54 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
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] |
14333 | Dispositions and categorical properties are two modes of presentation of the same thing [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] |
14336 | Categorical predicates are those unconnected to functions [Mumford] |
14302 | A lead molecule is not leaden, and macroscopic properties need not be microscopically present [Mumford] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
14294 | Dispositions are attacked as mere regularities of events, or place-holders for unknown properties [Mumford] |
14316 | If dispositions have several categorical realisations, that makes the two separate [Mumford] |
14317 | I say the categorical base causes the disposition manifestation [Mumford] |
14310 | Dispositions are classifications of properties by functional role [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] |
14293 | Dispositions are ascribed to at least objects, substances and persons [Mumford] |
14298 | Dispositions can be contrasted either with occurrences, or with categorical properties [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] |
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] |
14320 | Subatomic particles may terminate explanation, if they lack structure [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] |
14324 | Ontology is unrelated to explanation, which concerns modes of presentation and states of knowledge [Mumford] |
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] |
14340 | It is a regularity that whenever a person sneezes, someone (somewhere) promptly coughs [Mumford] |
14341 | Dretske and Armstrong base laws on regularities between individual properties, not between events [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] |
15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |