14 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. |
| 15567 | Some events involve no change; they must, because causal histories involve unchanges [Lewis] |
| Full Idea: Not all events involve change. We cannot afford to count the unchanges as nonevents, for the unchanges may be needed to complete causal histories. | |
| From: David Lewis (Events [1986], VI) | |
| A reaction: You end up calling non-changes 'events' if you commit to a simplistic theory that all causal histories consist of events. Why not allow conditions as well as events? Lewis concedes that he may be abusing language. |
| 15561 | The events that suit semantics may not be the events that suit causation [Lewis] |
| Full Idea: There is no guarantee that events made for semantics are the same as events that are causes and effects. | |
| From: David Lewis (Events [1986], I) | |
| A reaction: This little cri de couer could be a motto for a huge amount of analytic philosophy, which (for some odd reason) thought that mathematics, logic, set theory and formal semantics were good tools for explaining nature. |
| 15565 | Events have inbuilt essences, as necessary conditions for their occurrence [Lewis] |
| Full Idea: Events have their essences built in, in the form of necessary conditions for their occurrence. | |
| From: David Lewis (Events [1986], III) | |
| A reaction: Revealing. He thinks the essence of an event is something which precedes the event. I take it as obvious that if an event has an essence, it will be some features of the event that occur in it and during it. They need to be intrinsic. |
| 15566 | Events are classes, and so there is a mereology of their parts [Lewis] |
| Full Idea: If events are classes, as I propose, then they have a mereology in the way that all classes do: the parts of a class are its subclasses. | |
| From: David Lewis (Events [1986], V) | |
| A reaction: Lewis says events are properties, which he regards as classes. It is not clear that events are strictly mereological. Could one happening be two events? Is WWII a simple sum of its parts? [see p.260] |
| 15564 | An event is a property of a unique space-time region [Lewis] |
| Full Idea: I propose to identify an event with a property, or in other words with a class, a unique spatio-temporal region corresponding to where that event occurs. | |
| From: David Lewis (Events [1986], II) | |
| A reaction: [I've run together two separate bits, on p.244 and 245] Lewis cites Montague's similar view, that events are properties of times. |
| 15563 | Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis] |
| Full Idea: Properties are abundant, numbering at least beth-3 for properties of individuals alone; they are suited to serve as semantic values of arbitrarily complex predicates and gerunds, and higher-order variables. (If there are universals, they are sparse). | |
| From: David Lewis (Events [1986], II n2) | |
| A reaction: To me this is an outrageous hijacking of the notion of property which is needed for explaining the natural world. He seems to be talking about predicates. He wants to leave me with his silly universals - well I don't want them, thank you. |
| 15562 | Causation is a general relation derived from instances of causal dependence [Lewis] |
| Full Idea: Causation is the ancestral of causal dependence: event c causes event e iff either e depends on c, or e depends on an intermediate event which in turn depends on c, or.... | |
| From: David Lewis (Events [1986], I) | |
| A reaction: This is Lewis making sure that we don't postulate some huge bogus thing called 'Causation' which is supposed to be in charge of Nature. Good point. |
| 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. |