42 ideas
| 21355 | The Pre-Socratics are not simple naturalists, because they do not always 'leave the gods out' [Leroi] |
| 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] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 4761 | The 'error theory' of morals says there is no moral knowledge, because there are no moral facts [Mackie, by Engel] |
| 8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
| 8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
| 8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
| 8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
| 8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
| 8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
| 8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
| 8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
| 8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| 1473 | Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG] |
| 1472 | The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG] |