54 ideas
| 16440 | I don't think Lewis's cost-benefit reflective equilibrium approach offers enough guidance [Stalnaker] |
| 16468 | Non-S5 can talk of contingent or necessary necessities [Stalnaker] |
| 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] |
| 16449 | In modal set theory, sets only exist in a possible world if that world contains all of its members [Stalnaker] |
| 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] |
| 16464 | We regiment to get semantic structure, for evaluating arguments, and understanding complexities [Stalnaker] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 16465 | In 'S was F or some other than S was F', the disjuncts need S, but the whole disjunction doesn't [Stalnaker] |
| 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] |
| 16434 | Some say what exists must do so, and nothing else could possible exist [Stalnaker] |
| 16439 | A nominalist view says existence is having spatio-temporal location [Stalnaker] |
| 22014 | Consciousness is not entirely representational, because there are pains, and the self [Schulze, by Pinkard] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 16443 | Properties are modal, involving possible situations where they are exemplified [Stalnaker] |
| 16471 | I accept a hierarchy of properties of properties of properties [Stalnaker] |
| 16452 | Dispositions have modal properties, of which properties things would have counterfactually [Stalnaker] |
| 16467 | 'Socrates is essentially human' seems to say nothing could be Socrates if it was not human [Stalnaker] |
| 16453 | The bundle theory makes the identity of indiscernibles a necessity, since the thing is the properties [Stalnaker] |
| 16466 | Strong necessity is always true; weak necessity is cannot be false [Stalnaker] |
| 16438 | Necessity and possibility are fundamental, and there can be no reductive analysis of them [Stalnaker] |
| 16436 | Modal concepts are central to the actual world, and shouldn't need extravagant metaphysics [Stalnaker] |
| 16433 | Given actualism, how can there be possible individuals, other than the actual ones? [Stalnaker] |
| 16437 | Possible worlds are properties [Stalnaker] |
| 16444 | Possible worlds don't reduce modality, they regiment it to reveal its structure [Stalnaker] |
| 16445 | I think of worlds as cells (rather than points) in logical space [Stalnaker] |
| 16454 | Modal properties depend on the choice of a counterpart, which is unconstrained by metaphysics [Stalnaker] |
| 16450 | Anti-haecceitism says there is no more to an individual than meeting some qualitative conditions [Stalnaker] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 16474 | How can we know what we are thinking, if content depends on something we don't know? [Stalnaker] |
| 16461 | We still lack an agreed semantics for quantifiers in natural language [Stalnaker] |
| 16448 | Possible world semantics may not reduce modality, but it can explain it [Stalnaker] |
| 16442 | I take propositions to be truth conditions [Stalnaker] |
| 16447 | A theory of propositions at least needs primitive properties of consistency and of truth [Stalnaker] |
| 16446 | Propositions presumably don't exist if the things they refer to don't exist [Stalnaker] |