE]) by Alan D. Code - Aristotle
     A reaction: Productive knowledge we tend to label as 'knowing how'. The centrality of causes for knowledge would get Aristotle nowadays labelled as a 'naturalist'. It is hard to disagree with his three types, though they may overlap.
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
     Full Idea: Even where there is the highest degree of obviousness, we cannot assume that we are infallible - a sufficient conflict with other obvious propositions may lead us to abandon our belief, as in the case of a hallucination afterwards recognised as such.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279)
     A reaction: This approach to fallibilism seems to arise from the paradox that undermined Frege's rather obvious looking axioms. After Peirce and Russell, fallibilism has become a secure norm of modern thought.
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
The notion of a priori truth is absent in Aristotle [Aristotle, by Politis]
     Full Idea: The notion of a priori truth is conspicuously absent in Aristotle.
     From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5
     A reaction: Cf. Idea 11240.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M]
     Full Idea: Aristotle is a rationalist …but reason for him is a disposition which we only acquire over time. Its acquisition is made possible primarily by perception and experience.
     From: report of Aristotle (works [c.330 BCE]) by Michael Frede - Aristotle's Rationalism p.173
     A reaction: I would describe this process as the gradual acquisition of the skill of objectivity, which needs the right knowledge and concepts to evaluate new experiences.
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML]
     Full Idea: Since Aristotle generally prefers a metaphysical theory that accords with common intuitions, he frequently relies on facts about language to guide his metaphysical claims.
     From: report of Aristotle (works [c.330 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.5
     A reaction: I approve of his procedure. I take intuition to be largely rational justifications too complex for us to enunciate fully, and language embodies folk intuitions in its concepts (especially if the concepts occur in many languages).
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Believing a whole science is more than believing each of its propositions [Russell]
     Full Idea: Although intrinsic obviousness is the basis of every science, it is never, in a fairly advanced science, the whole of our reason for believing any one proposition of the science.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279)
14. Science / B. Scientific Theories / 1. Scientific Theory
Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik]
     Full Idea: Plato's unity of science principle states that all - legitimate - sciences are ultimately about the Forms. Aristotle's principle states that all sciences must be, ultimately, about substances, or aspects of substances.
     From: report of Aristotle (works [c.330 BCE], 1) by Julius Moravcsik - Aristotle on Adequate Explanations 1
14. Science / C. Induction / 2. Aims of Induction
Induction is inferring premises from consequences [Russell]
     Full Idea: The inferring of premises from consequences is the essence of induction.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274)
     A reaction: So induction is just deduction in reverse? Induction is transcendental deduction? Do I deduce the premises from observing a lot of white swans? Hm.
14. Science / D. Explanation / 1. Explanation / a. Explanation
Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis]
     Full Idea: For Aristotle things which explain (the explanantia) are facts, which should not be associated with the modern view that says explanations are dependent on how we conceive and describe the world (where causes are independent of us).
     From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 2.1
     A reaction: There must be some room in modern thought for the Aristotelian view, if some sort of robust scientific realism is being maintained against the highly linguistic view of philosophy found in the twentieth century.
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA]
     Full Idea: The standard Aristotelian doctrine of species and genus in the theory of anything whatever involves specifying what the thing is in terms of something more general.
     From: report of Aristotle (works [c.330 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.10
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung]
     Full Idea: The view that essential properties are those in virtue of which other significant properties of the subjects under investigation can be explained is encountered repeatedly in Aristotle's work.
     From: report of Aristotle (works [c.330 BCE]) by Joan Kung - Aristotle on Essence and Explanation IV
     A reaction: What does 'significant' mean here? I take it that the significant properties are the ones which explain the role, function and powers of the object.
18. Thought / A. Modes of Thought / 5. Rationality / c. Animal rationality
Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji]
     Full Idea: Aristotle, and also the Stoics, denied rationality to animals. …The Platonists, the Pythagoreans, and some more independent Aristotelians, did grant reason and intellect to animals.
     From: report of Aristotle (works [c.330 BCE]) by Richard Sorabji - Rationality 'Denial'
     A reaction: This is not the same as affirming or denying their consciousness. The debate depends on how rationality is conceived.
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
A new usage of a name could arise from a mistaken baptism of nothing [Sainsbury]
     Full Idea: A baptism which, perhaps through some radical mistake, is the baptism of nothing, is as good a propagator of a new use as a baptism of an object.
     From: Mark Sainsbury (The Essence of Reference [2006], 18.3)
     A reaction: An obvious example might be the Loch Ness Monster. There is something intuitively wrong about saying that physical objects are actually part of linguistic meaning or reference. I am not a meaning!
19. Language / B. Reference / 5. Speaker's Reference
Even a quantifier like 'someone' can be used referentially [Sainsbury]
     Full Idea: A large range of expressions can be used with referential intentions, including quantifier phrases (as in 'someone has once again failed to close the door properly').
     From: Mark Sainsbury (The Essence of Reference [2006], 18.5)
     A reaction: This is the pragmatic aspect of reference, where it can be achieved by all sorts of means. But are quantifiers inherently referential in their semantic function? Some of each, it seems.
19. Language / E. Analyticity / 2. Analytic Truths
The notion of analytic truth is absent in Aristotle [Aristotle, by Politis]
     Full Idea: The notion of analytic truth is conspicuously absent in Aristotle.
     From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5
     A reaction: Cf. Idea 11239.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin]
     Full Idea: To the best of my knowledge (and somewhat to my surprise), Aristotle never actually says that man is a rational animal; however, he all but says it.
     From: report of Aristotle (works [c.330 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1
     A reaction: When I read this I thought that this database would prove Fogelin wrong, but it actually supports him, as I can't find it in Aristotle either. Descartes refers to it in Med.Two. In Idea 5133 Aristotle does say that man is a 'social being'. But 22586!
25. Social Practice / E. Policies / 5. Education / a. Aims of education
It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle]
     Full Idea: It is the mark of an educated mind to be able to entertain an idea without accepting it.
     From: Aristotle (works [c.330 BCE])
     A reaction: The epigraph on a David Chalmers website. A wonderful remark, and it should be on the wall of every beginners' philosophy class. However, while it is in the spirit of Aristotle, it appears to be a misattribution with no ancient provenance.
25. Social Practice / E. Policies / 5. Education / b. Education principles
Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius]
     Full Idea: Aristotle was asked how much educated men were superior to those uneducated; "As much," he said, "as the living are to the dead."
     From: report of Aristotle (works [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 05.1.11
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
Things are thought to have a function, even when they can't perform them [Sainsbury]
     Full Idea: On one common use of the notion of a function, something can possess a function which it does not, or even cannot, perform. A malformed heart is to pump blood, even if such a heart cannot in fact pump blood.
     From: Mark Sainsbury (The Essence of Reference [2006], 18.2)
     A reaction: One might say that the heart in a dead body had the function of pumping blood, but does it still have that function? Do I have the function of breaking the world 100 metres record, even though I can't quite manage it? Not that simple.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
     Full Idea: Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent.
     From: report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3
     A reaction: Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins]
     Full Idea: Aristotle's conception of matter permits any kind of matter to become any other kind of matter.
     From: report of Aristotle (works [c.330 BCE]) by David Wiggins - Substance 4.11.2
     A reaction: This is obviously crucial background information when we read Aristotle on matter. Our 92+ elements, and fixed fundamental particles, gives a quite different picture. Aristotle would discuss form and matter quite differently now.
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The law of gravity has many consequences beyond its grounding observations [Russell]
     Full Idea: The law of gravitation leads to many consequences which could not be discovered merely from the apparent motions of the heavenly bodies.
     From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.275)
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus]
     Full Idea: Aristotle said that the conception of gods arose among mankind from two originating causes, namely from events which concern the soul and from celestial phenomena.
     From: report of Aristotle (works [c.330 BCE], Frag 10) by Sextus Empiricus - Against the Physicists (two books) I.20
     A reaction: The cosmos suggests order, and possible creation. What do events of the soul suggest? It doesn't seem to be its non-physical nature, because Aristotle is more of a functionalist. Puzzling. (It says later that gods are like the soul).