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Full Idea
The truth-grounds of '¬A' are precisely those possibilities that are incompatible with any truth-ground of A.
Gist of Idea
The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 7.1)
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.185
A Reaction
This is Rumfitt's proposal for the semantics of 'not', based on the central idea of a possibility, rather than a possible world. The incompatibility tracks back to an absence of shared grounding.
Related Idea
Idea 18828 If two possibilities can't share a determiner, they are incompatible [Rumfitt]
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| 1705 | It doesn't have to be the case that in opposed views one is true and the other false [Aristotle] |
| 12368 | Negation takes something away from something [Aristotle] |
| 16491 | If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell] |
| 12594 | If one proposition negates the other, which is the negative one? [Harman] |
| 12338 | We must either assert or deny any single predicate of any single subject [Badiou] |
| 19005 | Not-A is too strong to just erase an improper assertion, because it actually reverses A [Yablo] |
| 18906 | Negating a predicate term and denying its unnegated version are quite different [Engelbretsen] |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| 18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |