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Full Idea
It is not necessary that of every affirmation and opposite negation one should be true and the other false. For what holds for things that are does not hold for things that are not but may possibly be or not be.
Gist of Idea
It doesn't have to be the case that in opposed views one is true and the other false
Source
Aristotle (On Interpretation [c.330 BCE], 19a39)
Book Ref
Aristotle: 'Categories and De Interpretatione', ed/tr. Ackrill,J.R. [OUP 1963], p.53
A Reaction
Thus even if Bivalence holds, and the only truth-values are T and F, it doesn't follow that Excluded Middle holds, which says that every proposition must have one of those two values.
| 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] |