This is the collection of essays presented to Bochenski on his 60th birthday, and it contains, as a mirror of Bochenski's own work, a broad spectrum of studies ranging from formal logic and history of logic, to the philosophy of logic and language, and to the methodology of explanation in Greek philosophy. Of the seventeen articles, these are some of the more important to the reviewer: "Betrachtungen zum Sequenzen Kalkül" by Paul Bernays, which is an extensive study of Gentzen-type formulations (...) of logic; "Remarks on Formal Deduction," H. B. Curry, a further discussion of sequenzen-logics; "Marginalia on Gentzen's Sequenzen Kalkül" by Hughes Leblanc; "Method and Logic in Presocratic Explanation," Jerry Stannard; "On the Logic of Preference and Choice," H. S. Houthakker, a suggestive presentation of decision and utility theory in logical form; "Leibniz's Law in Belief Contexts," Chisholm; "On Ontology and the Province of Logic," R. M. Martin; and "N. A. Vasilev and the Development of Many-valued Logics," G. L. Kline, an important addition to the history of logic. Other contributors are: Storrs McCall, Albert Menne, E. W. Beth, Benson Mates, Ivo Thomas, J. F. Staal, F. R. Barbò, A.-T. Tymieniecka, and N. M. Luyten. There is a bibliography of Bochenski's writings through 1962.—P. J. M. (shrink)

Subtitled "Studies in Ethical Analysis," this collection of eleven essays, most of which have previously appeared in journals, deals with a number of problems central to modern ethical theory: the emotive interpretation of ethical language, persuasive definitions and their role in ethical reasoning, the cognitive versus emotive conceptions of ethics: many of these problems were first raised and examined by Stevenson in his earlier book Ethics and Language. Other essays are of a less retrospective nature: studies on Moore and Dewey, (...) naturalism and relativism in ethics, and a general discussion of the relations of linguistic analysis to philosophy as a whole. Stevenson is mainly concerned with analytical, as opposed to descriptive, ethics; and he completely avoids the topics of normative ethics except for a brief survey. The approach to ethics is therefore restricted, but there is enough here to interest the philosopher whose main area lies outside of ethics; although it presupposes no acquaintance with the author's previous work, some of the questions on emotivism and persuasive language are more motivated when seen in the context of that work.—P. J. M. (shrink)

This volume is published concurrently with the one reviewed below and together they unite a number of Quine's previously scattered papers into two compact volumes; this volume deals with his more philosophical work while the other is concerned with more purely technical logical studies. The twenty-one essays cover the period 1934-1964 and none have appeared between hard covers before. Several of the articles—"The ways of paradox," "Foundations of mathematics," "On the application of modern logic," and "Necessary truth"—are essentially popular expositions. (...) The others are generally more restricted in both scope and appeal, and deal with the ontology of the sentential calculus, truth by convention, implicit definition, modal logic, and ontological reduction in the sciences. Several articles concern the philosophy of science directly: "On simple theories of a complex world," "Posits and reality," and "The scope and language of science." This fine collection will be of significant help in presenting the work of a distinguished philosopher to a wider audience, as well as providing the professional with a source of discussion.—P. J. M. (shrink)

This book is a translation of some of the more important parts of the Grundgesetze of Frege: the introduction, the first part of the first volume which gives an exposition of the construction, rules, axioms of Frege's formal system, and two appendices, one of which is from the second volume and gives Frege's analysis of the paradox found by Russell in his system. The editor has provided a long introduction "for those not familiar with Frege," although it will benefit those (...) who have something more than acquaintance with his name as well. Frege's original two-dimensional symbolism has been preserved, but the editor has provided enough discussion in his introduction so as to make the going easier. Next to a complete translation of the Grundgesetze, this work is the most useful introduction to the magnum opus of the nineteenth century's greatest logician.—P. J. M. (shrink)

IntroductionBisphenol A is highly debated and studied in relation to a variety of health outcomes. This large variation in the literature makes BPA a topic that is prone to selective use of literature, in order to underpin one’s own findings and opinion. Over time, selective use of literature, by means of citations, can lead to a skewed knowledge development and a biased scientific consensus. In this study, we assess which factors drive citation and whether this results in the overrepresentation of (...) harmful health effects of BPA.MethodsA citation network analysis was performed to test various determinants of citation. A systematic search identified all relevant publications on the human health effect of BPA. Data were extracted on potential determinants of selective citation, such as study outcome, study design, sample size, journal impact factor, authority of the author, self-citation, and funding source. We applied random effect logistic regression to assess whether these determinants influence the likelihood of citation.ResultsOne hundred sixty-nine publications on BPA were identified, with 12,432 potential citation pathways of which 808 citations occurred. The network consisted of 63 cross-sectional studies, 34 cohort studies, 29 case-control studies, 35 narrative reviews, and 8 systematic reviews. Positive studies have a 1.5 times greater chance of being cited compared to negative studies. Additionally, the authority of the author and self-citation are consistently found to be positively associated with the likelihood of being cited. Overall, the network seems to be highly influenced by two highly cited publications, whereas 60 out of 169 publications received no citations.ConclusionIn the literature on BPA, citation is mostly driven by positive study outcome and author-related factors, such as high authority within the network. Interpreting the impact of these factors and the big influence of a few highly cited publications, it can be questioned to which extent the knowledge development in human literature on BPA is actually evidence-based. (shrink)

This rather compendious volume contains twelve articles, eleven of which have been published in the last twenty years; the last, from which the book takes its title, appears in print for the first time. There are four chapters: "Confirmation, Induction, and Rational Belief" contains the paper "Inductive Inconsistencies" as well as "Studies in the Logic of Confirmation"; "Empiricist Criteria of Cognitive Significance" appears in the section "Conceptions of Cognitive Significance"; the very well-known "The Theoretician's Dilemma" appears in the third chapter—"Structure (...) and Function of Scientific Concepts and Theories"—along with "Typological Methods in the Natural and Social Sciences"; "Scientific Explanation," the fourth chapter, contains "Studies in the Logic of Explanation" and "The Logic of Functional Analysis," as well as the title article. "Aspects" runs to nearly book length and is concerned to survey and contribute to the range of scientific explanation—from physics to history. Hempel discusses the Deductive-Nomological approach and compares it to certain forms of Statistical Explanation; the Covering-law Model of Explanation is introduced and defended against proponents of Explanation-by-Concept, Dispositional Explanation, and Genetic Explanation: Hempel asserts that these three can be subsumed under the Covering-law model. The relation of rationality and decision to Explanation, and the related pragmatic aspects of Explanation are also considered. These are postscripts to certain articles which bring their discussions up to date. There are several rather confusing misprints, but overall the presentation is workmanlike. Hempel's contributions in the philosophy of science have been influential and important, and it is gratifying to have the most important of these collected together.—P. J. M. (shrink)

The first edition of this now classical work appeared in 1953, the second heavily revised edition in 1961; this most recent edition is a revision in detail only of the previous one. The book is divided into three parts, the first two dealing with finite and infinite sets, infinite cardinals and their arithmetic, and related remarks on non-standard mathematics and the equivalence of various definitions of finitude. The third part considers ordered sets and isomorphism types, the special case of linearly (...) ordered sets, well-ordered sets in general, the relations of ordinals and cardinals. There is a very large bibliography and also a further list of literature pertaining to the companion volume. Fraenkel intended the book for philosophers as well as for mathematicians, and has kept to studying the most general and interesting problems of set theory; metamathematical results are kept in the background and the author works in an informal system of Zermelo-Fraenkel set theory. There is relatively little symbolism and Fraenkel's arguments are therefore more intuitive than rigorous, but clearly everything can be formalized in a proper language. There are many exercises in the book; these help to elaborate points only lightly touched upon in the main text and provide practice necessary for the growth of one's set-theoretical intuition. There are many alternative proofs of important theorems and alternative definitions for essential concepts; this lack of conceptual rigidity should especially please those who reject the now fairly widely held notion that Z-F set theory is the "true" one, the others proposed being ad hoc. Anyone who works his way through this delightfully written text will come away thoroughly prepared to attack more advanced work in the subject.—P. J. M. (shrink)

In this compact volume the author gives a sprightly introduction to modern symbolic logic, at no time side-stepping philosophical problems concerning the nature of formal logic. The first chapter is a brief comparison of traditional syllogistic logic and modern "logistic"; the next three chapters deal with the nature of logic as illustrated through various elementary logical systems: logic as ontology, logic as theory of language, logic as methodology of deductive sciences. Hasenjaeger then examines richer systems—many-sorted, those with definite descriptors, etc.—and (...) then the paradoxes. A chapter follows concerning logic developed in a combinatory style and its connections with the idea of a generative theory of formal structures—structures as calculi of concepts. The last chapter discusses formal logic as a branch of probability theory and inductive logic. This well-presented book would serve well in a study of the philosophy of mathematics and logic.—P. J. M. (shrink)

This rigorous treatment of elementary logic can best be characterized by noting that it relies heavily on semantical analyses of systems of logic running from the propositional calculus right through to a system of second-order arithmetic. The first chapter covers a multiplicity of topics: the concept of consequence, proofs and calculi, the symbolization of mathematical propositions. Hermes then painstakingly constructs quantification theory: first, the language itself, then its semantics; he then presents a completely set up predicate calculus, giving special attention (...) to derivability and decidability problems; a long, well-worked out completeness proof along the lines of Henkin is given, and some of its consequences are drawn out. Hermes then constructs a system of arithmetic in second-order logic, where he is especially concerned with categoricity of its interpretations. The last chapter provides further material on the functional calculus of first order: extended predicate calculi, normal forms for expressions. Excepting for a very few passages, this book should be accessible to everyone interested in formal logic.—P. J. M. (shrink)

Descartes considered the methods of reasoning put forth in the Discourse to be correct because, among other justifications, he had examples of scientific theories in which the techniques were successful: the Optics, Meteorology, and Geometry. The chief value of this edition is to have the Discourse back in its proper setting, as well as the more obvious one of having available three works of importance in the history of the exact sciences in one compact and readable edition. The Optics is (...) especially useful for the study of Descartes' theory of sight and perception. There are a large number of diagrams and figures which are quite helpful in making some rather schematic presentations more complete.—P. J. M. (shrink)

The author here constructs a system of simple type theory in which the type hierarchy does not extend merely to any finite height, but to an infinite height; this added part allows him to prove the existence of infinite sets within the theory, instead of taking it as an axiom in the usual simple type theory. The system has been presented in such sufficient generality so as to make it able to accommodate current scientific theories; the author has turned in (...) the direction of using type theory rather than set theory as the underlying logic of scientific theories. The system is formalized in Church's lambda-calculus notation; the semantics of the system are treated in great detail and appear to be the most complete study so far in print. The system is shown to contain at each type a "basic logic" somewhat similar to first-order logic; the author also shows that Peano's axioms for arithmetic appear as theorems when cast in suitable form. This book is one of a number of recent studies of type theory; together they represent a revival of interest in the subject, both as a foundation for mathematics and as an object of interest in itself. The book stems from Andrews' Princeton doctoral thesis.—P. J. M. (shrink)

To celebrate the four-hundredth anniversary of Galileo's birth, the University of Rochester held a series of lectures on the thought and influence of Galileo; there were six contributors and their work groups itself into three areas. The first of these is the importance and relevance of Galileo in modern thought and society: these were discussed by Giorgio di Santillana and Gilgerto Bernardino respectively. Norwood Hanson and E. W. Strong study the work of Galileo in dynamics and his theory of measurement. (...) The last two papers are concerned with the role of science in society—they spring from the confrontation of Galileo and the Church, the first indication of the special problems the scientific disciplines would face in their intercourse with the rest of society—and are by Philip Abelson and Erich Kahler. Although this brief collection cannot provide a full view of the scope of Galileo's activities and their subsequent impact, we are still able to feel that some of the vast gap between ourselves and the initiator of modern physics has been spanned, and that he can be seen more clearly for it.—P. J. M. (shrink)

This rigorous treatment of elementary logic can best be characterized by noting that it relies heavily on semantical analyses of systems of logic running from the propositional calculus right through to a system of second-order arithmetic. The first chapter covers a multiplicity of topics: the concept of consequence, proofs and calculi, the symbolization of mathematical propositions. Hermes then painstakingly constructs quantification theory: first, the language itself, then its semantics; he then presents a completely set up predicate calculus, giving special attention (...) to derivability and decidability problems; a long, well-worked out completeness proof along the lines of Henkin is given, and some of its consequences are drawn out. Hermes then constructs a system of arithmetic in second-order logic, where he is especially concerned with categoricity of its interpretations. The last chapter provides further material on the functional calculus of first order: extended predicate calculi, normal forms for expressions. Excepting for a very few passages, this book should be accessible to everyone interested in formal logic.—P. J. M. (shrink)

This volume contains papers and abstracts of papers delivered at the colloquium at Tihany, Hungary in 1962. There were seven sections; mathematical logic, computers and automata theory, circuit theory, mathematical linguistics, computers and programming, applications of computers in economics, artificial intelligence. Among the more interesting—to the reviewer—were these papers: one by Church concerning an independence problem in recursive arithmetic; Muller—characterizing classes of recursive functions; a long and philosophically stimulating study by Watanabe on a formalization of inductive logic; Kiefer—applications of set (...) theoretic techniques in linguistics; Abraham and Salapina—recognition of synonymity by machine; Gelernter—problem-solving graphs and heuristic programming. A number of papers which were read are not included in this volume.—P. J. M. (shrink)

This is a collection of papers read at an international logic colloquium held at Oxford in 1963. The first half contains articles on intuitionistic and modal logics, the propositional calculus, and languages with infinitely long expressions by such logicians as Kripke, Bull, Harrop, and Tait. The second part is primarily concerned with recursive functions and features a monograph by Crossley on constructive order types, as well as contributions by Goodstein, Schütte, and Wang, among others. Especially noteworthy is Kripke's paper which (...) applies Cohen's methods to the semantics of intuitionistic logic.—P. J. M. (shrink)

This is a collection of papers, all but one of which were previously published, by one of England's leading logicians. Goodstein has described his position in the philosophy of mathematics as that of a "constructive formalist": leaning toward the Hilbert school, but emphasizing the constructive nature of mathematical entities. The papers are more or less technical and symbolic; those most difficult are "The Nature of Mathematics," "The Decision Problem," and "The Definition of Number." Other titles are "Proof by Reductio ad (...) Absurdum," "Logic Paradoxes", "Language and Experience," "The Meaning of Counting," "Mathematical Systems," "The Axiomatic Method," "Pure and Applied Mathematics," and "The Significance of Incompleteness Theorems"; the last-mentioned paper is also quite difficult, but it constitutes not only one of the best semi-formal presentations of Gödel's theorems, but also helps make quite clear what their relevance is to considerations of the expressive power of formal languages in general. This collection constitutes a fine introduction to the philosophy of mathematics.—P. J. M. (shrink)

This monograph is the first really systematic study of the model theory of many-valued logic. The authors develop model theory for systems of logic whose truth-values lie in a compact topological space; the results are analogous to those for two-valued logic—they yield the two valued logics as special cases—but often the methods of proof are more complicated and tend to reveal some of the deep structure of these logics. There is presupposed a fair knowledge of naive set theory and point-set (...) topology, but no knowledge of classical logic is required although it will be of help in seeing the motivation behind various results. The first three chapters are concerned with preliminaries on topology, model theory, and continuous logic. The next chapter examines the relation of elementary equivalence among models, including the downward Skolem-Löwenheim theorem; the fifth chapter contains the generalizations of such classical results as the compactness and upward S-L theorems. The authors specialize their work in the sixth chapter to consider certain particular kinds of models: saturated models, universal models. The last chapter considers classes of models closed under various algebraic operations. There is a bibliography, historical notes, and indices of exercises, symbols, and definitions. This book is the prolegomenon to any future study of many-valued logic.—P. J. M. (shrink)

This well-written introduction to the theory of recursive functions and effective computability is an English translation of the 1960 German edition. The seven chapters deal with all the usual material, beginning with a treatment of Turing machines and their relation to the intuitive idea of computability, through general recursive functions, to a chapter on such diverse topics as the hierarchy of arithmetical predicates and Fitch's basic logic system. Rather than try to cover the whole subject sketchily, the author confines himself (...) to a narrower range of subjects which he elucidates with admirable clarity. The treatment of Turing machines is similar to that of Davis' book in using quadruples as instruction units in machine "programs," but the treatment differs in some details which might interest the connoisseur. In between technical discussions there are numerous remarks, often of more than a page in length, dealing with the more purely philosophical aspects of the theory under development. Each chapter terminates with a short bibliography. The publishers are to be congratulated for making this valuable work available to a wider range of readers.—P. J. M. (shrink)

This short monograph is a formulation and study of a system of first-order predicate logic of terms with a Hibert-Bernays selection-symbol E. The author proceeds through the primitive notation to recursive definitions of terms, relates the usual predicate calculi to this logic of terms, discusses an appropriate theory of models for the system, and finally proves it complete. This paper is one in a series of informal lecture notes in mathematics; hopefully more such studies in logic will appear in the (...) series.—P. J. M. (shrink)

Although conceived as a textbook, this extraordinary work contains a great deal of material which is either completely new or which has not appeared before in book form. It is intended as an upperlevel text for those with some familiarity with the subject already. After the introduction, there is a long chapter on formal systems which contains new material on algorithms and the theory of definition; epitheory of formal systems is then discussed, followed by an elegant algebraic treatment of logic. (...) Curry then formulates systems for negation and implication in the next two chapters, follows them by quantification theory, and ends with a sketch of modal logic. What distinguishes this from other logic texts which try to cover about the same ground is this: Curry exercises virtually exquisite care in his analysis of some of the more difficult points, variables and substitution, for example, that others often tend to gloss over. Each chapter has a section dealing with supplementary but related topics so as to give the reader some idea where the subject goes. There is an enormous bibliography and hundreds of references, including historical ones; these also increase its scholarly value. The author takes an informal semantical viewpoint about logic—trying to treat meaning as well as form as essential to logic. This view and a pellucid style make things move freely in the most difficult spots; only Curry's occasionally peculiar terminology might be confusing.—P. J. M. (shrink)

An enlargement of a previous work by the author, this work is intended as a reference source for study in the theory of models of logical systems, and as a textbook; the latter aim is reached by including numerous problems, many of them of a high level of difficulty, at the end of each chapter. The sections deal with, respectively, the lower predicate calculus, the structure of algebraic theories, concepts from model theory, completeness of various systems, definability of concepts, generalizations (...) of algebraic concepts, the metamathematical theories of ideals and varieties, and various selected topics including non-standard analysis. Unfortunately, there are numerous misprints which mar an otherwise excellent presentation. Much of the material presented is new, or is presented in new form. Robinson's approach is mildly idiosyncratic and often at variance with more conventional presentations, and this may make for difficulty in relating it to these presentations. Nevertheless, for the reader with a working knowledge of algebra and no small perseverance, this book will be rewarding.—P. J. M. (shrink)

There is little doubt that in the actual practice of science, models, metaphors, analogies, reasoning by similar cases, and other "parallel" forms of argument are often essential for the discovery of new phenomena and their theoretical interpretation. The author has assembled in five essays, culled and developed from previous ones, her ideas on some basic questions concerning models and analogies. The first chapter considers in dialogue form the role of models in science; the next section is an exploration of the (...) questions of what is an analogy and under what conditions analogical arguments are valid. The formal logic of analogy is then developed in the third part. The theory concerning analogy put forth by Aristotle is next discussed; the last chapter treats of the explanatory function of metaphor—we are brought back to our starting point, hopefully enlightened.—P. J. M. (shrink)

All the essays contained herein, with the exception of the last two—"On Suicide" and "On the Immortality of the Soul"—have appeared in the author's Essays, Moral, Political, and Literary ; the others were published posthumously. In this wide-ranging collection Hume addresses himself to aspects of aesthetics and literary criticism, the philosophy of history, philosophical "types", human nature and belief. The volume conveys a side of Hume too often forgotten in our present admiration of his foreshadowing of analytical philosophy: the man (...) of letters. The editor has provided a useful introduction setting Hume's work in its eighteenth century context.—P. J. M. (shrink)

This collection of seven papers by six authors centers about the relation of free action to determinism as both a metaphysical as well as a methodological hypothesis. Chisholm is concerned with the problem of whether a human whose behavior is completely controlled by outside forces can still be considered free; Danto studies the old problem of whether it can be said that actions of men are caused in the same way as the activities of other objects. Richard Taylor examines the (...) problem of free will in light of the apparent asymmetry of the prevention and the postvention—the doing of an act not ruled out by antecedent conditions—of events; Ginet develops a notion of "contingent necessitation" and proceeds to show that humans do not have a choice as to whether their actions satisfy certain conditions, these conditions following by contingent necessity from events not themselves in an individual's control. Wilfrid Sellars contributes two papers; the first is a study of the locution of "intending that," desiring and willing, intending, believing, the condition of being disposed to, and the practical syllogism; the second paper continues the tenor of the first—Sellars formalizes the notions of various kinds of "necessary" states of affairs, and uses this to make a distinction between being able to will and being able to do an act. The editor has the last paper which concerns the matter of whether there can be an empirical disproof of determinism.—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 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)

Hitherto unavailable except in the original French, Bergson's Durée et Simultanéité is an engaging contribution to the philosophy of relativity theory, space, and time. The book appeared during a period of great debate on the philosophical status of Einstein's Special Theory, and it treats, therefore, of it to the exclusion of the more conceptually difficult General Theory. Bergson is mainly concerned with trying to explicate the problems of the twin and clock 'paradoxes' which are presently again under some critical discussion. (...) Bergson tries to show that there is a symmetry in the aging of the two twins, not the usual asymmetry. Although Bergson is not usually considered a philosopher of science, those interested in the conceptual foundations of a modern physical theory might do well to consider his refreshing conclusions. The publishers are to be congratulated for making available this stimulating book.—P. J. M. (shrink)

The second volume in the Pittsburgh Series in the Philosophy of Science, this collection of papers covers a wide range of topics: the development of Newton's First Law comes under scrutiny in papers by Hanson and Ellis; Putnam attempts to clarify certain conceptual issues at the foundations of quantum theory; David Hawkins discusses the relation of teleology and thermodynamics from a neo-Aristotelian viewpoint; Morrison examines certain topics in astronomy; empiricism is studied by Feyerabend from a number of aspects, and is (...) found wanting; finally, Rescher looks at the connections of ethical principles and scientific research, with special reference to the goals, means, and standards of proof, and the dissemination of results of the latter. On the whole, a worthy successor to the first volume, just as certain to raise interest within diverse areas of philosophy.—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 collection of twenty-three papers from the period 1934-1960 is concerned with formal number theory and syntax, axiomatic set theory, truth functions, and quantification theory. In the first group appear "Concatenation as a basis for arithmetic" and "Definition of substitution," among others; the second includes "Set-theoretic foundations for logic," "On ω-inconsistency," and "Element and number." Quine's important articles "Completeness of the propositional calculus" and "Cores and prime implicants of truth functions" are in the third section; the last one includes "A (...) proof procedure for quantification theory" and "Church's theorem on the decision problem". These are but a few of many important articles. All the articles have been reset in a new, perspicuous type-face which makes study easier. Several important papers which were omitted should, in the reviewer's opinion, have been included, but this is a minor quibble. Quine's stature in modern logic can be gauged by examining these papers.—P. J. M. (shrink)

Although Machiavelli was never a military commander, he was throughout much of his life deeply concerned with the conduct of martial affairs; in short, a Renaissance Herman Kahn. This book is an essay on the technique of war: how on army is organized, who make the best soldiers, field manœuvers and battle formations, logistics, internal stability and control of military units, techniques of siege; these are considered both historically with reference to the ancients, as well as the present—the contemporary applications (...) of these techniques in the author's own time. The editor has provided a long critical and historical introduction—amounting to a small monograph in itself—which helps to place Machiavelli's ideas in the tradition of military-political theorists of Western Europe.—P. J. M. (shrink)

This volume is a collection of papers and selections of previously published books of Russell. The six divisions concern themselves with the distinction between formal and empirical sciences, the connexion of sense data with the structure of physical reality and with the philosophy of science, problems concerning mental phenomena, cause vs. inference, and finally, the relation of science to its cultural matrix.—P. J. M.

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)

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)

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)

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)

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)

This is the first English translation of the work of Eugenio Garin, one of the foremost modern historians of the Italian Renaissance. The present text, translated so intelligently, is based on the revised Italian edition of 1958.. Garin treats the growth of Italian humanism from Petrarch in the fourteenth century to its point of radical transformation with Tommaso Campanella at the beginning of the seventeenth century. The commentary on Giordano Bruno is especially clear, concise, and penetrating. For Garin, the elements (...) of Renaissance humanism are multiple. It sought its own rhetoric and shrank from the dry syllogistic reasoning of scholastic philosophy. It used philology as an essential tool and basis of a revolutionary historiography. As well, Renaissance humanism was engage in civic life. In seeing Renaissance humanism as the link with the modern world, Garin opposes those historians of science who posit medieval science and philosophy as the vital bridge. Garin minimizes the importance of Aristotelianism and finds Renaissance humanism severely hostile to scholasticism. Nevertheless, the book is a rich mine of facts, summarization, and syntheses of texts; the very index of the book, restricted to Italian Renaissance figures, occupies five pages of double columns. In addition, Peter Munz has written an introduction which is a full-blown critique—P. J. M. (shrink)