51 ideas
| 12585 | Most people can't even define a chair [Peacocke] |
| 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] |
| 12581 | Perceptual concepts causally influence the content of our experiences [Peacocke] |
| 6456 | Sense-data are neutral uninterpreted experiences, separated from objects and judgements [Angeles] |
| 12579 | Perception has proto-propositions, between immediate experience and concepts [Peacocke] |
| 12586 | Consciousness of a belief isn't a belief that one has it [Peacocke] |
| 12608 | Concepts are distinguished by roles in judgement, and are thus tied to rationality [Peacocke] |
| 18568 | Philosophy should merely give necessary and sufficient conditions for concept possession [Peacocke, by Machery] |
| 18571 | Peacocke's account of possession of a concept depends on one view of counterfactuals [Peacocke, by Machery] |
| 18572 | Peacocke's account separates psychology from philosophy, and is very sketchy [Machery on Peacocke] |
| 17722 | The concept 'red' is tied to what actually individuates red things [Peacocke] |
| 11127 | If concepts just are mental representations, what of concepts we may never acquire? [Peacocke] |
| 12577 | Possessing a concept is being able to make judgements which use it [Peacocke] |
| 12578 | A concept is just what it is to possess that concept [Peacocke] |
| 12587 | Employing a concept isn't decided by introspection, but by making judgements using it [Peacocke] |
| 12605 | A sense is individuated by the conditions for reference [Peacocke] |
| 12607 | Fregean concepts have their essence fixed by reference-conditions [Peacocke] |
| 12609 | Concepts have distinctive reasons and norms [Peacocke] |
| 12584 | An analysis of concepts must link them to something unconceptualized [Peacocke] |
| 12604 | Any explanation of a concept must involve reference and truth [Peacocke] |
| 9335 | Concepts are constituted by their role in a group of propositions to which we are committed [Peacocke, by Greco] |
| 9336 | A concept's reference is what makes true the beliefs of its possession conditions [Peacocke, by Horwich] |
| 12610 | Encountering novel sentences shows conclusively that meaning must be compositional [Peacocke] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |