50 ideas
| 14480 | Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson] |
| 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] |
| 14471 | Analytical entailments arise from combinations of meanings and inference rules [Thomasson] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 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] |
| 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] |
| 14493 | Existence might require playing a role in explanation, or in a causal story, or being composed in some way [Thomasson] |
| 14491 | Rival ontological claims can both be true, if there are analytic relationships between them [Thomasson] |
| 14489 | Theories do not avoid commitment to entities by avoiding certain terms or concepts [Thomasson] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 14485 | Ordinary objects may be not indispensable, but they are nearly unavoidable [Thomasson] |
| 14487 | The simple existence conditions for objects are established by our practices, and are met [Thomasson] |
| 21651 | It is analytic that if simples are arranged chair-wise, then there is a chair [Thomasson, by Hofweber] |
| 14467 | Ordinary objects are rejected, to avoid contradictions, or for greater economy in thought [Thomasson] |
| 14479 | To individuate people we need conventions, but conventions are made up by people [Thomasson] |
| 14486 | Eliminativists haven't found existence conditions for chairs, beyond those of the word 'chair' [Thomasson] |
| 14481 | Wherever an object exists, there are intrinsic properties instantiating every modal profile [Thomasson] |
| 14482 | If the statue and the lump are two objects, they require separate properties, so we could add their masses [Thomasson] |
| 14483 | Given the similarity of statue and lump, what could possibly ground their modal properties? [Thomasson] |
| 14476 | Identity claims between objects are only well-formed if the categories are specified [Thomasson] |
| 14477 | Identical entities must be of the same category, and meet the criteria for the category [Thomasson] |
| 14478 | Modal Conventionalism says modality is analytic, not intrinsic to the world, and linguistic [Thomasson] |
| 14466 | A chief task of philosophy is making reflective sense of our common sense worldview [Thomasson] |
| 19727 | Reliabilist knowledge is evidence based belief, with high conditional probability [Comesaña] |
| 19725 | In a sceptical scenario belief formation is unreliable, so no beliefs at all are justified? [Comesaña] |
| 19726 | How do we decide which exact process is the one that needs to be reliable? [Comesaña] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 14475 | How can causal theories of reference handle nonexistence claims? [Thomasson] |
| 14474 | Pure causal theories of reference have the 'qua problem', of what sort of things is being referred to [Thomasson] |
| 14488 | Analyticity is revealed through redundancy, as in 'He bought a house and a building' [Thomasson] |