53 ideas
| 1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
| 1627 | Any statement can be held true if we make enough adjustment to the rest of the system [Quine] |
| 1623 | Definition rests on synonymy, rather than explaining it [Quine] |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| 13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
| 13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
| 9204 | Quine's arguments fail because he naively conflates names with descriptions [Fine,K on Quine] |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
| 13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
| 13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
| 13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 17738 | Quine blurs the difference between knowledge of arithmetic and of physics [Jenkins on Quine] |
| 19492 | Quine is hopeless circular, deriving ontology from what is literal, and 'literal' from good ontology [Yablo on Quine] |
| 1628 | If physical objects are a myth, they are useful for making sense of experience [Quine] |
| 10929 | Aristotelian essence of the object has become the modern essence of meaning [Quine] |
| 12188 | Contrary to some claims, Quine does not deny logical necessity [Quine, by McFetridge] |
| 15090 | Quine's attack on the analytic-synthetic distinction undermined necessary truths [Quine, by Shoemaker] |
| 3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
| 9383 | Metaphysical analyticity (and linguistic necessity) are hopeless, but epistemic analyticity is a priori [Boghossian on Quine] |
| 12424 | Quine challenges the claim that analytic truths are knowable a priori [Quine, by Kitcher] |
| 9337 | Science is empirical, simple and conservative; any belief can hence be abandoned; so no a priori [Quine, by Horwich] |
| 9338 | Quine's objections to a priori knowledge only work in the domain of science [Horwich on Quine] |
| 9340 | Logic, arithmetic and geometry are revisable and a posteriori; quantum logic could be right [Horwich on Quine] |
| 1620 | Empiricism makes a basic distinction between truths based or not based on facts [Quine] |
| 1629 | Our outer beliefs must match experience, and our inner ones must be simple [Quine] |
| 19488 | The second dogma is linking every statement to some determinate observations [Quine, by Yablo] |
| 1625 | Statements about the external world face the tribunal of sense experience as a corporate body [Quine] |
| 1626 | It is troublesome nonsense to split statements into a linguistic and a factual component [Quine] |
| 7317 | 'Renate' and 'cordate' have identical extensions, but are not synonymous [Quine, by Miller,A] |
| 1621 | Once meaning and reference are separated, meaning ceases to seem important [Quine] |
| 9371 | Analytic statements are either logical truths (all reinterpretations) or they depend on synonymy [Quine] |
| 9366 | Quine's attack on analyticity undermined linguistic views of necessity, and analytic views of the a priori [Quine, by Boghossian] |
| 14473 | Quine attacks the Fregean idea that we can define analyticity through synonyous substitution [Quine, by Thomasson] |
| 7321 | The last two parts of 'Two Dogmas' are much the best [Miller,A on Quine] |
| 8803 | Erasing the analytic/synthetic distinction got rid of meanings, and saved philosophy of language [Davidson on Quine] |
| 17737 | The analytic needs excessively small units of meaning and empirical confirmation [Quine, by Jenkins] |
| 1624 | If we try to define analyticity by synonymy, that leads back to analyticity [Quine] |
| 1622 | Did someone ever actually define 'bachelor' as 'unmarried man'? [Quine] |
| 1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
| 1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
| 1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |