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

David Wiggins on Negation - Dictionary of Arguments

II 295
Inner/outer negation/Brian Medlin: E.g. paradox of movement - Problem: to choose between the last moment of rest and the first movement (two Dedekind cuts) - 1. "not moving rrr or rr (followed or led or both: of rest) 2. "it is not the case that x was moving: not rbr - 3. x was moving: only bb or bbb - this is a good example because no meaningless names.
II 299
Inner/outer negation/Wiggins: the problem: (distinguishing between final rest/first movement) appears in a simple language elsewhere, even if one has avoided "is in motion" - instead formula with "satisfies": "at which point did it stopped being true that "not (x moved)" even though x itself still does not move?" - No solution: intuitionistic, sentence of the excluded third: then a problem in the meta language: between predicate negation and sentence negation - Standard solution for single negation in object language/meta language (+) - Problem: it does not explain why it is attractive to make the difference: a) it can be true that it is not the case, that El Dorado is located in Venezuela - and b) not true that El Dorado is not-in-Venezuela (dashes) - this difference of predicate modification is not made clear in the modal logic.
II 300
Solution: uniform functor of predicates on predicates, long and short range, both forms derivable apart - semantically different interpretations, to build syntactically distinguishable structures - predicate negation: here the functor "no" leads from the predicate to its complement.
II 301
Sentence negation: here the functor leads from the predicate to predicate, e.g. from the universal predicate "lx (Socrates is bald)" (assuming he was bald) - to zero predicate "not[lx (Socrates is bald)])".
II 301
Necessary/Wiggins: analog to inner/outer negation: Tradition: to blurr difference after the first method: E.g. "necessarily Socrates is a human" and "Socrates is necessarily a human" - Wiggins pro second method -> Definition satisfaction for sentences with "necessaary": Wiggins pro existence as necessary property -> existential generalization.

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.

Wiggins I
D. Wiggins
Essays on Identity and Substance Oxford 2016

Wiggins II
David Wiggins
"The De Re ’Must’: A Note on the Logical Form of Essentialist Claims"
Truth and Meaning, G. Evans/J. McDowell, Oxford 1976

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