49 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] |
| 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] |
| 14064 | If a statue is identical with the clay of which it is made, that identity is contingent [Gibbard] |
| 14066 | A 'piece' of clay begins when its parts stick together, separately from other clay [Gibbard] |
| 14067 | Clay and statue are two objects, which can be named and reasoned about [Gibbard] |
| 14069 | We can only investigate the identity once we have designated it as 'statue' or as 'clay' [Gibbard] |
| 14076 | Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard] |
| 14077 | Essentialism for concreta is false, since they can come apart under two concepts [Gibbard] |
| 14070 | A particular statue has sortal persistence conditions, so its origin defines it [Gibbard] |
| 14073 | Claims on contingent identity seem to violate Leibniz's Law [Gibbard] |
| 14065 | Two identical things must share properties - including creation and destruction times [Gibbard] |
| 14074 | Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard] |
| 14072 | Possible worlds identity needs a sortal [Gibbard] |
| 14078 | Only concepts, not individuals, can be the same across possible worlds [Gibbard] |
| 14079 | Kripke's semantics needs lots of intuitions about which properties are essential [Gibbard] |
| 19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
| 19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
| 19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
| 19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
| 14071 | Naming a thing in the actual world also invokes some persistence criteria [Gibbard] |
| 19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |