50 ideas
7920 | Descriptive metaphysics aims at actual structure, revisionary metaphysics at a better structure [Strawson,P] |
7922 | Descriptive metaphysics concerns unchanging core concepts and categories [Strawson,P] |
7921 | Close examination of actual word usage is the only sure way in philosophy [Strawson,P] |
10842 | The fact which is stated by a true sentence is not something in the world [Strawson,P] |
10843 | Facts aren't exactly true statements, but they are what those statements say [Strawson,P] |
10844 | The statement that it is raining perfectly fits the fact that it is raining [Strawson,P] |
10841 | The word 'true' always refers to a possible statement [Strawson,P] |
15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
8358 | There are no rules for the exact logic of ordinary language, because that doesn't exist [Strawson,P] |
6413 | 'The present King of France is bald' presupposes existence, rather than stating it [Strawson,P, by Grayling] |
8354 | Russell asks when 'The King of France is wise' would be a true assertion [Strawson,P] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
16980 | We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P] |
16979 | It makes no sense to ask of some individual thing what it is that makes it that individual [Strawson,P] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
9282 | I can only apply consciousness predicates to myself if I can apply them to others [Strawson,P] |
9263 | A person is an entity to which we can ascribe predicates of consciousness and corporeality [Strawson,P] |
8356 | The meaning of an expression or sentence is general directions for its use, to refer or to assert [Strawson,P] |
10430 | Reference is mainly a social phenomenon [Strawson,P, by Sainsbury] |
10448 | If an expression can refer to anything, it may still instrinsically refer, but relative to a context [Bach on Strawson,P] |
8355 | Expressions don't refer; people use expressions to refer [Strawson,P] |
8357 | If an utterance fails to refer then it is a pseudo-use, though a speaker may think they assert something [Strawson,P] |
9281 | The idea of a predicate matches a range of things to which it can be applied [Strawson,P] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |