display all the ideas for this combination of texts
3 ideas
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3) |
| 21668 | Epicurus rejected excluded middle, because accepting it for events is fatalistic [Epicurus, by Cicero] |
| Full Idea: Epicurus said that not every proposition is either true or false. ...Epicurus was afraid that if he admits that every proposition is true or false he will also have to admit that all events are caused by fate (if they are so from all eternity). | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 10.21 | |
| A reaction: Epicurus proposed his 'swerve' in the movements of atoms to avoid this fatalism. Epicurus is agreeing with Aristotle, who did not accept excluded middle for a future contingent sea-fight. |
| 21676 | Epicureans say disjunctions can be true whiile the disjuncts are not true [Epicurus, by Cicero] |
| Full Idea: Epicureans make the impudent assertion that disjunctions consisting of contrary propositions are true, but that the statements contained in the propositions are neither of them true. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 16.36 | |
| A reaction: Is that 'it is definitely one or the other, but we haven't a clue which one'? Seems to fit speculations about Goldbach's Conjecture. It doesn't sound terribly impudent to me. Or is it the crazy 'It's definitely one of them, but it's neither of them'? |