10 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. |
| 16025 | If things change they become different - but then no one thing undergoes the change! [Gallois] |
| Full Idea: If things really change, there can't literally be one thing before and after the change. However, if there isn't one thing before and after the change, then no thing has really undergone any change. | |
| From: André Gallois (Identity over Time [2011], Intro) | |
| A reaction: [He cites Copi for this way of expressing the problem of identity through change] There is an obvious simple ambiguity about 'change' in ordinary English. A change of property isn't a change of object. Painting a red ball blue isn't swapping it. |
| 16026 | 4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois] |
| Full Idea: We have four versions of Four-Dimensionalism: the relativistic view that time is space-like; a persisting thing is identical with its history (so objects are events); past and future are equally real; or (Lewis) things extend in time, with temporal parts. | |
| From: André Gallois (Identity over Time [2011], §2.5) | |
| A reaction: Broad proposed the second one. I prefer 3-D: at any given time a thing is wholly present. At another time it is wholly present despite having changed. It is ridiculous to think that small changes destroy identity. We acquire identity by dying?? |
| 16027 | If two things are equal, each side involves a necessity, so the equality is necessary [Gallois] |
| Full Idea: The necessity of identity: a=b; □(a=a); so something necessarily = a; so something necessarily must equal b; so □(a=b). [A summary of the argument of Marcus and Kripke] | |
| From: André Gallois (Identity over Time [2011], §3) | |
| A reaction: [Lowe 1982 offered a response] The conclusion seems reasonable. If two things are mistakenly thought to be different, but turn out to be one thing, that one thing could not possibly be two things. In no world is one thing two things! |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |