50 ideas
| 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] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 9204 | Quine's arguments fail because he naively conflates names with descriptions [Fine,K on Quine] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 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] |
| 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] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |