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Early Analytic Philosophy - New Perspectives on the TraditionIdentity in Frege’s Shadow

Early Analytic Philosophy - New Perspectives on the Tradition: Identity in Frege’s Shadow [Frege overlooked the role of quantifiers as expressing, by their formal dependence on each other, the actual dependences between variables bound to them. The resulting flaw in Frege’s and other logicians’ logic began to be corrected only in IF logic. The dependence relations are codified in the Skolem functions that correspond to existential-force quantifiers. Their existence is the natural truth condition. Such functions are not adequately handled in first-order predicate logic. In any adequate logic, a fixed mode of identification is presupposed. The frameworks of identification can be perspectival or public. Kripke makes the same mistake about quantifiers as Frege and in addition assumes that only perspectival indentification is needed in the last analysis. He also overlooks dependence relations between modal operators and quantifiers.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Early Analytic Philosophy - New Perspectives on the TraditionIdentity in Frege’s Shadow

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-24212-5
Pages
21 –29
DOI
10.1007/978-3-319-24214-9_2
Publisher site
See Chapter on Publisher Site

Abstract

[Frege overlooked the role of quantifiers as expressing, by their formal dependence on each other, the actual dependences between variables bound to them. The resulting flaw in Frege’s and other logicians’ logic began to be corrected only in IF logic. The dependence relations are codified in the Skolem functions that correspond to existential-force quantifiers. Their existence is the natural truth condition. Such functions are not adequately handled in first-order predicate logic. In any adequate logic, a fixed mode of identification is presupposed. The frameworks of identification can be perspectival or public. Kripke makes the same mistake about quantifiers as Frege and in addition assumes that only perspectival indentification is needed in the last analysis. He also overlooks dependence relations between modal operators and quantifiers.]

Published: Jan 22, 2016

Keywords: Skolem Functions; Natural Truth Condition; Dependency Relations; Substitutional Interpretation; Quantificational Sentences

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