40 ideas
16943 | Philosophy is continuous with science, and has no external vantage point [Quine] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
16949 | Klein summarised geometry as grouped together by transformations [Quine] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
16939 | Mass terms just concern spread, but other terms involve both spread and individuation [Quine] |
16948 | Once we know the mechanism of a disposition, we can eliminate 'similarity' [Quine] |
16945 | We judge things to be soluble if they are the same kind as, or similar to, things that do dissolve [Quine] |
16944 | Science is common sense, with a sophisticated method [Quine] |
16940 | Induction is just more of the same: animal expectations [Quine] |
16941 | Induction relies on similar effects following from each cause [Quine] |
16933 | Grue is a puzzle because the notions of similarity and kind are dubious in science [Quine] |
16934 | General terms depend on similarities among things [Quine] |
16938 | To learn yellow by observation, must we be told to look at the colour? [Quine] |
8486 | Standards of similarity are innate, and the spacing of qualities such as colours can be mapped [Quine] |
16947 | Similarity is just interchangeability in the cosmic machine [Quine] |
16932 | Projectible predicates can be universalised about the kind to which they refer [Quine] |
5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |
7375 | Quine probably regrets natural kinds now being treated as essences [Quine, by Dennett] |
16935 | If similarity has no degrees, kinds cannot be contained within one another [Quine] |
16936 | Comparative similarity allows the kind 'colored' to contain the kind 'red' [Quine] |
16937 | You can't base kinds just on resemblance, because chains of resemblance are a muddle [Quine] |
16942 | It is hard to see how regularities could be explained [Quine] |