display all the ideas for this combination of texts
4 ideas
| 13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
| Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments. | |
| From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2) |
| 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. |
| 13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
| Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things. | |
| From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1) |