86 ideas
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 18019 | People have dreams which involve category mistakes [Magidor] |
| 17998 | Category mistakes are either syntactic, semantic, or pragmatic [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] |
| 18011 | Category mistakes seem to be universal across languages [Magidor] |
| 18016 | Two good sentences should combine to make a good sentence, but that might be absurd [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] |
| 18021 | Category mistakes are meaningful, because metaphors are meaningful category mistakes [Magidor] |
| 18030 | A good explanation of why category mistakes sound wrong is that they are meaningless [Magidor] |
| 18031 | If a category mistake has unimaginable truth-conditions, then it seems to be 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] |
| 18041 | Category mistakes suffer from pragmatic presupposition failure (which is not mere triviality) [Magidor] |
| 18055 | In 'two is green', 'green' has a presupposition of being coloured [Magidor] |
| 18056 | Category mistakes because of presuppositions still have a truth value (usually 'false') [Magidor] |
| 18057 | 'Numbers are coloured and the number two is green' seems to be acceptable [Magidor] |
| 18058 | Maybe the presuppositions of category mistakes are the abilities of things? [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] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| 17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 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] |
| 17999 | Strong compositionality says meaningful expressions syntactically well-formed are meaningful [Magidor] |
| 18000 | Weaker compositionality says meaningful well-formed sentences get the meaning from the parts [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] |
| 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] |
| 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] |
| 18027 | Metaphors as substitutes for the literal misses one predicate varying with context [Magidor] |