Karel Lambert, Free Logics: Their Foundations, Character, and Some Applications Thereof (Prophil Projekte zur Philosophie Bd. 1. Eine Schriftenreihe des Forschungsinstituts Philosophie/Technik/Wirtschaft an der Universität Salzburg). Sankt Augustin: Academia-Verlag, 1997. 156 pp. Asch. 239. ISBN 3-89665-000-9 [Book Review]

History and Philosophy of Logic 22:233-236 (2001)
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Abstract

Free logics aim at freeing logic from existence assumptions by making them explicit, e.g., by adding an existence premisse to the antecedence of the classical axiom-schema of Universal Instantiation. Their historical development was motivated by the problem of empty singular terms, and that one of simple statements containing at least one such singular term: what is the referential status of such singular terms and what truth-value, if any, do such statemants have? Free logics can be classified with regard to their respective answers to these problems. Negative free logics assume that non-existent objects cannot have any properties at all; hence, in particular, they cannot be self-identical or rotate. Positive free logics believe that non-existents can be self-identical according to the Leibnizian concept of identity. Neutral free logics think that statements of self-identity are truth-valueless because of the Fregean principle of compositionality. Since only in negative free logic, but not in positive free logic, two statements of the forms "a = a" and "E!a" are logically equivalent, one also can define only for NFL, but not for PFL, existence by self-identity.

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Hans-Peter Leeb
University of Salzburg

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References found in this work

Philosophical applications of free logic.Karel Lambert (ed.) - 1991 - New York: Oxford University Press.
Free Logic: Selected Essays.Karel Lambert - 2002 - New York: Cambridge University Press.
Existential import revisited.Karel Lambert - 1963 - Notre Dame Journal of Formal Logic 4 (4):288-292.
Bielefelder Philosophische Vorlesungen.Karel Lambert - 1997 - Sankt Augustin [Germany]: Academia Verlag.

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