46 ideas
| 11223 | Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta] |
| 11215 | Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta] |
| 11225 | A definition needs to apply to the same object across possible worlds [Gupta] |
| 11227 | The 'revision theory' says that definitions are rules for improving output [Gupta] |
| 11224 | Traditional definitions are general identities, which are sentential and reductive [Gupta] |
| 11226 | Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta] |
| 11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta] |
| 11217 | Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta] |
| 11216 | If definitions aim at different ideals, then defining essence is not a unitary activity [Gupta] |
| 11218 | Stipulative definition assigns meaning to a term, ignoring prior meanings [Gupta] |
| 11220 | Ostensive definitions look simple, but are complex and barely explicable [Gupta] |
| 14965 | Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta] |
| 14968 | A weakened classical language can contain its own truth predicate [Gupta] |
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| 11222 | The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta] |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| 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] |
| 14964 | The Liar reappears, even if one insists on propositions instead of sentences [Gupta] |
| 14969 | Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 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] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |