display all the ideas for this combination of texts
3 ideas
| 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. |
| 21539 | Excluded middle can be stated psychologically, as denial of p implies assertion of not-p [Russell] |
| Full Idea: The law of excluded middle may be stated in the form: If p is denied, not-p must be asserted; this form is too psychological to be ultimate, but the point is that it is significant and not a mere tautology. | |
| From: Bertrand Russell (Meinong on Complexes and Assumptions [1904], p.41) | |
| A reaction: 'Psychology' is, of course, taboo, post-Frege, though I think it is interesting. Stated in this form the law looks more false than usual. I can be quite clear than p is unacceptable, but unclear about its contrary. |
| 18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
| Full Idea: Tarski showed that the only binary relations invariant under arbitrary permutations are the universal relation, the empty relation, identity and non-identity, thus giving us a reason to include '=' among the logical terms. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 6 | |
| A reaction: Tarski was looking for a criterion to distinguish logical from non-logical terms, since his account of logical validity depended on it. This idea lies behind whether a logic is or is not specified to be 'with identity' (i.e. using '='). |