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2 ideas
19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
Full Idea: A plausible account is that the syntactic notion of consequence is for positive results, that some form of argument is valid; the semantic notion is required for negative results, that some argument is invalid, because a counterexample can be found. | |
From: Michael Dummett (The Justification of Deduction [1973], p.292) | |
A reaction: This rings true for the two strategies of demonstration, the first by following the rules in steps, the second by using your imagination (or a tableau) to think up problems. |
8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true. |