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] |
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] |
16657 | Substance, Quantity and Quality are real; other categories depend on those three [Henry of Ghent] |
16658 | The only reality in the category of Relation is things from another category [Henry of Ghent] |
16645 | Accidents are diminished beings, because they are dispositions of substance (unqualified being) [Henry of Ghent] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
22012 | Kant says things-in-themselves cause sensations, but then makes causation transcendental! [Henry of Ghent, by Pinkard] |
23529 | Conduct is not isolated from its effect on the moral code [Hart,HLA] |
23530 | The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA] |
23522 | In an organised society all actions have some effect on other people [Hart,HLA] |
23528 | The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA] |
21004 | Hart (against Bentham) says human rights are what motivate legal rights [Hart,HLA, by Sen] |
23523 | The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA] |
23524 | Some private moral issues are no concern of the law [Hart,HLA] |
23521 | Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA] |
23525 | Is the enforcement of morality morally justifiable? [Hart,HLA] |
23526 | Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA] |
20932 | Positive law needs secondary 'rules of recognition' for their correct application [Hart,HLA, by Zimmermann,J] |
20931 | Hart replaced positivism with the democratic requirement of the people's acceptance [Hart,HLA, by Zimmermann,J] |
23527 | Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |