|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._____________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. |
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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._____________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.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980