46 ideas
| 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] |
| 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] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 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] |
| 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] |
| 8502 | Realism doesn't explain 'a is F' any further by saying it is 'a has F-ness' [Devitt] |
| 8503 | The particular/universal distinction is unhelpful clutter; we should accept 'a is F' as basic [Devitt] |
| 8501 | Quineans take predication about objects as basic, not reference to properties they may have [Devitt] |
| 17368 | Essentialism concerns the nature of a group, not its category [Devitt] |
| 17370 | Things that gradually change, like species, can still have essences [Devitt] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 21912 | Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB] |
| 21911 | Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB] |
| 9354 | Why should necessities only be knowable a priori? That Hesperus is Phosporus is known empirically [Devitt] |
| 19565 | How could the mind have a link to the necessary character of reality? [Devitt] |
| 9353 | We explain away a priori knowledge, not as directly empirical, but as indirectly holistically empirical [Devitt] |
| 9356 | The idea of the a priori is so obscure that it won't explain anything [Devitt] |
| 19564 | Some knowledge must be empirical; naturalism implies that all knowledge is like that [Devitt] |
| 17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| 17369 | We name species as small to share properties, but large enough to yield generalisations [Devitt] |
| 17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |
| 17367 | Species are phenetic, biological, niche, or phylogenetic-cladistic [Devitt, by PG] |
| 17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |