@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Field,Hartry}, subject = {Existence}, note = {I 80 Necessary existence/KantVs/Field: nothing can be negated with all its predicates, and nevertheless leave a contradiction. - (VsOntological proof of God). >Proofs of God's existence. 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. >Infinity, >Properties. I 155 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. >Syntax, >Semantics, >Proofs, >Criteria, >Singular terms. I 167 Existence/Ontology/FieldVsWright: existence does not follow from "explanation of the term", otherwise God's existence would follow from the explanation of the term "God". >Explanations. Term explanation is only conditionally: "if there is a God, he is omnipotent". Cf. >Omnipotence. Solution: the term-introducing theory must not be true - existence generalization. >Introduction, >Existential generalization. False: from self-identity no existence can be concluded, only in the reverse direction. >Identity, >Self-identity.}, note = { Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich, Aldershot 1994 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=219694} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=219694} }