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19. Language / F. Communication / 3. Denial

[stating something while rejecting its truth]

10 ideas
Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind]
     Full Idea: Prodicus insists that contradiction is impossible, since if two people are contradicting each other, they cannot both be speaking of the same fact. Only the one who is speaking the truth is speaking of facts as they are; the other does not speak facts.
     From: report of Prodicus (fragments/reports [c.423 BCE]) by Didymus the Blind - Commentary on Ecclesiastes (frags)
     A reaction: cf. Kant's 100 thalers example
It doesn't have to be the case that in opposed views one is true and the other false [Aristotle]
     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.
     From: Aristotle (On Interpretation [c.330 BCE], 19a39)
     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.
Negation takes something away from something [Aristotle]
     Full Idea: The part of a contradictory pair which says something of something is an affirmation; the part which takes something from something is a negation.
     From: Aristotle (Posterior Analytics [c.327 BCE], 72a14)
     A reaction: So affirmation is predication about an object ['Fa'], and negation is denial of predication. We have a scope problem: there is nothing which is F [¬∃x(Fx)], or there is a thing which is not-F [∃x(¬Fx)]. Aristotle seems to mean the latter.
If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell]
     Full Idea: We can reintroduce 'not' by a definition: the words 'this is not blue' are defined as expressing disbelief in what is expressed by the words 'this is blue'. In this way the need of 'not' as an indefinable constituent of facts is avoided.
     From: Bertrand Russell (Human Knowledge: its scope and limits [1948], 9)
     A reaction: This is part of Russell's programme of giving a psychological account of logical connectives. See other ideas from his 1940 and 1948 works. He observes that disbelief is a state just as positive as belief. I love it.
If one proposition negates the other, which is the negative one? [Harman]
     Full Idea: A relation of negation might hold between two beliefs without there being anything that determines which belief is the negative one.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.4)
     A reaction: [He attributes this thought to Brian Loar] This seems to give us a reason why we need a semantics for a logic, and not just a structure of inferences and proofs.
We must either assert or deny any single predicate of any single subject [Badiou]
     Full Idea: There can be nothing intermediate to an assertion and a denial. We must either assert or deny any single predicate of any single subject.
     From: Alain Badiou (Briefings on Existence [1998], 1011b24)
     A reaction: The first sentence seems to be bivalence, and the second sentence excluded middle.
Not-A is too strong to just erase an improper assertion, because it actually reverses A [Yablo]
     Full Idea: The idea that negation is, or can be, a cancellation device raises an interesting question. What does one do to wipe the slate clean after an improper assertion? Not-A is too strong; it reverses our stand on A rather than nullifying it.
     From: Stephen Yablo (Aboutness [2014], 09.8)
     A reaction: [He is discussing a remark of Strawson 1952] It seems that 'not' has two meanings or uses: a weak use of 'nullifying' an assertion, and a strong use of 'reversing' an assertion. One could do both: 'that's not right; in fact, it's just the opposite'.
Negating a predicate term and denying its unnegated version are quite different [Engelbretsen]
     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'.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 2)
     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.
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
     Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
     From: Ian Rumfitt ("Yes" and "No" [2000], IV)
     A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).
The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt]
     Full Idea: The truth-grounds of '¬A' are precisely those possibilities that are incompatible with any truth-ground of A.
     From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.1)
     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.