64 ideas
23027 | Ideals and metaphysics are practical, not imaginative or speculative [Green,TH, by Muirhead] |
23030 | Truth is a relation to a whole of organised knowledge in the collection of rational minds [Green,TH, by Muirhead] |
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] |
472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
23044 | All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead] |
23034 | The ultimate test for truth is the systematic interdependence in nature [Green,TH, by Muirhead] |
23029 | Knowledge is secured by the relations between its parts, through differences and identities [Green,TH, by Muirhead] |
22511 | Some reasonings are stronger than we are [Philolaus] |
23035 | The good life aims at perfections, or absolute laws, or what is absolutely desirable [Green,TH] |
23032 | What is distinctive of human life is the desire for self-improvement [Green,TH, by Muirhead] |
23033 | Hedonism offers no satisfaction, because what we desire is self-betterment [Green,TH, by Muirhead] |
23046 | States only have full authority if they heed the claims of human fellowship [Green,TH] |
23045 | Politics is compromises, which seem supported by a social contract, but express the will of no one [Green,TH] |
23050 | The ideal is a society in which all citizens are ladies and gentlemen [Green,TH] |
23052 | Enfranchisement is an end in itself; it makes a person moral, and gives a basis for respect [Green,TH] |
23036 | The good is identified by the capacities of its participants [Green,TH, by Muirhead] |
23039 | A true state is only unified and stabilised by acknowledging individuality [Green,TH, by Muirhead] |
23037 | People are improved by egalitarian institutions and habits [Green,TH] |
23051 | Equality also implies liberty, because equality must be of opportunity as well as possessions [Green,TH] |
23043 | All talk of the progress of a nation must reduce to the progress of its individual members [Green,TH] |
23038 | People only develop their personality through co-operation with the social whole [Green,TH, by Muirhead] |
23028 | The highest political efforts express our deeper social spirit [Green,TH, by Muirhead] |
23054 | Communism is wrong because it restricts the freedom of individuals to contribute to the community [Green,TH, by Muirhead] |
23047 | Original common ownership is securing private property, not denying it [Green,TH, by Muirhead] |
23042 | National spirit only exists in the individuals who embody it [Green,TH, by Muirhead] |
23048 | The ground of property ownership is not force but the power to use it for social ends [Green,TH, by Muirhead] |
23049 | Property is needed by all citizens, to empower them to achieve social goods [Green,TH] |
23040 | If something develops, its true nature is embodied in its end [Green,TH] |
473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
469 | Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus] |
476 | Self-created numbers make the universe stable [Philolaus] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
1787 | Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius] |
23031 | God is the ideal end of the mature mind's final development [Green,TH] |
23041 | God is the realisation of the possibilities of each man's self [Green,TH] |