Logics Without Existence Assumptions [Book Review]

Review of Metaphysics 23 (3):565-565 (1970)
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Abstract

In this book the author develops his own systems of and semantics for presupposition free logic. He calls his systems logics without existence assumptions, by which he means logical systems which are sound and complete with respect to a semantic theory in which a universe of discourse can be empty but any term which denotes must denote something in the universe, all predicates including identity represent relations holding among members of the universe and the quantifiers range over just all the members of the universe. In a brief introductory chapter the author reviews the motivations for constructing non-standard logics of this kind and briefly discusses what he takes to be the limitations of previous work done in the field. Persons interested in the philosophical problems and uses of such logics are likely to find this chapter interesting though disappointingly brief. Four of the eight chapters are devoted to the development of a natural deduction system N which is a logic without existence assumptions in the author's sense. The system N is shown to be sound and complete with respect to the author's semantics. An axiomatic system L is later developed and shown to be equivalent to N. The final chapter is devoted to discussing the relation of his work to many-valued logics, modal logics, intuitionistic logic and the theory of classes among other topics. The author believes that logics without existence assumptions "will in the long run displace the less natural and more narrow standard logics."--R. H. K.

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