Psychology Dictionary of Arguments

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Negation, philosophy, logic: negation of a sentence. In logic, this is done by prefixing the negation symbol. Colloquially expressed by the word "not", which can be at different positions in the sentence. If the negation refers only to one sentence part, this must be made clear by the position, e.g. a predicate can be denied without negating the whole sentence. In logic, therefore, inner and outer negation is distinguished by the use of different symbols.

Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

Author Concept Summary/Quotes Sources

Maxwell J. Cresswell on Negation - Dictionary of Arguments

II 73
Double Negation/possible worlds/Proposition/indirect speech/Cresswell: Solution: if propositions are nothing but sets of possible worlds.
Then not-not-a means the same as a - (because of the complement formation of the set).
>Double negation, >Possible worlds.
Indirect speech: problem: if propositions should be something else than sets of possible worlds: then it may be that the speaker has said nothing at all.
Then the double negation is something else.
((s) "He has not said anything to this" does not mean that he rejects a.)
>Indirect speech.
II 73
Problem: but then the truth value differs against the logic.
>Truth values.
Solution/Cresswell: Hyperintensionality: hyperintensional propositions express (despite the same intension of a and not-not-a) different propositions.
((s) Then intension is unequal proposition).
Solution/Cresswell: Structural ambiguity: "saying" is sometimes applied to whole sentence, sometimes to parts.
VsHyperintensionality: before, the meaning of "not" was clear, it is now unclear.
II 74f
Double Negation/Cresswell: another problem: we can add to maximum consistent sets of propositions further inconsistent propositions. - The sets are then equal with respect to the consistent propositions and differ only in the inconsistent ones.
>maximum consistent.
N.B.: if there are only possible worlds (no impossible world), a and ~~a are equal.
Impossible world: if they are admitted, there is a difference between position and double negation. - that is because "~" is then no real negation.
>Impossible world.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Cr I
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988

M. J. Cresswell
Structured Meanings Cambridge Mass. 1984

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