84 ideas
| 12027 | There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
| 15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
| 15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
| 15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
| 15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
| 15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
| 15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
| 12005 | The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
| 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] |
| 15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
| 12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
| 15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
| 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] |
| 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] |
| 12023 | Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G] |
| 12017 | In all instances of identity, there must be some facts to ensure the identity [Forbes,G] |
| 12024 | If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G] |
| 11885 | Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P] |
| 12014 | An individual essence is a set of essential properties which only that object can have [Forbes,G] |
| 12015 | Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G] |
| 12013 | Essential properties depend on a category, and perhaps also on particular facts [Forbes,G] |
| 12012 | Essential properties are those without which an object could not exist [Forbes,G] |
| 12022 | Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G] |
| 12025 | Artefacts have fuzzy essences [Forbes,G] |
| 12020 | An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G] |
| 11888 | Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P] |
| 12003 | De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G] |
| 12028 | De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G] |
| 12008 | Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G] |
| 12009 | The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G] |
| 12007 | Possible worlds are points of logical space, rather like other times than our own [Forbes,G] |
| 12011 | Transworld identity concerns the limits of possibility for ordinary things [Forbes,G] |
| 12016 | The problem of transworld identity can be solved by individual essences [Forbes,G] |
| 12004 | Counterpart theory is not good at handling the logic of identity [Forbes,G] |
| 12021 | Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G] |
| 12029 | We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |