|Existential generalization, logic: if an object that can be named, has a certain property, then there is at least one object with this property. See also universal generalization, universal instantiation.|
|Quine, Willard Van Orman
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|Existential Generalization||VII 119ff
Existential generalization/Quine: takes us from a theorem f to a theorem (Ex)y where f is like y, unless it has free occurrences of "y" in all those positions where y has free occurrences of "x" - e.g. "Fy ↔ Fy" leads to "(Ex)(Fy ↔ Fx)".
Existential generalization/Quine: no longer justified if the singular term does not denote anything: E.g. There is no such thing as Pegasus - from this we cannot infer: (Ex)(there is no thing x)- - It would be just as wrong: (Ex)(x was named like this because of its size) - modality/existential generalization: is not working. E.g. (Ex)(x is necessarily greater than 7) - (E.g.)(necc. if there is life on AS, then there is life on x).
Existential generalization: replaces name by variable - vice versa: specialization: replaces variable by name and eradicates a universal prefix: leads from (x)(..x..) to "... Paris ..." - if one is valid, the other is valid, too.
Wort und Gegenstand Stuttgart 1980
Theorien und Dinge Frankfurt 1985
Grundzüge der Logik Frankfurt 1978
Mengenlehre und ihre Logik Wiesbaden 1967
Die Wurzeln der Referenz Frankfurt 1989
Unterwegs zur Wahrheit Paderborn 1995
From a logical point of view Cambridge, Mass. 1953
Bezeichnung und Referenz
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982
Philosophie der Logik Bamberg 2005
Ontologische Relativität Frankfurt 2003