3 ideas
| 9879 | NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett] |
| Full Idea: Quine's New Foundations system of set theory, devised with no model in mind, but on the basis of a hunch that a purely formal restriction on the comprehension axiom would block all contradictions. | |
| From: report of Willard Quine (New Foundations for Mathematical Logic [1937]) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: The point is that Quine (who had an ontological preference for 'desert landscapes') attempted to do without an ontological commitment to objects (and their subsequent models), with a purely formal system. Quine's NF is not now highly regarded. |
| 10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
| Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth. | |
| From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong. |
| 8141 | He that does evil has not seen God [John] |
| Full Idea: He that doeth evil hath not seen God. | |
| From: St John (25: Third Epistle of John [c.90], 11) | |
| A reaction: This gives God a role striking similar to Plato's Form of the Good. Plato thought the Good was prior to the gods, but he gives the good a quasi-religious role. I say we would only be inspired by the sight of God if we already had a moral sense. |