46 ideas
6161 | Structuralism is neo-Kantian idealism, with language playing the role of categories of understanding [Rowlands] |
15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
6163 | If bivalence is rejected, then excluded middle must also be rejected [Rowlands] |
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] |
6155 | Supervenience is a one-way relation of dependence or determination between properties [Rowlands] |
6154 | It is argued that wholes possess modal and counterfactual properties that parts lack [Rowlands] |
6157 | Tokens are dated, concrete particulars; types are their general properties or kinds [Rowlands] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
6159 | Strong idealism is the sort of mess produced by a Cartesian separation of mind and world [Rowlands] |
6152 | Minds are rational, conscious, subjective, self-knowing, free, meaningful and self-aware [Rowlands] |
6173 | Content externalism implies that we do not have privileged access to our own minds [Rowlands] |
6174 | If someone is secretly transported to Twin Earth, others know their thoughts better than they do [Rowlands] |
6158 | Supervenience of mental and physical properties often comes with token-identity of mental and physical particulars [Rowlands] |
6168 | The content of a thought is just the meaning of a sentence [Rowlands] |
6167 | Action is bodily movement caused by intentional states [Rowlands] |
6177 | Moral intuition seems unevenly distributed between people [Rowlands] |
6156 | The 17th century reintroduced atoms as mathematical modes of Euclidean space [Rowlands] |
6170 | Natural kinds are defined by their real essence, as in gold having atomic number 79 [Rowlands] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
6178 | It is common to see the value of nature in one feature, such as life, diversity, or integrity [Rowlands] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |