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)

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)

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 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)

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 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)

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)

This introductory logic text for philosophers stresses decision procedures for the propositional and predicate calculi. In the treatment of the former the authors first present the apparatus for constructing logical inferences and establishing their validity; they then reformulate the system in an axiomatic way and prove its consistency and completeness; they also discuss, for example, techniques for proving independence of axioms. The lower predicate calculus is then developed, first in a monadic form, then in an extended one for which decision (...) procedures are available. Although the authors introduce predicates of degree two or more along with multiple quantification, they do not prove this system of the full predicate calculus complete. The last chapter provides a well-articulated treatment of syllogistic in connexion with quantification theory. There are appendices on conjunctive normal forms and notation without parentheses. The answers to the exercises are at the end of the book.—P. J. M. (shrink)

This is a well-written analysis of the interpreters and interpretations of the Buddhist nirvana from the West. The first chapter treats the West's encounters with Buddhism before 1800, Marco Polo, etc. The remainder of the book deals with the interpretations of nirvana by Eugène Burnouf, Friedrich Max Müller, James D'Alwis, Robert Caesar Childres, Schopenhauer, Wagner, Nietzsche, Hermann Oldenberg, the Rhys Davidses, La Vallée Poussin, and Stcherbatsky. The author's own opinion is given in a few pages at the end of the (...) book; however, his opinion is not so much an exposition of nirvana but a short essay on the methodology of a study of nirvana. He quotes Richard Robinson to bring home his point that this long array of scholars could not forsake their cultural bias and that one needs therefore to approach non-Western ideas from the inside of a non-Western culture. Welbon's intention is to present an outline of the history of Western discussions on the meaning of the Buddhist nirvana. His research is thorough; his presentation is clear; this is a chronicle of heroic but club-footed attempts to learn about a non-Western idea. The book should be read by all aspiring Buddhologists, for it will convince them of the absolute necessity of learning the language of a Buddhist culture and of searching out qualified native informants. Its value for non-Buddhologists is not to learn more about nirvana but to learn the history of this burgeoning study. Welbon has admirably succeeded in his aim; he has concisely presented Western opinion on nirvana up to World War II.--P. J. H. (shrink)

The Reverend Hozen Seki, President of the American Buddhist Academy, says in his two-page preface that this book is the result of the transcription of five lectures given by Suzuki in the New York Buddhist Church in 1958. It is a detailing of Suzuki's own personal view of what Shin Buddhism is. This is the system that stems from the Japanese saint Shinran of the thirteenth century who was a follower of Honen, the founder of the Pure Land doctrine in (...) Japan. The aim of the book is not to trace down the background of the Pure Land teaching in India, nor is it to present Shinran's teaching as is. Rather, it is an expression of Suzuki's own insights into the Pure Land teaching.--P. J. H. (shrink)

The aim of the authors is to present a comprehensive study of the basis of intuitionistic mathematics by means of modern meta-mathematical devices. The first author, for whom this book is a capstone of twenty years' work on the subject, contributes three chapters on a formal system of intuitionistic analysis, notions of realizability, and order in the continuum; the second provides an analysis of the intuitionistic continuum. An extensive bibliography which includes references to almost every article on the subject makes (...) this book especially valuable; for those interested in intuitionism and its relations to classical mathematics this work will be essential.—P. J. M. (shrink)

This study, under the title of an explanation of the New Nyäya views on negation, deals with the Navya-nyäya as a whole. The peculiarity of their theory of negation is that one can see the absence of an object in a given place. It includes the Sanskrit texts and translations of the Abhäva-väda of Gangesa and the Nañ-väda of Raghunätha. Though written for both Sanskritists and philosophers, the frequent use of Sanskrit terms almost requires that the reader be a Sanskritist--though (...) by keeping in mind the translations, previously given, it could be valuable. This is not an exposition of logic for beginners, but an exposition for scholars of a particular system. Renditions into modern logic are given throughout. Chapter headings include: On Cognition; The Content of Cognition and the Meaning Problem; On Relation; The Counterpositive of an Absence; The Ontological Status of Content-ness; The Relational Adjuncts; The Limitors and Quantificational Logic; Circularity; On Negation.--P. J. H. (shrink)

A translation of the 1913 volume Dernières Pensées, this collection of papers contains much material of interest to the logician and the philosopher of science. In "The Logic of Infinity" Poincaré clarifies the notion of "predicative set" and discusses Zermelo's and Russell's approaches to set theory. "The Evolution of Laws" attempts to formulate the question "do laws of nature evolve?" Two papers concern space and time, two others, the electrostatic and quantum theories of matter. The collection concludes with a pair (...) of papers on the ethical import of science.—P. J. M. (shrink)

In this lecture Evans studies one of the basic presuppositions of empiricism: the central doctrine of the theory of meaning of propositions, with special reference to the cleavage between verbal definition—the defining of words by reference to other words—and ostensive definition—the defining of a word by "pointing" to its object. The author shows that ostensive definition is wholly inadequate to the task of defining such words as nouns and adjectives—one can point only to their instances in the world and not (...) to what the noun or adjective actually refers. Thus with the breakdown of this distinction in definition goes the weakening of the division between mathematical and empirical sentences which together were believed to exhaust all possible meaningful expressions.—P. J. M. (shrink)

Name der Zeitschrift: Nietzsche-Studien Jahrgang: 42 Heft: 1 Seiten: 298-298.

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 infinitary languages studied in this book are those in which quantification of infinitely many variables simultaneously, and conjunctions or alternations of infinitely many are permitted. Infinitary concatenation and infinitary propositional logics are first discussed, and a completeness theorem is proved about the latter. The later chapters deal with infinitary predicate languages and Scott's proof of incompleteness is introduced. Throughout the discussion, unsolved problems are mentioned and areas undergoing current development are emphasized. A short bibliography lists most recent articles on (...) this new branch of logic.—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)

A quick, information-packed introduction to the early history of the Church as known from the New Testament and of the origin and transmission of the New Testament itself, with considerable detail on manuscript traditions and reconstruction.--P. J.

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 is an annotated translation of the "King Dohäs," a work by the Indian Tantric sage Saraha. It is sub-titled "A Study in the History of Buddhist Thought." The first part is commentary by the translator on "The Tradition about Saraha and His Works," "The Teaching of the Dohäs," and "Existence versus Essence." The second part is the song itself, only nine pages. The third part is two commentaries, one by the Nepalese scholar sKye-med bde-chen and the other by the (...) Tibetan Lama Karma Phrin-las-pa. The original texts are not given though two sample pages are given for the sake of satisfying curiosity about the form of the books, etc. Because the translation is interspersed with terms taken from modern existential philosophy, the average reader and even the Buddhist scholar will have difficulty with the work. It is best suited for someone who is familiar with existential works and who would like to see the terminology applied to Buddhism.--P. J. H. (shrink)

This is not a textbook in mathematical physics—excepting for one chapter one need not possess much more than geometry and elementary algebra—rather it is a philosophically reflective examination of the cardinal features of special relativity theory. Throughout the book Bohm is not merely doing physics, but thinking about doing physics as well. This metatheoretical reflexion appears in chapters concerning pre-Einsteinian notions of relativity, attempts to save the aether theories, the "ambiguity" of space-time measurements in the new cosmology, "common sense" notions (...) of space and time, and the falsification of scientific theories. There is a long appendix dealing with physics and perception—the relation between scientific objects and perceptual processes. One will, however, by working through the text learn plenty of physics in a rigorous and concise fashion. The author wisely does not attempt to cover the mathematically far more difficult and philosophically more profound General Theory of Einstein. In the area chosen, Bohm has written clearly and felicitously; this should serve a model for others who like to take their physics with a dollop of philosophy.—P. J. M. (shrink)

This is an explanation of the New Nyäya system of Indian logic. The first two chapters are an introduction to the main topics of Navya-nyäya logic, relations, absence, definition, inference, quantifiers and limitors, accident, and the theory of pervasion. Following are the text, transliteration, translation, and commentary of Anumitinirüpana and Vyäptiväda by Gangeäopädhyäya. Its audience is strictly limited to those who are profoundly interested in and acquainted with logical theory. The style is lucid and will provide interesting insights for the (...) professional: however, knowledge of Sanskrit is not required. For those who are familiar with the symbols of mathematical logic, symbolic interpretations are given from time to time.--P. J. H. (shrink)

This interesting collection is the Festschrift presented to W. Britzelmayr on his seventieth birthday, and it contains several excellent papers which ought to interest the logician and philosophical analyst alike. The most exciting paper is one by Stegmüller in which a system of set theory combining ideas from Bernays and Quine is formulated; one by Kurt Schütte discusses the limitations imposed by constructive logic on the theory of trans finite arithmetic; there are papers by each of the editors: the first (...) analyzes the deduction theorem for the first order predicate calculus, while the second treats logics with predicate quantifiers. Other papers include studies by Behmann on the philosophico-logical status of identity; by Beth on the application of his semantic tableaux to classical logic; by Wilhelmy on the semantics of quantified, many-valued logics; and by E. M. Fels concerning the work of Markov and his school in the theory of canonical systems. There are still further papers which take as their topics the logical analysis of legal concepts and reasoning, the logic of questions, the semantics of implication in ordinary language, and the relation of the theory of logical types to Frege's work. In general, this is an excellent collection which affords a wide view of the logico-linguistic concerns of recent German philosophy.—P. J. M. (shrink)

This is a translation of a catalogue of Buddhist Tantra written by a student of the Tibetan teacher Tsong-kha-pa. The author, Mkhas-grub-rje, was thoroughly familiar with the whole of the Tantra preserved in Tibet, and thus the book serves as a most valuable source of hitherto unavailable information. The book catalogues the four divisions of Tantra by way of books, practitioners, rites, and tenets. There is a great deal of discussion on the varieties of acceptances with respect to those subjects, (...) and thus most readers would find the book tedious. However, the book contains a veritable mine of information for the Tantric scholar. The Tibetan text is given in transcription opposite the translation and is broken into paragraphs which correspond with the translation. At times, rites, practices, and tenets are explained, but the main purport of the book is to set in order the many, many technicalities of the Tantra as preserved in Tibet.--P. J. H. (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)

Unlike many other introductions to propositional calculus, analysis of propositions, and logic of relations, this one contains an excellent chapter presenting in short scope and in a very readable manner the historical origins of modal logic, many-valued logic, and intuitionistic logic.--P. J.

Aiming to present the traditional philosophy of nature, it consists of exposition of Aristotelian texts and parallel commentaries of St. Thomas on moving beings, motion, time, and space, with a minimum of critical comment. The author urges rather than strictly argues the thesis that the fundamentals of the Aristotelian philosophy of nature, as opposed to the details, are still viable. Relevant texts of St. Thomas are appended.--P. J.

This book originally appeared in 1920 under the title Relativitätstheorie und Erkenntnis Apriori and was the first of Reichenbach's numerous writings on the philosophical problems of relativity theory, space, and time. In this book the author attempted to show how Kant's theory of the a priori, especially concerning the concept of the a priori as "constituting the concept of [the] object" in question, comes into irrevocable conflict with certain facts of both the General and Special theories of relativity; and that, (...) therefore, we must amend Kant's treatment of the role of the a priori in knowledge accordingly. The translator, Maria Reichenbach, has provided a long and useful introduction, placing the work in the context of Reichenbach's philosophical career and activities, and providing background material on the author himself. This is the second of a continuing series of works by Reichenbach to appear under the California Press imprint.—P. J. M. (shrink)

A book for pleasant reading. It contains some 600 passages in which James is spoken about by philosophers, statesmen, theologians, and other public figures.--P. J.

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)

Here in volume II are the Tibetan texts of the biographies of four Lamas of Dolpo of western Tibet. They are written in the headless form of Tibetan script with both clarity and beauty with the Khams-pa style of cursive script. It includes four appendixes: transliterated extracts without translation, transliterated extracts with translation, two pages of notes to the first volume, a lay-out of the Tibetan alphabet together with the system of transliteration, and a table of abbreviated words to facilitate (...) reading the text. This is a beautiful edition, especially helpful in that it provides a good example of Tibetan cursive writing. The transliteration scheme also accords with that gaining wide acceptance amongst Tibetan scholars, even though not chosen by the Library of Congress. --P. J. H. (shrink)

In this collection the authors have attempted to bring together a number of the essential papers in the subjective interpretation of probability theory; several of them—Borel's "Apropos of a theory on probability" and de Finetti's "Foresight: its logical laws, its subjective sources"—have never appeared before in English. Other articles include Venn's pioneering study as well as the more recent work of Ramsey, Koopman, and Savage. The editors provide an introduction which presents the three basic elements of any subjectivistic theory: probability (...) as degree of belief, the coherence of beliefs of an individual, and the notion of exchangeable events. A bibliography includes references to virtually all the more important works in subjective probability, with special emphasis on the development of the mathematical side of the theory. This anthology belongs on the shelf of any philosopher concerned with inductive logic, statistical inference, or the foundations of probability theory.—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 book was translated from the French by Marco Pallis. It is divided into three parts: in The Tracks of Buddhism, Buddhism's Ally in Japan Shintö or the Way of the Gods, and Vistas of the Mahäyäna. The first has ten short essay chapters, Originality of Buddhism, Message and Messenger, Charity and Existence, The Question of Illusion, A Buddhist Eye on Science, Cosmological and Eschatological Viewpoints, More About Human Destinies--the Function of Mercy, What is Matter and Who is Mära?, Some (...) fallacies and facts concerning Buddhism, and Glimpses into Zen. These essays do not present the philosophical systems of Buddhism but rather attempt to give a picture of the spirit of Buddhism. The second part has three short essay chapters: Science, Myth, and the Meaning of Ancestors, Ethics and Mythology of Shinto, and The Noble Virtues: Some lessons of Shinto. The third part contains four essay chapters: Treasures of Buddhism, Mystery of the Bodhisattva, The Feminine Element in Mahayana, and Synthesis of the Päramitäs. Contrary to the trend of recent books which are attempting to differentiate the acceptances of the various schools within Buddhism, this book tends to stress similarities even with non-Buddhist Indian systems. It is best suited for those who would like to enter into the general spirit of Indian religions without necessarily concentrating on Buddhism.--P. J. H. (shrink)

This extensive work is both a systematization of past developments, and an extension to new areas, of the application of mathematical apparatus to the study of logical systems; it does not aim to include all such metamathematical devices, Gödel-numbering for example, but to emphasize algebraic and topological ones. The first part surveys required algebraic and topological notions; in the second part they are applied to classical logic—propositional and predicate calculi; in the final section, modal and intuitionistic, non-classical logics come under (...) scrutiny. The reader should come prepared with a working knowledge of the forementioned areas of mathematics; but the pace is leisurely, and the book tries to be self-contained. It succeeds admirably and may become the standard examination of the topic.—P. J. M. (shrink)

This is a text for a one or two semester course on axiomatic set theory; the goal is to introduce and develop one system of set theory in a complete and thorough way, presupposing only the elusive "mathematical maturity" of the reader. There are nine chapters which begin with a development of propositional and predicate logic oriented toward set theory and develop the Zermelo-Fraenkel system in exceptional detail. The book starts slowly, the first 120 pages being devoted to logical preliminaries (...) and the introduction of axioms; it gathers speed, however, and the remaining chapters include treatment of the algebra of classes, relations and functions, order of various sorts and Zorn's lemma, real numbers and equivalence classes, the equipollence of sets, similarity as a relation of sets, the ordinal numbers and their arithmetic, the cardinal numbers and their arithmetic. These later chapters are extremely detailed and comprehensive, presenting a wealth of material. There are numerous exercises, many quite difficult, at the end of each chapter, along with a summary of that chapter's content. Because of the single-mindedness of the book, there is little reference to other systems of set theory, but this is not a drawback at all. The presentation is orthodox, but not dull; careful, but not generally pedantic or repetitive. This makes it a good text for self-study.—P. J. M. (shrink)

A book of this title needs indeed to be written, but it should be done so after careful study of at least Bhävaviveka's Tarka-jvälä which is preserved in Tibetan. The historical and doctrinal relationships of the four major Buddhist schools, the Vaibhäsikas, the Sauträntikas, the Yogäcärins, and Mädhyamikas, are sufficiently complex that a book of this small size could only present a bare outline of their emergence. And even such an outline can be accurately made only after the pursuit of (...) Buddhist thought through its transformations as presented in Indian and Tibetan texts on tenets. Secondary materials simply are not adequate to take account even of how the Buddhists themselves perceived the development of these texts. Therefore, this work, which relies on the few available translations and much of the older, less adequate scholarship on Buddhism, cannot help but present a scanty picture of such a complicated topic. Such difficulties render the comparisons with Whitehead, existentialism, etc., somewhat weak.--P. J. H. (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)

For this volume Professor Davis has assembled a number of the most important papers on undecidable propositions, unsolvable problems and computable functions. Several papers appear here in print for the first time: Gödel's remarks at the Princeton Bicentennial Conference on Problems in Mathematics, and Post's paper on Absolutely Unsolvable Problems. Other authors whose work is included are Church, Turing, Rosser, and Kleene. Gödel's classic "On Formally Undecidable Propositions..." appears in a new translation, and all papers have been corrected, many such (...) corrections provided by the original authors. The editor has contributed brief notes preceding each paper, these notes are intended to clarify and otherwise expatiate upon the contents of those articles. A valuable collection both for original source material as well as historical formulations of current problems.—P. J. M. (shrink)

This book is an attempt to relate the operative and constructive formulation of symbolic logic carried out by Lorenzen—and to a lesser degree Kolmogorov and Markov—to both Wittgenstein's philosophy of logic as set forth in the Tractatus and later modified in the Investigations, and to Brouwer's critique of classical logic, especially the principles of excluded middle. The first chapter contains an exposition of Wittgenstein's critical analysis of the "mythical" views of Russell and Frege; and it develops his own "operative" theory (...) of elementary logic. The second chapter concerns the relations of the theories of Brouwer and Wittgenstein; the last section is a detailed survey of chiefly Lorenzen's operative logic in which the presentation of a dialogue-like interpretation of logic is exhaustively analyzed: the notion of a "winning strategy" in such a two-person dialogue is set forth, the technique is extended to classical logic from its original, weaker operational form, and its relations to Gentzen's Sequenzen-kalkül is discussed. The work was the author's Habilitationsschrift at Innsbruck University.—P. J. M. (shrink)

An account of the life and teachings of the Austrian thinker, Josef Popper-Lynkeus, based upon private conversation as well as upon close study of his works in social and economic theory.--J. P.

This is a reprinted version of Born's 1948 Waynflete Lectures at Oxford; there are several appendices: one elaborates in much greater detail the elements of physical theory developed in the lectures; the second is bibliographical; the last concerns the role of symbols in the construction of physical theory.—P. J. M.

Abraham Robinson has twice been the initiator of trends in the foundations of mathematics which have later become recognized as profound and important, although they were generally ignored at first: metamathematical problems of algebra and non-standard analysis. This book considers the second topic; before we begin analysis—especially a treatment of the classical theorems of calculus—we need basic results from logic, model theory in particular. Robinson then sketches non-standard arithmetic and proceeds to develop the usual properties and relations of differentiability and (...) integrability of functions, convergence; he then examines general topology in this new context and fortified with these results develops "modern" functional analysis in some detail: measure theory and functions of a real variable, functions of a complex variable, normed and linear spaces, topological groups and some harmonic analysis. The last two chapters cover selected topics in analysis drawn principally from applied mathematics and the history of the calculus with special reference to infinitesimals. Robinson views the development of non-standard mathematics as the renaissance of ideas about infinitesimals as serious topics of mathematical study. Robinson primarily has confined himself to analysis and not attempted to cover non-standard algebraic systems; several important results of Alling concerning non-standard arithmetic and rings of continuous functions appeared too late to be included. Of course, the real test of non-standard analysis will come in allowing us to prove new theorems about standard analysis, but although Robinson does not attempt to do this here—although he has obtained results in this direction—other mathematicians have already begun to do so: the future of this new branch of mathematics already looks secure.—P. J. M. (shrink)