101 ideas
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 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] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18040 | Intensional logic maps logical space, showing which predicates are compatible or incompatible [Magidor] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 10009 | Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| 17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| 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] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 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] |