Chomsky is widely mentioned in those philosophical circles whose interest centers on the analysis of language, but until now he has really been little read; this new work will remedy that situation. Here Chomsky, building on a presupposed acquaintance with linguistics, provides a stimulating examination of four major areas of linguistic theory: first, generative grammars are studied in their relation to language learning and understanding, then they are further considered as theories of linguistic use and competence; Chomsky here sets out (...) the criteria required for a grammar to be considered adequate—the justification of grammars. The second chapter examines syntactic theory with reference to depth structure and the problem of the relation of syntactic description to the traditional, correct account of how language is used. Depth structures and their import with reference to transformations within grammars are the subject matter of the third chapter. The last section considers, among other problems, the interface between syntax and semantics, especially the problems of degrees of grammaticality. A number of notes which go further into certain topics appear after the main text, and there is a useful bibliography. The main thrust of the book is a syntactical treatment of natural language by using transformational generative grammars as descriptive. Although he suggests empirical tests for the models he has constructed, he does not provide an attempt to fully verify the proposed system. This book will certainly be essential for an understanding of the structure of language viewed from the syntactic point of view.—P. J. M. (shrink)

Although Frege is now one of the most important figures in analytical philosophy, there are virtually no full-length studies available. Walker does not try to present all of Frege—that would be a monumental undertaking—but only to consider the philosophical aspects of his thought. Frege's theory of functions, concepts, and objects is first studied; then naming and describing are related to predication and thence to concepts; the notion of the sense of words and expressions, and then the notion of truth, especially (...) as picture-truth, is analyzed with their assistance. The last sections view Frege's general idea of the use of language and symbols, the nature of scientific laws, and the nature of numbers. The author sees Frege as tending to shift his interest from logic to ordinary language and so to the problems of expression in general; this view is reflected in the book itself. The affinities which the author sees with the work of Frege and Wittgenstein is only occasionally treated, but he does make it clear that the Tractatus owes much to Frege. Generally, this compact work will serve well in the study and interpretation of the work of the nineteenth century's greatest logician.—P. J. M. (shrink)

This concise work is a study of the semantical aspects of various paradoxes arising in formal logic. The author constructs a second-order system T with an interpretation in order to provide apparatus for stating and dodging the antinomies. After presenting a number of paradoxes, the author discusses a semantic vicious-circle principle, and provides a clarification of the problems by its application. He then discusses semantic aspects of some classical meta-mathematical results of Gödel, Tarski, Kleene, and Turing on unsolvable problems. Also (...) treated is the topic of impredicative definition in mathematics, especially as it relates to the vicious-circle principle.—P. J. M. (shrink)

Novikov is one of Russia's leading logicians and the appearance of this fine textbook is a good indicator of increasing American interest in Soviet logic. The book contains some new material, including a new independence proof of the rule of complete induction from the remaining axioms of first-order arithmetic. The first third of this work consists in chapters on propositional algebra and the propositional calculus. The first-order predicate calculus comes next under discussion: here a number of important classical results—Gödel's incompleteness (...) theorem, the Compactness theorem, Skolem-Löwenheim theorem—are proved rigorously. The author throughout the book leans fairly heavily on model-theoretic techniques, hence knowledge of some algebra, especially elementary field theory, will be useful. The last two chapters are concerned with first order arithmetic and the elements of proof theory. The only shortcoming is the lack of a bibliography and related scholarly apparatus; the student using this text may have difficulty locating material in other publications relevant to that in the book without outside assistance. The translation is very smooth and clear. Altogether, a first-class job.—P. J. M. (shrink)

The first of the authors is an engineer, the second a logician, and they have collaborated to produce a systematic and comprehensive treatise and textbook on the theory of automata—computing machines viewed abstractly—which presupposes only a slight familiarity with logic; there is a long first chapter which develops propositional and predicate logic; the stipulation of logical operators, the "nets" constructed therefrom, and their physical realization comprise the next two chapters. The representation of automata in input-output tables and flow diagrams, and (...) the study of operators in structures come next; the last two chapters concern various practical ways of synthesizing automata and measuring the complexity of logical nets. This is one of the series on logic and foundations of mathematics; the translation from Russian was edited by J. C. Shepherdson.—P. J. M. (shrink)

This is the first book-length study published of the structure of reasoning and argument dependent on hypotheses. It encompasses far more than the, by now, familiar discussion of contrafactual conditional—this is but one chapter—since it ranges over such topics as the nature of hypothetical inference, belief-contravening hypotheses, contrafactual conditionals and modality, and entailment of conclusion from premisses under restriction. There are three appendices which concern, respectively, the historical roots of hypothetical reasoning and its attendant perplexities, the difficulty concerned in the (...) mutual compatibility of hypotheses in a proof, and certain properties of laws of nature expressed in conditional form. There is a fair-sized bibliography listing all the more important works on hypothetical reasoning. Rescher's logical apparatus designed to facilitate hypothetical reasoning and its study is controversial; but anyone wishing to understand the logic of the problems set forth in current philosophical discussion must begin with Rescher's book.—P. J. M. (shrink)

As inductive logic and the philosophy of probability theory have become of wider interest, it has become clear that a book of readings in these and related topics would be useful for courses since most of the important articles are scattered and inaccessible. The editors have fashioned an extensive collection of papers in four main areas: the meaning of probability, confirmation theory, simplicity of theories and structures, the justification of induction. Each chapter is preceded by an introduction which sets out (...) the basic problems of the topic under consideration. There are thirty-six papers in all, two-thirds of them in the first and last chapters. The first chapter includes articles by Ramsey, Carnap, Nagel, and Reichenbach. The second chapter is dominated by the work of Hempel, Oppenheim, and Kemeny; the third chapter features a long article by D. J. Hillman which takes as its basis the work of Goodman, and there are other papers by Bunge, Quine, and Barker. The discussion of induction and its justification contains articles by Hume and Mill, but the bulk of the papers are contemporary. There is a bibliography for each chapter at the end of the book.—P. J. M. (shrink)