50 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] |
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] |
15127 | A categorical basis could hardly explain a disposition if it had no powers of its own [Hawthorne] |
15123 | Is the causal profile of a property its essence? [Hawthorne] |
15122 | Could two different properties have the same causal profile? [Hawthorne] |
15124 | If properties are more than their powers, we could have two properties with the same power [Hawthorne] |
14590 | If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne] |
15128 | We can treat the structure/form of the world differently from the nodes/matter of the world [Hawthorne] |
15121 | An individual essence is a necessary and sufficient profile for a thing [Hawthorne] |
14591 | Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne] |
8970 | Our notion of identical sets involves identical members, which needs absolute identity [Hawthorne] |
14589 | A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
15126 | Maybe scientific causation is just generalisation about the patterns [Hawthorne] |
15125 | We only know the mathematical laws, but not much else [Hawthorne] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
14588 | Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne] |