9 ideas
11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by 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] |
13832 | Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking] |
10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
13165 | Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus] |
9569 | The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |