13 ideas
| 2676 | Didactic argument starts from the principles of the subject, not from the opinions of the learner [Aristotle] |
| Full Idea: Didactic arguments are those which reason from the principles appropriate to each branch of learning and not from the opinions of the answerer (for he who is learning must take things on trust). | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 165b01) |
| 2675 | Reasoning is a way of making statements which makes them lead on to other statements [Aristotle] |
| Full Idea: Reasoning is based on certain statements made in such a way as necessarily to cause the assertion of things other than those statements and as a result of those statements. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 165a01) |
| 2677 | Dialectic aims to start from generally accepted opinions, and lead to a contradiction [Aristotle] |
| Full Idea: Dialectical arguments are those which, starting from generally accepted opinions, reason to establish a contradiction. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 165b03) |
| 2674 | Competitive argument aims at refutation, fallacy, paradox, solecism or repetition [Aristotle] |
| Full Idea: Those who compete and contend in argument aim at five objects: refutation, fallacy, paradox, solecism, and the reduction of one's opponent to a state of babbling, that is, making him say the same thing over and over again. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 165b15) |
| 16967 | 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle] |
| Full Idea: If you ask 'Are Coriscus and Callias at home or not at home?', whether they are both at home or not there, the number of propositions is more than one. For if the answer is true, it does not follow that the question is a single one. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 176a08) | |
| A reaction: [compressed] Aristotle is saying that some questions should not receive a 'yes' or 'no' answer, because they are equivocal. Arthur Prior cites this passage, on 'and'. Ordinary use of 'and' need not be the logical use of 'and'. |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michčle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 16149 | Generic terms like 'man' are not substances, but qualities, relations, modes or some such thing [Aristotle] |
| Full Idea: 'Man', and every generic term, denotes not an individual substance but a quality or relation or mode or something of the kind. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 179a01) | |
| A reaction: This is Aristotle's denial that species constitutes the essence of anything. I take 'man' to be a categorisation of individuals, and is ontologically nothing at all in its own right. |
| 11840 | Only if two things are identical do they have the same attributes [Aristotle] |
| Full Idea: It is only to things which are indistinguishable and one in essence [ousia] that all the same attributes are generally held to belong. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 179a37) | |
| A reaction: This simply IS Leibniz's Law (to which I shall from now on quietly refer to as 'Aristotle's Law'). It seems that it just as plausible to translate 'ousia' as 'being' rather than 'essence'. 'Indistinguishable' and 'one in ousia' are not the same. |
| 8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
| Full Idea: Sceptics respond to the regress problem by denying knowledge; Foundationalists accept justifications without reasons; Positists say reasons terminate is mere posits; Coherentists say mutual support is justification; Infinitists accept the regress. | |
| From: James Van Cleve (Why coherence is not enough [2005], I) | |
| A reaction: A nice map of the territory. The doubts of Scepticism are not strong enough for anyone to embrace the view; Foundationalist destroy knowledge (?), as do Positists; Infinitism is a version of Coherentism - which is the winner. |
| 8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
| Full Idea: Contemporary foundationalists are seldom of the strong Cartesian variety: they do not insist that basic beliefs be absolutely certain. They also tend to allow that coherence can enhance justification. | |
| From: James Van Cleve (Why coherence is not enough [2005], III) | |
| A reaction: It strikes me that they have got onto a slippery slope. How certain are the basic beliefs? How do you evaluate their certainty? Could incoherence in their implications undermine them? Skyscrapers need perfect foundations. |