68 ideas
| 11912 | Substantive metaphysics says what a property is, not what a predicate means [Molnar] |
| 11920 | A real definition gives all the properties that constitute an identity [Molnar] |
| 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] |
| 11919 | Ontological dependence rests on essential connection, not necessary connection [Molnar] |
| 11929 | The three categories in ontology are objects, properties and relations [Molnar] |
| 11927 | Reflexive relations are syntactically polyadic but ontologically monadic [Molnar] |
| 11915 | If atomism is true, then all properties derive from ultimate properties [Molnar] |
| 11916 | 'Being physical' is a second-order property [Molnar] |
| 11956 | 'Categorical properties' are those which are not powers [Molnar] |
| 11928 | Are tropes transferable? If they are, that is a version of Platonism [Molnar] |
| 11933 | A power's type-identity is given by its definitive manifestation [Molnar] |
| 11932 | Powers have Directedness, Independence, Actuality, Intrinsicality and Objectivity [Molnar] |
| 11934 | The physical world has a feature very like mental intentionality [Molnar] |
| 11947 | Dispositions and external powers arise entirely from intrinsic powers in objects [Molnar] |
| 11952 | The Standard Model suggest that particles are entirely dispositional, and hence are powers [Molnar] |
| 11953 | Some powers are ungrounded, and others rest on them, and are derivative [Molnar] |
| 11943 | Dispositions can be causes, so they must be part of the actual world [Molnar] |
| 11939 | If powers only exist when actual, they seem to be nomadic, and indistinguishable from non-powers [Molnar] |
| 11914 | Platonic explanations of universals actually diminish our understanding [Molnar] |
| 11913 | For nominalists, predicate extensions are inexplicable facts [Molnar] |
| 11962 | Nominalists only accept first-order logic [Molnar] |
| 11917 | Structural properties are derivate properties [Molnar] |
| 11955 | There are no 'structural properties', as properties with parts [Molnar] |
| 11918 | The essence of a thing need not include everything that is necessarily true of it [Molnar] |
| 11963 | What is the truthmaker for a non-existent possible? [Molnar] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 11951 | Hume allows interpolation, even though it and extrapolation are not actually valid [Molnar] |
| 11936 | The two ways proposed to distinguish mind are intentionality or consciousness [Molnar] |
| 11935 | Physical powers like solubility and charge also have directedness [Molnar] |
| 11944 | Rule occasionalism says God's actions follow laws, not miracles [Molnar] |
| 11960 | Singular causation is prior to general causation; each aspirin produces the aspirin generalization [Molnar] |
| 11937 | We should analyse causation in terms of powers, not vice versa [Molnar] |
| 11954 | We should analyse causation in terms of powers [Molnar] |
| 11961 | Causal dependence explains counterfactual dependence, not vice versa [Molnar] |
| 11959 | Science works when we assume natural kinds have essences - because it is true [Molnar] |
| 9448 | Location in space and time are non-power properties [Molnar, by Mumford] |
| 11930 | One essential property of a muon doesn't entail the others [Molnar] |
| 11957 | It is contingent which kinds and powers exist in the world [Molnar] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| 11921 | The laws of nature depend on the powers, not the other way round [Molnar] |
| 11931 | Energy fields are discontinuous at the very small [Molnar] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |