19 ideas
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |