42 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] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
23805 | Some explanations offer to explain a mystery by a greater mystery [Schulte] |
23806 | Naturalist accounts of representation must match the views of cognitive science [Schulte] |
23793 | On the whole, referential content is seen as broad, and sense content as narrow [Schulte] |
23796 | Naturalists must explain both representation, and what is represented [Schulte] |
23792 | Phenomenal and representational character may have links, or even be united [Schulte] |
23795 | Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte] |
23804 | Maybe we can explain mental content in terms of phenomenal properties [Schulte] |
23802 | Conceptual role semantics says content is determined by cognitive role [Schulte] |
23797 | Cause won't explain content, because one cause can produce several contents [Schulte] |
23799 | Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte] |
23800 | Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte] |
23798 | Information theories say content is information, such as smoke making fire probable [Schulte] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |