37 ideas
13252 | Some truths have true negations [Beall/Restall] |
13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
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] |
13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
13254 | A doesn't imply A - that would be circular [Beall/Restall] |
13255 | Relevant logic may reject transitivity [Beall/Restall] |
13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
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13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |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] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
13253 | There are several different consequence relations [Beall/Restall] |
13240 | A sentence follows from others if they always model it [Beall/Restall] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
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] |
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] |