60 ideas
1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
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] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
448 | No necessity could produce Being either later or earlier, so it must exist absolutely or not at all [Parmenides] |
447 | Being must be eternal and uncreated, and hence it is timeless [Parmenides] |
449 | Being is not divisible, since it is all alike [Parmenides] |
1503 | There is no such thing as nothing [Parmenides] |
445 | The realm of necessary non-existence cannot be explored, because it is unknowable [Parmenides] |
21820 | Parmenides at least saw Being as the same as Nous, and separate from the sensed realm [Parmenides, by Plotinus] |
452 | All our concepts of change and permanence are just names, not the truth [Parmenides] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
1504 | Something must be unchanging to make recognition and knowledge possible [Aristotle on Parmenides] |
444 | The first way of enquiry involves necessary existence [Parmenides] |
450 | Necessity sets limits on being, in order to give it identity [Parmenides] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
451 | Thinking implies existence, because thinking depends on it [Parmenides] |
1506 | Parmenides treats perception and intellectual activity as the same [Theophrastus on Parmenides] |
3058 | Only reason can prove the truth of facts [Parmenides] |
555 | People who say that the cosmos is one forget that they must explain movement [Aristotle on Parmenides] |
5081 | There could be movement within one thing, as there is within water [Aristotle on Parmenides] |
1509 | The one can't be divisible, because if it was it could be infinitely divided down to nothing [Parmenides, by Simplicius] |
20900 | Defenders of the One say motion needs the void - but that is not part of Being [Parmenides, by Aristotle] |
226 | The one is without any kind of motion [Parmenides] |
1505 | Reason sees reality as one, the senses see it as many [Aristotle on Parmenides] |
453 | Reality is symmetrical and balanced, like a sphere, with no reason to be greater one way rather than another [Parmenides] |
1792 | He taught that there are two elements, fire the maker, and earth the matter [Parmenides, by Diog. Laertius] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
5115 | It is feeble-minded to look for explanations of everything being at rest [Aristotle on Parmenides] |
13217 | The void can't exist, and without the void there can't be movement or separation [Parmenides, by Aristotle] |
22918 | What could have triggered the beginning [of time and being]? [Parmenides] |
1794 | He was the first to discover the identity of the Morning and Evening Stars [Parmenides, by Diog. Laertius] |
1791 | He was the first person to say the earth is spherical [Parmenides, by Diog. Laertius] |