Philosophy Lexicon of Arguments

Non-existence, philosophy: non-existence is not simply expressible for the classical predicate logic which attributes properties through quantification in the form of (Ex)(Fx) "There is at least one x, with the property F" (in short "There is at least one F"), since existence is not a property. The form "There is at least one x that does not exist" is contradictory. See also existence predicate, "There is", existence, unicorn example, pegasus example, round square, proof of God's existence.
Author Item Excerpt Meta data

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I 193
Non-existence/Empty Names/Unicorn/Solution/Moore/Millikan: Moore introduced "concepts" so that names such as "Pegasus" have something they can correspond to.
Solution/Frege: "meaning" to which referentially equivalent terms with different meaning can correspond to.
Solution/Carnap/Millikan: E.g. "Pegasus": here we are talking about our linguistic usage or of the words, not the object. ((s) semantic rise).
Identity/Existence/Sentence/Representation/Millikan: Thesis: neither sentences that contain the "is" of existence, nor the "is" of identity are representations!
Identity statement/Millikan: no representation.
Existence assertion/existence statement/Existence/Millikan: are no representation.
Intentional icon: however, identity statements and existence statements are intentional icons. However, they are more primitive icons than representations.
Identity Theorem/Existence/Millikan: although they must map in accordance with mapping rules to perform their eigenfunction,...
I 194
...the variants of the facts in the world which they map do not have to be identified.
These sentences are icons of the relations of words to the world.
That is, we do not translate them into inner icons of facts.
I 203
Moved use/move/disengaged/non-existence/Millikan: E.g: "x does not exist":
1. This is not a representation. (Also not e.g. "x exists").
2. It is not a referential use.

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 2017-05-23