75 ideas
| 6396 | A sentence is held true because of a combination of meaning and belief [Davidson] |
| 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] |
| 14334 | Modest realism says there is a reality; the presumptuous view says we can accurately describe it [Mumford] |
| 14306 | Anti-realists deny truth-values to all statements, and say evidence and ontology are inseparable [Mumford] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 14333 | Dispositions and categorical properties are two modes of presentation of the same thing [Mumford] |
| 14336 | Categorical predicates are those unconnected to functions [Mumford] |
| 14315 | Categorical properties and dispositions appear to explain one another [Mumford] |
| 14332 | There are four reasons for seeing categorical properties as the most fundamental [Mumford] |
| 14302 | A lead molecule is not leaden, and macroscopic properties need not be microscopically present [Mumford] |
| 14294 | Dispositions are attacked as mere regularities of events, or place-holders for unknown properties [Mumford] |
| 14310 | Dispositions are classifications of properties by functional role [Mumford] |
| 14317 | I say the categorical base causes the disposition manifestation [Mumford] |
| 14316 | If dispositions have several categorical realisations, that makes the two separate [Mumford] |
| 14313 | All properties must be causal powers (since they wouldn't exist otherwise) [Mumford] |
| 14318 | Intrinsic properties are just causal powers, and identifying a property as causal is then analytic [Mumford] |
| 14298 | Dispositions can be contrasted either with occurrences, or with categorical properties [Mumford] |
| 14293 | Dispositions are ascribed to at least objects, substances and persons [Mumford] |
| 14326 | Unlike categorical bases, dispositions necessarily occupy a particular causal role [Mumford] |
| 14314 | If dispositions are powers, background conditions makes it hard to say what they do [Mumford] |
| 14325 | Maybe dispositions can replace powers in metaphysics, as what induces property change [Mumford] |
| 14312 | Orthodoxy says dispositions entail conditionals (rather than being equivalent to them) [Mumford] |
| 14291 | Dispositions are not just possibilities - they are features of actual things [Mumford] |
| 14299 | There could be dispositions that are never manifested [Mumford] |
| 14323 | If every event has a cause, it is easy to invent a power to explain each case [Mumford] |
| 14328 | Traditional powers initiate change, but are mysterious between those changes [Mumford] |
| 14331 | Categorical eliminativists say there are no dispositions, just categorical states or mechanisms [Mumford] |
| 14295 | Many artefacts have dispositional essences, which make them what they are [Mumford] |
| 14309 | Truth-functional conditionals can't distinguish whether they are causal or accidental [Mumford] |
| 14311 | Dispositions are not equivalent to stronger-than-material conditionals [Mumford] |
| 11145 | Having a belief involves the possibility of being mistaken [Davidson] |
| 6397 | The concept of belief can only derive from relationship to a speech community [Davidson] |
| 14319 | Nomothetic explanations cite laws, and structural explanations cite mechanisms [Mumford] |
| 14342 | General laws depend upon the capacities of particulars, not the other way around [Mumford] |
| 14322 | If fragile just means 'breaks when dropped', it won't explain a breakage [Mumford] |
| 14337 | Maybe dispositions can replace the 'laws of nature' as the basis of explanation [Mumford] |
| 14343 | To avoid a regress in explanations, ungrounded dispositions will always have to be posited [Mumford] |
| 14320 | Subatomic particles may terminate explanation, if they lack structure [Mumford] |
| 14324 | Ontology is unrelated to explanation, which concerns modes of presentation and states of knowledge [Mumford] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 6392 | Thought depends on speech [Davidson] |
| 6393 | A creature doesn't think unless it interprets another's speech [Davidson] |
| 11144 | Concepts are only possible in a language community [Davidson] |
| 6395 | An understood sentence can be used for almost anything; it isn't language if it has only one use [Davidson] |
| 6394 | The pattern of sentences held true gives sentences their meaning [Davidson] |
| 14344 | Natural kinds, such as electrons, all behave the same way because we divide them by dispositions [Mumford] |
| 14338 | In the 'laws' view events are basic, and properties are categorical, only existing when manifested [Mumford] |
| 14339 | Without laws, how can a dispositionalist explain general behaviour within kinds? [Mumford] |
| 14341 | Dretske and Armstrong base laws on regularities between individual properties, not between events [Mumford] |
| 14340 | It is a regularity that whenever a person sneezes, someone (somewhere) promptly coughs [Mumford] |
| 14345 | The necessity of an electron being an electron is conceptual, and won't ground necessary laws [Mumford] |
| 14307 | Some dispositions are so far unknown, until we learn how to manifest them [Mumford] |