72 ideas
18019 | People have dreams which involve category mistakes [Magidor] |
17998 | Category mistakes are either syntactic, semantic, or pragmatic [Magidor] |
18011 | Category mistakes seem to be universal across languages [Magidor] |
18012 | Category mistakes as syntactic needs a huge number of fine-grained rules [Magidor] |
18013 | Embedded (in 'he said that…') category mistakes show syntax isn't the problem [Magidor] |
18021 | Category mistakes are meaningful, because metaphors are meaningful category mistakes [Magidor] |
18015 | The normal compositional view makes category mistakes meaningful [Magidor] |
18017 | If a category mistake is synonymous across two languages, that implies it is meaningful [Magidor] |
18031 | If a category mistake has unimaginable truth-conditions, then it seems to be meaningless [Magidor] |
18016 | Two good sentences should combine to make a good sentence, but that might be absurd [Magidor] |
18030 | A good explanation of why category mistakes sound wrong is that they are meaningless [Magidor] |
18032 | Category mistakes are neither verifiable nor analytic, so verificationism says they are meaningless [Magidor] |
18034 | Category mistakes play no role in mental life, so conceptual role semantics makes them meaningless [Magidor] |
18037 | Maybe when you say 'two is green', the predicate somehow fails to apply? [Magidor] |
18039 | If category mistakes aren't syntax failure or meaningless, maybe they just lack a truth-value? [Magidor] |
18058 | Maybe the presuppositions of category mistakes are the abilities of things? [Magidor] |
18041 | Category mistakes suffer from pragmatic presupposition failure (which is not mere triviality) [Magidor] |
18056 | Category mistakes because of presuppositions still have a truth value (usually 'false') [Magidor] |
18055 | In 'two is green', 'green' has a presupposition of being coloured [Magidor] |
18057 | 'Numbers are coloured and the number two is green' seems to be acceptable [Magidor] |
18059 | The presuppositions in category mistakes reveal nothing about ontology [Magidor] |
13520 | A 'tautology' must include connectives [Wolf,RS] |
13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
18040 | Intensional logic maps logical space, showing which predicates are compatible or incompatible [Magidor] |
13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
594 | Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle] |
18060 | We can explain the statue/clay problem by a category mistake with a false premise [Magidor] |
18020 | Propositional attitudes relate agents to either propositions, or meanings, or sentence/utterances [Magidor] |
18035 | Two sentences with different meanings can, on occasion, have the same content [Magidor] |
18018 | To grasp 'two' and 'green', must you know that two is not green? [Magidor] |
18008 | Generative semantics says structure is determined by semantics as well as syntactic rules [Magidor] |
18010 | 'John is easy to please' and 'John is eager to please' have different deep structure [Magidor] |
18053 | The semantics of a sentence is its potential for changing a context [Magidor] |
18000 | Weaker compositionality says meaningful well-formed sentences get the meaning from the parts [Magidor] |
17999 | Strong compositionality says meaningful expressions syntactically well-formed are meaningful [Magidor] |
18014 | Understanding unlimited numbers of sentences suggests that meaning is compositional [Magidor] |
18001 | Are there partial propositions, lacking truth value in some possible worlds? [Magidor] |
18036 | A sentence can be meaningful, and yet lack a truth value [Magidor] |
18051 | In the pragmatic approach, presuppositions are assumed in a context, for successful assertion [Magidor] |
18043 | The infelicitiousness of trivial truth is explained by uninformativeness, or a static context-set [Magidor] |
18042 | The infelicitiousness of trivial falsity is explained by expectations, or the loss of a context-set [Magidor] |
18047 | A presupposition is what makes an utterance sound wrong if it is not assumed? [Magidor] |
18048 | A test for presupposition would be if it provoked 'hey wait a minute - I have no idea that....' [Magidor] |
18049 | The best tests for presupposition are projecting it to negation, conditional, conjunction, questions [Magidor] |
18050 | If both s and not-s entail a sentence p, then p is a presupposition [Magidor] |
18054 | Why do certain words trigger presuppositions? [Magidor] |
18024 | One theory says metaphors mean the same as the corresponding simile [Magidor] |
18023 | Theories of metaphor divide over whether they must have literal meanings [Magidor] |
18025 | The simile view of metaphors removes their magic, and won't explain why we use them [Magidor] |
18026 | Maybe a metaphor is just a substitute for what is intended literally, like 'icy' for 'unemotional' [Magidor] |
18028 | Gricean theories of metaphor involve conversational implicatures based on literal meanings [Magidor] |
18029 | Non-cognitivist views of metaphor says there are no metaphorical meanings, just effects of the literal [Magidor] |
18022 | Metaphors tend to involve category mistakes, by joining disjoint domains [Magidor] |
18027 | Metaphors as substitutes for the literal misses one predicate varying with context [Magidor] |
2632 | Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero] |