16 ideas
| 18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Quine says the large sets should be regarded as 'uninterpreted'. |
| 18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
| Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2 |
| 8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
| Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence | |
| A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines! |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
| A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
| A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
| 20298 | The traditional a priori is justified without experience; post-Quine it became unrevisable by experience [Rey] |
| Full Idea: Where Kant and others had traditionally assumed that the a priori concerned beliefs 'justifiable independently of experience', Quine and others of the time came to regard it as beliefs 'unrevisable in the light of experience'. | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 3.7) | |
| A reaction: That throws a rather striking light on Quine's project. Of course, if the a priori is also necessary, then it has to be unrevisable. But is a bachelor necessarily an unmarried man? It is not necessary that 'bachelor' has a fixed meaning. |
| 20300 | Externalist synonymy is there being a correct link to the same external phenomena [Rey] |
| Full Idea: Externalists are typically committed to counting expressions as 'synonymous' if they happen to be linked in the right way to the same external phenomena, even if a thinker couldn't realise that they are by reflection alone. | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.2) | |
| A reaction: [He cites Fodor] Externalists always try to link to concrete things in the world, but most of our talk is full of generalities, abstractions and fiction which don't link directly to anything. |
| 20294 | 'Married' does not 'contain' its symmetry, nor 'bigger than' its transitivity [Rey] |
| Full Idea: If Bob is married to Sue, then Sue is married to Bob. If x bigger than y, and y bigger than z, x is bigger than z. The symmetry of 'marriage' or transitivity of 'bigger than' are not obviously 'contained in' the corresponding thoughts. | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 1.2) | |
| A reaction: [Also 'if something is red, then it is coloured'] This is a Fregean criticism of Kant. It is not so much that Kant was wrong, as that the concept of analyticity is seen to have a much wider application than Kant realised. Especially in mathematics. |
| 20293 | Analytic judgements can't be explained by contradiction, since that is what is assumed [Rey] |
| Full Idea: Rejecting 'a married bachelor' as contradictory would seem to have no justification other than the claim that 'All bachelors are unmarried is analytic, and so cannot serve to justify or explain that claim. | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 1.2) | |
| A reaction: Rey is discussing Frege's objection to Kant (who tried to prove the necessity of analytic judgements, on the basis of the denial being a contradiction). |
| 20297 | Analytic statements are undeniable (because of meaning), rather than unrevisable [Rey] |
| Full Idea: What's peculiar about the analytic is that denying it seem unintelligible. Far from unrevisability explaining analyticity, it seems to be analyticitiy that explains unrevisability; we only balk at denying unmarried bachelors because that's what it means! | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 3.7) | |
| A reaction: This is a criticism of Quine, who attacked analyticity when it is understood as unrevisability. Obviously we could revise the concept of 'bachelor', if our marriage customs changed a lot. Rey seems right here. |
| 20301 | The meaning properties of a term are those which explain how the term is typically used [Rey] |
| Full Idea: It may be that the meaning properties of a term are the ones that play a basic explanatory role with regard to the use of the term generally, the ones in virtue ultimately of which a term is used with that meaning. | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.3) | |
| A reaction: [He cites Devitt 1996, 2002, and Horwich 1998, 2005) I spring to philosophical life whenever I see the word 'explanatory', because that is the point of the whole game. They are pointing to the essence of the concept (which is explanatory, say I). |
| 20302 | An intrinsic language faculty may fix what is meaningful (as well as grammatical) [Rey] |
| Full Idea: The existence of a separate language faculty may be an odd but psychologically real fact about us, and it may thereby supply a real basis for commitments about not only what is or is not grammatical, but about what is a matter of natural language meaning. | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.4) | |
| A reaction: This is the Chomskyan view of analytic sentences. An example from Chomsky (1977:142) is the semantic relationships of persuade, intend and believe. It's hard to see how the secret faculty on its own could do the job. Consensus is needed. |
| 20303 | Research throws doubts on the claimed intuitions which support analyticity [Rey] |
| Full Idea: The movement of 'experimental philosophy' has pointed to evidence of considerable malleability of subject's 'intuitions' with regard to the standard kinds of thought experiments on which defenses of analytic claims typically rely. | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.4) | |
| A reaction: See Cappelen's interesting attack on the idea that philosophy relies on intuitions, and hence his attack on experimental philosophy. Our consensus on ordinary English usage hardly qualifies as somewhat vague 'intuitions'. |
| 20299 | If we claim direct insight to what is analytic, how do we know it is not sub-consciously empirical? [Rey] |
| Full Idea: How in the end are we going to distinguish claims or the analytic as 'rational insight', 'primitive compulsion', inferential practice or folk belief from merely some deeply held empirical conviction, indeed, from mere dogma. | |
| From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.1) | |
| A reaction: This is Rey's summary of the persisting Quinean challenge to analytic truths, in the face of a set of replies, summarised by the various phrases here. So do we reject a dogma of empiricism, by asserting dogmatic empiricism? |