85 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] |
| 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] |
| 18016 | Two good sentences should combine to make a good sentence, but that might be absurd [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] |
| 18040 | Intensional logic maps logical space, showing which predicates are compatible or incompatible [Magidor] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 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] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |