LOGIC, PHILOSOPHY OF

the study, from a philosophical perspective, of the nature and types of logic, including problems in the field and the relation of logic to mathematics and other disciplines. The term logic comes from the Greek word logos. The variety of senses that logos possesses may suggest the difficulties to be encountered in characterizing the nature and scope of logic. Among the partial translations of logos, there are sentence, discourse, reason, rule, ratio, account (especially the account of the meaning of an expression), rational principle, and definition. Not unlike this proliferation of meanings, the subject matter of logic has been said to be the laws of thought, the rules of right reasoning, the principles of valid argumentation, the use of certain words labelled logical constants', truths (true propositions) based solely on the meanings of the terms they contain, and so on. Additional reading W.V. Quine, Philosophy of Logic (1970), is the best compact introductory exposition. Hilary Putnam, Philosophy of Logic (1971), is useful as a complement to Quine. Much of the important literature, however, is in the form of brief papers rather than monographs. The most successful anthologies of such papers are perhaps L.W. Sumner and John Woods (eds.), Necessary Truth (1969), on logical truth and analyticity; and Leonard Linsky (ed.), Reference and Modality (1971), on modal concepts and intensional logic. Raymond Klibansky (ed.), Contemporary Philosophy, vol. 1 (1968), contains several survey articles thoroughly covering the whole field. Still central are the classical writings of the great modern philosophers of logic: Peter Geach and Max Black (eds.), Translations from the Philosophical writings of Gottlob Frege, 2nd ed. (1960); Bertrand Russell, Logic and Knowledge (1956); Ludwig Wittgenstein, Tractatus logico-philosophicus (Eng. trans., 1922) and Philosophical Investigations (Eng. trans., 1953); Alfred Tarski, Logic, Semantics, and Metamathematics (1956); and Rudolf Carnap, Meaning and Necessity (1947). The period 18791931 is also covered in a magnificent volume by Jean Van Heijenoort (ed.), From Frege to Gdel: A Source Book in Mathematical Logic, 18791931 (1967), which contains valuable introductions to the different selections and comments on them. Of later literature, especially noteworthy are the writings of Strawson and Quine: P.F. Strawson, Logico-Linguistic Papers (1971); W.V. Quine, From a Logical Point of View (1953), Word and Object (1960), and Ontological Relativity and Other Essays (1969). Quine's ideas are discussed critically in Donald Davidson and Jaakko Hintikka (eds.), Words and Objections (1969). A broad spectrum of new work on the borderline of philosophical logic and linguistics is represented in Donald Davidson and Gilbert Harman (eds.), Semantics of Natural Language (1972). Several problems mentioned above are discussed in Jaakko Hintikka, Logic, Language-Games, and Information (1972); and in J.W. Davis, D.J. Hockney, and W.K. Wilson (eds.), Philosophical Logic (1969). Later monographs include John Marenbon, From the Circle of Alcuin to the School of Auxerre: Logic, Theology, and Philosophy in the Early Middle Ages (1981), an examination of the progress of medieval philosophical logic; Rudy Rucker, Infinity and the Mind: The Science and Philosophy of the Infinite (1982), a book on the interface of philosophy and computer science; and George Bealer, Quality and Concept (1982), an appraisal of elementary symbolic logic.