76 ideas
9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
13252 | Some truths have true negations [Beall/Restall] |
13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
19100 | Truth makes disagreements matter, or worth settling [Misak] |
19094 | For pragmatists the loftiest idea of truth is just a feature of what remains forever assertible [Misak] |
19099 | 'True' is used for emphasis, clarity, assertion, comparison, objectivity, meaning, negation, consequence... [Misak] |
19103 | 'That's true' doesn't just refer back to a sentence, but implies sustained evidence for it [Misak] |
19105 | Truth isn't a grand elusive property, if it is just the aim of our assertions and inquiries [Misak] |
19108 | Truth is proper assertion, but that has varying standards [Misak] |
19101 | Disquotation is bivalent [Misak] |
19106 | Disquotations says truth is assertion, and assertion proclaims truth - but what is 'assertion'? [Misak] |
19096 | Disquotationalism resembles a telephone directory [Misak] |
19098 | Deflating the correspondence theory doesn't entail deflating all the other theories [Misak] |
19104 | Deflationism isn't a theory of truth, but an account of its role in natural language [Misak] |
13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
13254 | A doesn't imply A - that would be circular [Beall/Restall] |
13255 | Relevant logic may reject transitivity [Beall/Restall] |
13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
10101 | Cartesian Product A x B: the set of all ordered pairs in which a∈A and b∈B [George/Velleman] |
10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
13253 | There are several different consequence relations [Beall/Restall] |
13240 | A sentence follows from others if they always model it [Beall/Restall] |
10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
10107 | Real numbers provide answers to square root problems [George/Velleman] |
9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
17902 | A successor is the union of a set with its singleton [George/Velleman] |
10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
10130 | Set theory can prove the Peano Postulates [George/Velleman] |
10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
19109 | The anti-realism debate concerns whether indefeasibility is a plausible aim of inquiry [Misak] |
13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |