56 ideas
16512 | Semantic facts are preferable to transcendental philosophical fiction [Wiggins] |
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
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] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
16523 | Realist Conceptualists accept that our interests affect our concepts [Wiggins] |
16524 | Conceptualism says we must use our individuating concepts to grasp reality [Wiggins] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
16526 | Animal classifications: the Emperor's, fabulous, innumerable, like flies, stray dogs, embalmed…. [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] |
16496 | Singling out extends back and forward in time [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] |
16509 | Natural kinds are well suited to be the sortals which fix substances [Wiggins] |
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] |
16503 | 'What is it?' gives the kind, nature, persistence conditions and identity over time of a thing [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] |
16517 | Priests prefer the working ship; antiquarians prefer the reconstruction [Wiggins] |
16497 | Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins] |
16502 | Identity is primitive [Wiggins] |
16498 | Identity cannot be defined, because definitions are identities [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] |
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] |
16525 | Our sortal concepts fix what we find in experience [Wiggins] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
16518 | We conceptualise objects, but they impinge on us [Wiggins] |
16511 | A 'conception' of a horse is a full theory of what it is (and not just the 'concept') [Wiggins] |
20713 | God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B] |