38 ideas
12268 | Contradiction is impossible [Antisthenes (I), by Aristotle] |
602 | Some fools think you cannot define anything, but only say what it is like [Antisthenes (I), by Aristotle] |
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] |
1664 | I would rather go mad than experience pleasure [Antisthenes (I)] |
21385 | Antisthenes said virtue is teachable and permanent, is life's goal, and is like universal wealth [Antisthenes (I), by Long] |
23601 | Leaders can only attack foreigners who have done wrong (as with their own subjects) [Vitoria] |
23569 | The only just cause for a war is a wrong received [Vitoria] |
23566 | Princes should not justify a war to their subjects, and doing so would undermine the state [Vitoria] |
23576 | Sacking a city is lawful if it motivates the attacking troops [Vitoria] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
2631 | Antisthenes says there is only one god, which is nature [Antisthenes (I), by Cicero] |