47 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] |
4020 | The modern self has disengaged reason, self-exploration, and personal commitment [Taylor,C] |
4002 | My aim is to map the connections between our sense of self and our moral understanding [Taylor,C] |
4006 | I can only be aware of myself as a person who changes by means of my personal history [Taylor,C] |
4003 | Selfhood and moral values are inextricably intertwined [Taylor,C] |
4021 | Willingness to risk life was the constitutive quality of the man of honour [Taylor,C] |
4005 | To have respect for people, you must feel their claims, or their injustices, or hold them in awe [Taylor,C] |
4004 | Consistency presupposes intrinsic description [Taylor,C] |
4010 | In later utilitarianism the modern stress on freedom leads to the rejection of paternalism [Taylor,C] |
22809 | The social contract sees society as constituted by and for individuals [Taylor,C] |
22811 | Assigning a right based on a human capacity implies that the capacity should be developed [Taylor,C] |
22815 | If freedom depends on society and culture, the greatest freedom is in shaping them [Taylor,C] |
22814 | Our reliance on other people close to us does not imply any political obligations [Taylor,C] |
22812 | For most people the primacy of rights mainly concerns freedom [Taylor,C] |
22810 | A right is not just a rule, but also asserts certain ideas of moral worth [Taylor,C] |
22813 | Property is not essential for life, but it may be essential for independence [Taylor,C] |
23417 | If the state is neutral, there won't be sufficient community to support a welfare state [Taylor,C, by Kymlicka] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
4009 | Nominalists defended the sovereignty of God against the idea of natural existing good and evil [Taylor,C] |
3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |