16 ideas
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| 14187 | If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read] |
| 14188 | Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read] |
| 14182 | If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read] |
| 14183 | Maybe arguments are only valid when suppressed premises are all stated - but why? [Read] |
| 14184 | In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read] |
| 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] |
| 14186 | Logical connectives contain no information, but just record combination relations between facts [Read] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| 14185 | Conditionals are just a shorthand for some proof, leaving out the details [Read] |