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Full Idea
There is a crucial distinction in term logic between affirming a negated predicate term of some subject and denying the unnegated version of that term of that same subject. We must distinguish 'X is non-P' from 'X is not P'.
Gist of Idea
Negating a predicate term and denying its unnegated version are quite different
Source
George Engelbretsen (Trees, Terms and Truth [2005], 2)
Book Ref
'The Old New Logic', ed/tr. Oderberg,David S. [MIT 2005], p.32
A Reaction
The first one affirms something about X, but the second one just blocks off a possible description of X. 'X is non-harmful' and 'X is not harmful' - if X had ceased to exist, the second would be appropriate and the first wouldn't? I'm guessing.
Related Ideas
Idea 18903 Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen]
Idea 18904 'Predicable' terms come in charged pairs, with one the negation of the other [Sommers, by Engelbretsen]
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] |