Philosophy Lexicon of Arguments

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 Item Excerpt Meta data

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I 221
Not/"not"/Tractatus/Wittgenstein/Millikan: Thesis: "not" is an operator who operates on the rest of the sentence by changing the sense of the entire sentence.
Negative sentence/negation/existence/Millikan: negative sentences cannot have non-existent facts as the real value.
Reason: Negative facts do not have causal forces that could play a role in a normal explanation.
Negative sentence/Millikan: we could assume that negative sentences are not representations. E.g. "not-p" is called "the fact that -p does not exist" In a similar way, Wittgenstein has understood it as well.
N.B.: we had said above, that existence sentences are not representations.
Image theory/picture theory/Tractatus/Wittgenstein/Millikan: but understood sentences of the form "x
does not exist" are understood in this way as to map a non-existent fact. Then the variable
"x" in "x does not exist" does not go via names of single objects (objects, elementary objects) but via representations of possible states (possible facts).
Meaning/Non-existence/Negation/Wittgenstein/Millikan: so it was possible for him to maintain that sentences of the form "x does not exist" have a meaning ((s)> Meinong).
Millikan: in our terminology it means that they are representations (MillikanVs).
I 222
And at the same time, he could claim that the most basic elements of all propositions correspond to real objects.
N.B.: that made it possible that he could say "x does not exist" is always equivalent to a sentence of the form "not-p".
Millikan: could we not maintain at least half of this equivalence? The from "not-p" to "that -p does not exist"?
MillikanVsWittgenstein: No, not even this we can do.
If Wittgenstein was right and "not-p" says "that -p does not exist," then that would mean for my position that negative sentences do not map world states and are not representations.
Millikan: instead, they would represent linguistic facts, "not-p" would then be an icon, but it does not represent, whereby a world state would have the sentence type "p" as a variant.
Protoreferent/Millikan. "p" would not be a representative of "not-p" but a protoreferent.
Question: would "not-p" be an icon of which the "p is false" ((s) linguistically) explicitly represented?
Vs: then "not" would be no operator anymore!
Not/Negation/Operator/Wittgenstein/Millikan: i.e. The mapping rule for "not-p" is a function of the mapping rule for "p".
1. If "not" is not an operator, it might happen that someone does not understand the meaning of "p," but still the sense of "not-p" absurd.
2. If "not-p" says "that -p does not exist", "not-p" must also be true if some variant in "p" is not fully determined, i.e. has no adapted meaning. E.g. "Pegasus was not a winged horse" e.g. "The present king of France is not bald" would be true sentences!
3. Certainly, it is the case that "'p' is false" at least maps (icons) that "p" has no real value. Correspondingly, "x does not exist" maps then the fact that "x" does not have referents.
N.B.: if "not-p" says "that -p does not exist" it still maps a negative fact. > Facts.
I 224
Opposite/Negative Sentence/Representation/Millikan: Thesis: negative sentences, whose opposites are normal representative sentences, must themselves represent positive facts.
I 224
Negation/stabilization function/not/representation/Millikan: what is the stabilization function of "not" in normal representing sentences? It is not needed to "erase" the rest of the sentence.
"Erase": sometimes occurs, but then it is called "Sorry" or "I did not mean that".
Negation/"not": its function is not to produce no believe. That would not be a function.
Eigenfunction: of "not" is relational. That is, it is a (mathematical) function of the eigenfunction of the sentence without "not".
Sentence: has the function of producing a belief. Likewise, a sentence with "not" has to produce something that has a potential benefit.
Negative sentence: perhaps it should eliminate a false belief? But that would be similar to "does not exist" works.
I 224
Negative sentence/"not"/imperative/Millikan: an imperative like "bring no dirt into the house" has very well a positive function.
E.g. if you do it anyway, it is not done with an excuse "I did not want it". For the command was not, to do it without purpose.
Not sufficient: "I did not intend it".
Correct: I intended not to do it.
Not sufficient: "I did not know I did it"
Correct: you have to know that you do not do it.
Not/imperative: here the usage is not parallel to the function of "does not exist".
I 257
Negative sentence/Millikan: a negative sentence maps a positive fact (world state), not the absence of a fact.

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.

Millk I
R. G. Millikan
Language, Thought, and Other Biological Categories: New Foundations for Realism Cambridge 1987

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Ed. Martin Schulz, access date 2017-06-23