display all the ideas for this combination of texts
4 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. |
| 15525 | Plural quantification lacks a complete axiom system [Lewis] |
| Full Idea: There is an irremediable lack of a complete axiom system for plural quantification. | |
| From: David Lewis (Parts of Classes [1991], 4.7) |
| 15518 | I like plural quantification, but am not convinced of its connection with second-order logic [Lewis] |
| Full Idea: I agree fully with Boolos on substantive questions about plural quantification, though I would make less than he does of the connection with second-order logic. | |
| From: David Lewis (Parts of Classes [1991], 3.2 n2) | |
| A reaction: Deep matters, but my inclination is to agree with Lewis, as I have never been able to see why talk of plural quantification led straight on to second-order logic. A plural is just some objects, not some higher-order entity. |