69 ideas
5515 | Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit] |
15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
15879 | The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré] |
18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
15891 | Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré] |
15878 | Some quantifiers, such as 'any', rule out any notion of order within their range [Harré] |
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] |
5516 | Reduction can be by identity, or constitution, or elimination [Parfit, by PG] |
15874 | Scientific properties are not observed qualities, but the dispositions which create them [Harré] |
15884 | Laws of nature remain the same through any conditions, if the underlying mechanisms are unchanged [Harré] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
15880 | In physical sciences particular observations are ordered, but in biology only the classes are ordered [Harré] |
15869 | Reports of experiments eliminate the experimenter, and present results as the behaviour of nature [Harré] |
15881 | We can save laws from counter-instances by treating the latter as analytic definitions [Harré] |
15882 | Since there are three different dimensions for generalising laws, no one system of logic can cover them [Harré] |
15888 | The grue problem shows that natural kinds are central to science [Harré] |
15887 | 'Grue' introduces a new causal hypothesis - that emeralds can change colour [Harré] |
15889 | It is because ravens are birds that their species and their colour might be connected [Harré] |
15890 | Non-black non-ravens just aren't part of the presuppositions of 'all ravens are black' [Harré] |
15885 | The necessity of Newton's First Law derives from the nature of material things, not from a mechanism [Harré] |
15868 | Idealisation idealises all of a thing's properties, but abstraction leaves some of them out [Harré] |
3539 | Personal identity is just causally related mental states [Parfit, by Maslin] |
5514 | Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit] |
1393 | One of my future selves will not necessarily be me [Parfit] |
5521 | If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit] |
5522 | Over a period of time what matters is not that 'I' persist, but that I have psychological continuity [Parfit] |
1392 | If we split like amoeba, we would be two people, neither of them being us [Parfit] |
5519 | It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit] |
5520 | If two humans are merged surgically, the new identity is a purely verbal problem [Parfit] |
1391 | Concern for our own lives isn't the source of belief in identity, it is the result of it [Parfit] |
5518 | It doesn't matter whether I exist with half my components replaced (any more than an audio system) [Parfit] |
9762 | We should focus less on subjects of experience, and more on the experiences themselves [Parfit] |
15886 | Science rests on the principle that nature is a hierarchy of natural kinds [Harré] |
15864 | Classification is just as important as laws in natural science [Harré] |
15865 | Newton's First Law cannot be demonstrated experimentally, as that needs absence of external forces [Harré] |
15862 | Laws can come from data, from theory, from imagination and concepts, or from procedures [Harré] |
15870 | Are laws of nature about events, or types and universals, or dispositions, or all three? [Harré] |
15871 | Are laws about what has or might happen, or do they also cover all the possibilities? [Harré] |
15876 | Maybe laws of nature are just relations between properties? [Harré] |
15860 | We take it that only necessary happenings could be laws [Harré] |
15872 | Must laws of nature be universal, or could they be local? [Harré] |
15867 | Laws describe abstract idealisations, not the actual mess of nature [Harré] |
15892 | Laws of nature state necessary connections of things, events and properties, based on models of mechanisms [Harré] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
15875 | In counterfactuals we keep substances constant, and imagine new situations for them [Harré] |