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3 ideas
| 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. |
| 6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
| Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38 | |
| A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc. |
| 15091 | Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker] |
| Full Idea: I favour restricting the term 'logical truth' to what logicians would count as such, excluding both analytic truths like 'Bachelors are unmarried' and Kripkean necessities like 'Gold is an element'. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], I) | |
| A reaction: I agree. There is a tendency to splash the phrases 'logical truth' and 'logical necessity around in vague ways. I take them to strictly arise out of the requirements of formal systems of logic. |