|Existence, philosophy, logic: the fact that there is something to which properties can be attributed. That does not mean that something has to be given immediately or can be perceived by the senses. See also ontology, properties, predicates, existence statements, realism, quantification, ascription.|
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Necessary Existence/KantVs/Field: nothing can be negated with all its predicates, and nevertheless leave a contradiction. - (VsOntological proof of God) - Existence/Field: should not be part of the logic. - Therefore, mathematics cannot be reduced to logic. - Otherwise, too many properties would have to be assumed.
Semantic/syntactic/singular Term/Denotation/Ontology/FieldVsWright: it is not built into the syntax that, e.g. The singular term "4" denotes. - (i.e. that the number is an object). - Just as little as "God". - So syntax cannot be the criterion for existence.
Existence/Ontology/FieldVsWright: does not follow from "explanation of the term", otherwise God's existence would follow from the explanation of the term "God". - term explanation only conditionally: "if there is a God, he is omnipotent" - solution: the term-introducing theory must not be true - existence generalization. - false: from self-identity no existence can be concluded, only reversed.
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