47 ideas
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] |
10405 | In the iterative conception of sets, they form a natural hierarchy [Swoyer] |
9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
10407 | Logical Form explains differing logical behaviour of similar sentences [Swoyer] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [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] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [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] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic 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] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
10421 | Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer] |
10410 | Anti-realists can't explain different methods to measure distance [Swoyer] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
10416 | Can properties have parts? [Swoyer] |
10399 | If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer] |
10417 | There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer] |
10413 | The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer] |
10402 | Various attempts are made to evade universals being wholly present in different places [Swoyer] |
10400 | Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer] |
10403 | If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer] |
9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
10406 | One might hope to reduce possible worlds to properties [Swoyer] |
10404 | Extreme empiricists can hardly explain anything [Swoyer] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
10408 | Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer] |
10409 | Research suggests that concepts rely on typical examples [Swoyer] |
10401 | The F and G of logic cover a huge range of natural language combinations [Swoyer] |
10420 | Maybe a proposition is just a property with all its places filled [Swoyer] |
10412 | If laws are mere regularities, they give no grounds for future prediction [Swoyer] |
10411 | Two properties can have one power, and one property can have two powers [Swoyer] |