68 ideas
5486 | Essentialism says metaphysics can't be done by analysing unreliable language [Ellis] |
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] |
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] |
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] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [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] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
5468 | Properties are 'dispositional', or 'categorical' (the latter as 'block' or 'intrinsic' structures) [Ellis, by PG] |
5469 | The passive view of nature says categorical properties are basic, but others say dispositions [Ellis] |
5456 | Redness is not a property as it is not mind-independent [Ellis] |
5481 | Properties have powers; they aren't just ways for logicians to classify objects [Ellis] |
5458 | Nearly all fundamental properties of physics are dispositional [Ellis] |
4442 | Most thinkers now reject self-predication (whiteness is NOT white) so there is no Third Man problem [Armstrong] |
5443 | Kripke and others have made essentialism once again respectable [Ellis] |
5444 | 'Individual essences' fix a particular individual, and 'kind essences' fix the kind it belongs to [Ellis] |
5462 | Essential properties are usually quantitatively determinate [Ellis] |
5448 | 'Real essence' makes it what it is; 'nominal essence' makes us categorise it a certain way [Ellis] |
5477 | One thing can look like something else, without being the something else [Ellis] |
5479 | Scientific essentialists say science should define the limits of the possible [Ellis] |
5483 | Essentialists deny possible worlds, and say possibilities are what is compatible with the actual world [Ellis] |
5447 | Metaphysical necessities are true in virtue of the essences of things [Ellis] |
5476 | Essentialists say natural laws are in a new category: necessary a posteriori [Ellis] |
5478 | Imagination tests what is possible for all we know, not true possibility [Ellis] |
5482 | Possible worlds realism is only needed to give truth conditions for modals and conditionals [Ellis] |
5453 | Essentialists mostly accept the primary/secondary qualities distinction [Ellis] |
5466 | Primary qualities are number, figure, size, texture, motion, configuration, impenetrability and (?) mass [Ellis] |
5485 | Emeralds are naturally green, and only an external force could turn them blue [Ellis] |
5484 | Essentialists don't infer from some to all, but from essences to necessary behaviour [Ellis] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
5457 | Predicates assert properties, values, denials, relations, conventions, existence and fabrications [Ellis, by PG] |
5488 | Regularity theories of causation cannot give an account of human agency [Ellis] |
5489 | Humans have variable dispositions, and also power to change their dispositions [Ellis] |
5490 | Essentialism fits in with Darwinism, but not with extreme politics of left or right [Ellis] |
5472 | Natural kinds are of objects/substances, or events/processes, or intrinsic natures [Ellis] |
5471 | Essentialism says natural kinds are fundamental to nature, and determine the laws [Ellis] |
5446 | For essentialists two members of a natural kind must be identical [Ellis] |
5480 | The whole of our world is a natural kind, so all worlds like it necessarily have the same laws [Ellis] |
5445 | Essentialists regard inanimate objects as genuine causal agents [Ellis] |
5463 | Essentialists believe causation is necessary, resulting from dispositions and circumstances [Ellis] |
5491 | A general theory of causation is only possible in an area if natural kinds are involved [Ellis] |
5442 | For 'passivists' behaviour is imposed on things from outside [Ellis] |
5473 | The laws of nature imitate the hierarchy of natural kinds [Ellis] |
5474 | Laws of nature tend to describe ideal things, or ideal circumstances [Ellis] |
5475 | We must explain the necessity, idealisation, ontology and structure of natural laws [Ellis] |
5460 | Causal relations cannot be reduced to regularities, as they could occur just once [Ellis] |
5459 | Essentialists say dispositions are basic, rather than supervenient on matter and natural laws [Ellis] |
5461 | The essence of uranium is its atomic number and its electron shell [Ellis] |
5464 | For essentialists, laws of nature are metaphysically necessary, being based on essences of natural kinds [Ellis] |
5487 | Essentialism requires a clear separation of semantics, epistemology and ontology [Ellis] |