9 ideas
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| Full Idea: Gentzen introduced a natural deduction calculus (NK) in 1934. | |
| From: report of Gerhard Gentzen (works [1938]) by Stephen Read - Thinking About Logic Ch.8 |
| 11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
| Full Idea: Gentzen argued that the inferential role of a logical constant constitutes its meaning. | |
| From: report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3 | |
| A reaction: Possibly inspired by Wittgenstein's theory of meaning as use? This idea was the target of Prior's famous connective 'tonk', which has the role of implying anything you like, proving sentences which are not logical consequences. |
| 11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
| Full Idea: The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions. | |
| From: Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8 | |
| A reaction: If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here? |
| 11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
| Full Idea: To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these. | |
| From: Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III | |
| A reaction: [1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives. |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic. | |
| From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5 | |
| A reaction: This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 20595 | You can't distribute goods from behind a veil, because their social meaning is unclear [Walzer, by Tuckness/Wolf] |
| Full Idea: Walzer says behind the veil of ignorance there would be no way to know how a particular good should be distributed, because we would not know the social meaning of the good in question. | |
| From: report of Michael Walzer (Spheres of Justice [1983]) by Tuckness,A/Wolf,C - This is Political Philosophy 4 'Communitarian' | |
| A reaction: Is Rawls actually proposing to decide details of distribution from behind the veil? There is just the maximin principle. What that means in practice would surely come once the society was under way. |
| 20592 | Complex equality restricts equalities from spilling over, like money influencing politics and law [Walzer, by Tuckness/Wolf] |
| Full Idea: Complex equality tries to keep advantages in one area (such as money) from translating into advantages in politics or before the law. | |
| From: report of Michael Walzer (Spheres of Justice [1983]) by Tuckness,A/Wolf,C - This is Political Philosophy 3 'Complex' | |
| A reaction: Put like that, Walzer's complex equality becomes very interesting, and pinpoints a major problem of our age, where discrepancies of wealth have become staggeringly large at the top end. |
| 20549 | Equality is complex, with different spheres of equality where different principles apply [Walzer, by Swift] |
| Full Idea: Michael Walzer argues for 'complex equality', saying different goods belong to different distributive 'spheres', each with its own distributive principles. | |
| From: report of Michael Walzer (Spheres of Justice [1983]) by Adam Swift - Political Philosophy (3rd ed) 3 'Egalitarian' | |
| A reaction: Sounds interesting. Equality seems to make different demands when it concerns basic food for survival, or fine wines. You can spend your money freely, but hording in a crisis is frowned on. |