2014 | Logical Consequence |
2 | p.31 | 18751 | Natural language includes connectives like 'because' which are not truth-functional |
4 | p.36 | 18753 | An ontologically secure semantics for predicate calculus relies on sets |
4 | p.36 | 18754 | Logically valid sentences are analytic truths which are just true because of their logical words |
4 | p.36 | 18755 | Validity is explained as truth in all models, because that relies on the logical terms |
5 | p.40 | 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs |
6 | p.42 | 18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term |
7 | p.45 | 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic |
7 | p.47 | 18761 | Second-order variables need to range over more than collections of first-order objects |
8 | p.50 | 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true |