Logic, Semantics, Metamathematics

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Summary: Truth and Conseqence Both Defined in One Book
Review: This book collects seventeen classic papers on logic, semantics and metamathematics authored or co-authored by the late Alfred Tarski (1901-1983), who is considered to be one of the five greatest logicians of all time (the others being Aristotle, Boole, Frege, and Gödel). Tarski is as famous for his contributions to philosophy as for his contributions to mathematics. His most important contributions to philosophy are two definitions in which he proposes characterizations of concepts that are central to our understanding of the axiomatic method and, more generally, of rationality. In 1933 he published an essay in Polish giving a mathematically precise definition of TRUTH and building the axiomatic foundations on which this definition rests. This truth-definition paper, which has been translated into many languages, may well be the most important paper in philosophical semantics, if not in analytic philosophy broadly considered. This article alone is worth the price of the book. Its 120-page length qualifies it to be regarded as a monograph, not just as an article. It has spawned a huge literature and it continues to be studied not only as an historic breakthrough paper but also as a source of fresh ideas. A revised and corrected version of a 1956 English translation of the truth-definition paper appears in this book in its entirety. In 1936 he wrote two 10-page papers sketching a mathematically precise definition of logical CONSEQUENCE (needed to define validity of arguments), one in German for international readers and one in his native Polish. This book contains an English translation of the German version. This is the only publication of the English translation of the entire Tarski truth-definition paper and it is also the only publication of the original English translation of the German-language consequence-definition paper. Tarski's definitions of truth and of consequence employ the tools of modern mathematical logic in order to characterize classically accepted concepts. They were not intended to displace classical concepts with modern constructions. Accordingly both are based on comprehensive knowledge of the relevant parts of Western philosophy going back to Aristotle and on a deep appreciation of modern mathematics, a field to which Tarski had already made important contributions on his own and in collaboration with acknowledged masters such as Banach and Kuratowski. As Tarski emphasizes in his 1969 "Scientific American" article "Truth and Proof", just as truth, which is ontic and objective, is a precondition for proof (or demonstrative knowledge), which is epistemic and to an extent subjective, consequence is an ontic and objective precondition for inference, which like proof is epistemic and inescapably subjective. Without an understanding of truth and consequence it is impossible to understand proof. Included is an editor's introduction indicating "how Tarski's development of the conceptual framework of the methodology of deductive science can be traced through the articles in this volume". The volume ends with a nearly forty-page analytical index which greatly facilitates use of this work as a reference book on logical terminology.