Philosophy Lexicon of Arguments

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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 54
Non-existence / truth / quantification / Field: if the quantified object does not exist, every statement with a existential quantifier is wrong - and every statement with a universal quantifier is trivially true. - ((s)talking of mathematical entities we do not have a problem with empty names). - ((s) universal statements are true for the conditional "if there are mathematical entities, then ..") - Mathematics / Field: if you wanted to keep only the true statements thereafter, mathematics would be uninteresting.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


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Ed. Martin Schulz, access date 2017-05-23