116 ideas
11832 | We learn a concept's relations by using it, without reducing it to anything [Wiggins] |
16512 | Semantic facts are preferable to transcendental philosophical fiction [Wiggins] |
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] |
11863 | (λx)[Man x] means 'the property x has iff x is a man'. [Wiggins] |
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] |
17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
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] |
14746 | What exists can't depend on our conceptual scheme, and using all conceptual schemes is too liberal [Sider on Wiggins] |
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] |
16523 | Realist Conceptualists accept that our interests affect our concepts [Wiggins] |
16524 | Conceptualism says we must use our individuating concepts to grasp reality [Wiggins] |
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] |
16526 | Animal classifications: the Emperor's, fabulous, innumerable, like flies, stray dogs, embalmed…. [Wiggins] |
12056 | An ancestral relation is either direct or transitively indirect [Wiggins] |
12050 | Substances contain a source of change or principle of activity [Wiggins] |
16492 | Individuation needs accounts of identity, of change, and of singling out [Wiggins] |
16493 | Individuation can only be understood by the relation between things and thinkers [Wiggins] |
11900 | We can accept criteria of distinctness and persistence, without making the counterfactual claims [Mackie,P on Wiggins] |
11870 | Activity individuates natural things, functions do artefacts, and intentions do artworks [Wiggins] |
16496 | Singling out extends back and forward in time [Wiggins] |
11866 | The idea of 'thisness' is better expressed with designation/predication and particular/universal [Wiggins] |
12052 | We never single out just 'this', but always 'this something-or-other' [Wiggins] |
13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
16495 | The only singling out is singling out 'as' something [Wiggins] |
16501 | In Aristotle's sense, saying x falls under f is to say what x is [Wiggins] |
16506 | Every determinate thing falls under a sortal, which fixes its persistence [Wiggins] |
12055 | Sortal predications are answers to the question 'what is x?' [Wiggins] |
12059 | A river may change constantly, but not in respect of being a river [Wiggins] |
12063 | Sortal classification becomes science, with cross reference clarifying individuals [Wiggins] |
12051 | If the kinds are divided realistically, they fall into substances [Wiggins] |
12053 | 'Human being' is a better answer to 'what is it?' than 'poet', as the latter comes in degrees [Wiggins] |
12054 | Secondary substances correctly divide primary substances by activity-principles and relations [Wiggins] |
11896 | A sortal essence is a thing's principle of individuation [Wiggins, by Mackie,P] |
15835 | Wiggins's sortal essentialism rests on a thing's principle of individuation [Wiggins, by Mackie,P] |
11841 | The evening star is the same planet but not the same star as the morning star, since it is not a star [Wiggins] |
10679 | 'Sortalism' says parts only compose a whole if it falls under a sort or kind [Wiggins, by Hossack] |
14363 | Identity a=b is only possible with some concept to give persistence and existence conditions [Wiggins, by Strawson,P] |
14364 | A thing is necessarily its highest sortal kind, which entails an essential constitution [Wiggins, by Strawson,P] |
11851 | Many predicates are purely generic, or pure determiners, rather than sortals [Wiggins] |
11865 | The possibility of a property needs an essential sortal concept to conceive it [Wiggins] |
12047 | We refer to persisting substances, in perception and in thought, and they aid understanding [Wiggins] |
14744 | Objects can only coincide if they are of different kinds; trees can't coincide with other trees [Wiggins, by Sider] |
11852 | Is the Pope's crown one crown, if it is made of many crowns? [Wiggins] |
11875 | Boundaries are not crucial to mountains, so they are determinate without a determinate extent [Wiggins] |
12057 | Matter underlies things, composes things, and brings them to be [Wiggins] |
14749 | Identity is an atemporal relation, but composition is relative to times [Wiggins, by Sider] |
11844 | If I destroy an item, I do not destroy each part of it [Wiggins] |
11861 | We can forget about individual or particularized essences [Wiggins] |
16509 | Natural kinds are well suited to be the sortals which fix substances [Wiggins] |
11871 | Essences are not explanations, but individuations [Wiggins] |
11879 | Essentialism is best represented as a predicate-modifier: □(a exists → a is F) [Wiggins, by Mackie,P] |
16514 | Artefacts are individuated by some matter having a certain function [Wiggins] |
16510 | Nominal essences don't fix membership, ignore evolution, and aren't contextual [Wiggins] |
11835 | The nominal essence is the idea behind a name used for sorting [Wiggins] |
16503 | 'What is it?' gives the kind, nature, persistence conditions and identity over time of a thing [Wiggins] |
11876 | It is easier to go from horses to horse-stages than from horse-stages to horses [Wiggins] |
16499 | A restored church is the same 'church', but not the same 'building' or 'brickwork' [Wiggins] |
16515 | A thing begins only once; for a clock, it is when its making is first completed [Wiggins] |
11858 | The question is not what gets the title 'Theseus' Ship', but what is identical with the original [Wiggins] |
16517 | Priests prefer the working ship; antiquarians prefer the reconstruction [Wiggins] |
11843 | Identity over a time and at a time aren't different concepts [Wiggins] |
11864 | Hesperus=Hesperus, and Phosphorus=Hesperus, so necessarily Phosphorus=Hesperus [Wiggins] |
16498 | Identity cannot be defined, because definitions are identities [Wiggins] |
11831 | The formal properties of identity are reflexivity and Leibniz's Law [Wiggins] |
16497 | Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins] |
16502 | Identity is primitive [Wiggins] |
14362 | Relative Identity is incompatible with the Indiscernibility of Identicals [Wiggins, by Strawson,P] |
11838 | Relativity of Identity makes identity entirely depend on a category [Wiggins] |
11847 | To identify two items, we must have a common sort for them [Wiggins] |
16521 | A is necessarily A, so if B is A, then B is also necessarily A [Wiggins] |
16505 | By the principle of Indiscernibility, a symmetrical object could only be half of itself! [Wiggins] |
11839 | Do both 'same f as' and '=' support Leibniz's Law? [Wiggins] |
11845 | Substitutivity, and hence most reasoning, needs Leibniz's Law [Wiggins] |
16494 | We want to explain sameness as coincidence of substance, not as anything qualitative [Wiggins] |
16522 | It is hard or impossible to think of Caesar as not human [Wiggins] |
11869 | Possible worlds rest on the objects about which we have suppositions [Wiggins] |
11850 | Not every story corresponds to a possible world [Wiggins] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
16525 | Our sortal concepts fix what we find in experience [Wiggins] |
12064 | The category of substance is more important for epistemology than for ontology [Wiggins] |
12049 | Naming the secondary substance provides a mass of general information [Wiggins] |
11848 | Asking 'what is it?' nicely points us to the persistence of a continuing entity [Wiggins] |
12065 | Seeing a group of soldiers as an army is irresistible, in ontology and explanation [Wiggins] |
11859 | The mind conceptualizes objects; yet objects impinge upon the mind [Wiggins] |
16518 | We conceptualise objects, but they impinge on us [Wiggins] |
11836 | We can use 'concept' for the reference, and 'conception' for sense [Wiggins] |
16511 | A 'conception' of a horse is a full theory of what it is (and not just the 'concept') [Wiggins] |
11860 | Lawlike propensities are enough to individuate natural kinds [Wiggins] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |