15 ideas
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| 11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
| 11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
| 11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| 13832 | Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking] |
| 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] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |