3 ideas
| 9560 | S5 provides the correct logic for necessity in the broadly logical sense [Fine,K] |
| Full Idea: S5 provides the correct logic for necessity in the broadly logical sense. | |
| From: Kit Fine (Model Theory for Modal Logic I [1978], 151), quoted by Charles Chihara - A Structural Account of Mathematics | |
| A reaction: I have no view on this, but I am prejudiced in favour of the idea that there is a correct logic for such things, whichever one it may be. Presumably the fact that S5 has no restrictions on accessibility makes it more comprehensive and 'metaphysical'. |
| 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. |
| 7803 | Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle] |
| Full Idea: C.I.Lewis began his groundbreaking work in modal logic because he was concerned about the unreliability of the material conditional as a translation of 'If ... then' conditionals. | |
| From: report of C.I. Lewis (Symbolic Logic (with Langford) [1932]) by Rod Girle - Modal Logics and Philosophy 12.3 | |
| A reaction: Compare 'if this is square then it has four corners' with 'if it rains then our afternoon is ruined'. Different modalities seem to be involved. We even find that 'a square has four corners' will be materially implied if it rains! |