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 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)

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)

Even though integrity is widely considered to be an essential aspect of research, there is an ongoing debate on what actually constitutes research integrity. The understanding of integrity ranges from the minimal, only considering falsification, fabrication and plagiarism, to the maximum, blending into science ethics. Underneath these obvious contrasts, there are more subtle differences that are not as immediately evident. The debate about integrity is usually presented as a single, universal discussion, with shared concerns for researchers, policymakers and ‘the public’. (...) In this article, we show that it is not. There are substantial differences between the language of research integrity in the scientific arena and in the public domain. Notably, scientists and policymakers adopt different approaches to research integrity. Scientists tend to present integrity as a virtue that must be kindled, while policy documents and newspapers stress norm enforcement. Rather than performing a conceptual analysis through philosophical reasoning and discussion, we aimed to clarify the discourse of ‘scientific integrity’ by studying its usage in written documents. To this end, large numbers of scientific publications, policy documents and newspaper articles were analysed by means of scientometric and content analysis techniques. The texts were analysed on their usage of the term ‘integrity’ and of frequently co-occurring terms and concepts. A comparison was made between the usage in the various media, as well as between different periods in which they were published through co-word analysis, mapping co-occurrence networks of significant terms and themes. (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)

The author is interested in discussing various aspects of the propositional calculus; in particular, the relationships among the various propositional connectives in various systems of logic such as Intuitionistic and modal are scrutinized. The first three chapters survey the notation to be used and describe the general notion of logistic system; the author then describes the concept of a deductive system in exceptional generality, then treats the connexions of equivalence and independence among such deductive systems in what are essentially algebraic (...) terms. Building on the latter work, he then treats the idea of one system's being an extension of the other, going into the details concerning the fine structure of exactly what sort of extension it is—conservative, consistent, and thus arrives at Lindenbaum's lemma. The equivalence relations of congruence and equipollence among propositional systems form the central core around which Porte's discussion of axiomatizability of systems of connectives constituting various propositional calculi is based. Porte is one of the best of the several young logicians now working in France and this book is useful both as a technical treatise containing a sophisticated treatment of sentential logic, and as a guide to at least one direction and trend of contemporary French logical thought.—P. J. M. (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)

Although this excellent introductory and intermediate level text is intended for students of mathematics, it could serve well in any course for philosophers on that level. The first two chapters present the propositional and predicate calculi, along with an informal discussion of some of the set-theoretic concepts needed to study logic. The third chapter discusses what exactly an axiomatic system is, and examples of various mathematical systems cast in axiomatic form are provided; the discussion here, as elsewhere in the book, (...) is generally self-contained and presupposes only an ability to deal with abstract ideas. The study of the propositional calculus is resumed in chapter four, but its formulation is now more rigorous and thoroughly axiomatic; in a similar manner the predicate calculus is treated in the next chapter, and the usual metatheorems are proved about each, but the specific techniques differ from the usual. The last chapter concentrates on the completeness proof of quantification theory, relating it to some of the axiomatic algebraic systems considered earlier. An appendix sketches some sophisticated results of Vaught and Robinson on model theory and completeness. In sum, this is one of the very best of a plethora of logic texts on the market, and it should serve well for years to come.—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)

In this monograph the author presents the special and general theories of relativity from a geochronometrical viewpoint. The amount of mathematics demanded is not too great, and one can get quite far along on the material on vectors presented early in the book. The first three chapters especially derive from the work of A. A. Robb several decades ago: they treat foundations of geochronometry, one-plus-one geochronometry and its generalization to a one-plus-three system. Later chapters cover such staples as the Lorentz (...) transformation, the metric and dynamical tensors, dynamical relationships of particles, accelerating and curving events, geodesics, and applications to the red-shift of spectral lines and bending of light-rays. The best introduction to the study of the foundation of physics is physics itself; so those philosophers interested in the foundations of relativity theory will find here a lucid and logically respectable exposition of that theory, and in that way an understanding of its fundamentals and problems will be reached.—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)

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)

This is easily the most systematic survey of the foundations of logic and mathematics available today. Although Beth does not cover the development of set theory in great detail, all other aspects of logic are well represented. There are nine chapters which cover, though not in this order, the following: historical background and introduction to the philosophy of mathematics; the existence of mathematical objects as expressed by Logicism, Cantorism, Intuitionism, and Nominalism; informal elementary axiomatics; formalized axiomatics with reference to finitary (...) theory of proof; non-elementary metamathematics, embracing formal syntax and semantics; applications of set theory and topology in metamathematics—especially in the theory of models; recursive function theory; the logical paradoxes; the relation of philosophy of mathematics to general philosophy. This is a mere skeleton of the whole, but it indicates the broad sweep of the work. One unifying feature is the author's use of his "semantic tableau" method of examining the truth or falsity of sentences. Although the author is an Intuitionist, classical metamathematical proof techniques are by no means slighted; they are used throughout much of the book, and are indispensable, of course, when dealing with classical logic. Exercises are scattered throughout and at the end; few of them are trivial. There is a very extensive bibliography, brought up to date from the first edition. This extraordinary book will be of use to logicians as a reference tool and to philosophers trying to survey the field of modern formal logic; its appearance in a fine paper edition is therefore doubly welcome—P. J. M. (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)

For a long while Bayesian techniques in statistics in general, and decision theory in particular, were considered suspect at best, and to be avoided; but now along comes Jeffrey with a system of subjective probability and utility functions determined by the individual's preferences, and a strongly Bayesian approach to decision-making, and by so doing puts the whole matter in a new light and makes it quite important to reassess the prior rejection of Bayesian methods. There are twelve chapters, each with (...) exercises, which begin with the model of deliberation, progress though scaling and ranking desirability, preference and propositional attitudes, thence to probability and measurement of desirability, and finally to induction and confirmation. The author's theory bears some resemblances to that sketched by Ramsey, but it draws somewhat on the later work of Von Neumann and Morgenstern. The author examines probability as viewed both statically—when the agent's attitudes are constant—and dynamically-when desirability and, consequently, probability assignments change. This text is one of the small but growing library of works whose interest is induction and probability theory; in that library, it will occupy an important place.—P. J. M. (shrink)

What is attempted in this book is a presentation of various areas of science in such ways that their attendant philosophical problems are displayed, and their philosophical relevance is made evident. Essentially, there are three parts to the book: the first, comprising chapters on the nature of number, geometry, and the mathematical treatments of motion and measurement, presents the usual problems of conventionalism in geometry, physical vs. formal geometry, but also discusses Turing machines and information theory. The next five chapters (...) analyze the laws of motion, probability, chance, and credibility, order in nature, and the conceptual structure of modern physics. The last four chapters constitute a study of evolutionary theory, psychology, ethics, and economic theory, the last topic not often appearing in studies of scientific philosophy. The selection of topics is judicious and balanced, but the author often overuses certain ideas and theories, for example, information theory, as both heuristic devices and as factually true of various situations; in this sense he is misleading and conceptually unrigorous. A number of illustrations, visually interesting and enlightening, help to add interest.—P. J. M. (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 textbook in symbolic logic comprising sentential and quantificational theory only. The logic of the propositional calculus is developed in a natural-deduction form reminiscent of Fitch's technique; therefore, most of the theorems take the form of metamathematical assertions and possess corresponding meta-proofs. The classical propositional calculus SCc is then formulated in the Hilbert-style axiomatic way which naturally leads to consistency, completeness, and decidability theorems for the system. The theory of quantifiers is also first set up in natural deduction (...) form, and then reformulated classically. Leblanc spends considerable time in a careful treatment of satisfiability and validity in first-order logic, this leading naturally to the Löweheim-Skolem [[sic]] theorem and related completeness results. There is an appendix containing some relevant results from set theory. In general this is a most thorough and neat job which succeeds admirably in giving in semantical form a rigorous introduction to logic.—P. J. M. (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 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)

This volume contains the proceedings of the 1963 Berkeley symposium on the theory of models, and is one of the three or four most important collections of papers in logic ever to appear. There are forty-four papers, grouped into eight categories: model theory of first-order languages, model theory of richer classical languages, model theory of nonclassical languages, mathematical structures, model-theoretic results in set-theory, model-theoretic results in number theory and analysis, model-theoretic results in algebra and geometry, model-theoretic results in the empirical (...) sciences. One could not begin to list here the contributors and their papers, but the list of sections does exhibit the vast sweep of the topics. The scholarly value of the collection is increased by an attempt to standardize terminology and notation, notes on what model theory is—its place in logic and foundational studies—and does, and a huge bibliography which not only lists nearly all papers on model theory up to 1963, but which serves as a common reference source for all papers. A list of participants in the symposium is included. All the papers are in English.—P. J. M. (shrink)

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)

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)

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, 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)

The author's central thesis is that a knowledge of set theory can be put to good use by the linguist interested in the syntax of natural languages. The author first points out the role of set theory in formal science, and then gives a short summary of some of the more important ideas. He then develops certain relations in set theory which are of special importance in the study of languages. A fair number of examples—admittedly in rather trivial form—which occur (...) in the study of language are exhibited to show some of the applications in mind. The last few pages are devoted to a review of how his thesis has fared. Although it may seem obvious to some that set theory is the means par excellence for the formal study of any discipline, many linguists apparently do not yet see this; this book will go some way toward demonstrating this.—P. J. M. (shrink)

While attention to research integrity has been growing over the past decades, the processes of signalling and denouncing cases of research misconduct remain largely unstudied. In this article, we develop a theoretically and empirically informed understanding of the causes and consequences of reporting research misconduct in terms of power relations. We study the reporting process based on a multinational survey at eight European universities. Using qualitative data that witnesses of research misconduct or of questionable research practices provided, we aim to (...) examine actors’ rationales for reporting and not reporting misconduct, how they report it and the perceived consequences of reporting. In particular we study how research seniority, the temporality of work appointments, and gender could impact the likelihood of cases being reported and of reporting leading to constructive organisational changes. Our findings suggest that these aspects of power relations play a role in the reporting of research misconduct. Our analysis contributes to a better understanding of research misconduct in an academic context. Specifically, we elucidate the processes that affect researchers’ ability and willingness to report research misconduct, and the likelihood of universities taking action. Based on our findings, we outline specific propositions that future research can test as well as provide recommendations for policy improvement. (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)

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)

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)

BackgroundTriggered by a series of controversies and diversifying expectations of editorial practices, several innovative peer review procedures and supporting technologies have been proposed. However, adoption of these new initiatives seems slow. This raises questions about the wider conditions for peer review change and about the considerations that inform decisions to innovate. We set out to study the structure of commercial publishers’ editorial process, to reveal how the benefits of peer review innovations are understood, and to describe the considerations that inform (...) the implementation of innovations.MethodsWe carried out field visits to the editorial office of two large academic publishers housing the editorial staff of several hundreds of journals, to study their editorial process, and interviewed editors not affiliated with large publishers. Field notes were transcribed and analysed using coding software.ResultsAt the publishers we analysed, the decision-making structure seems to show both clear patterns of hierarchy and layering of the different editorial practices. While information about new initiatives circulates widely, their implementation depends on assessment of stakeholder’s wishes, impact on reputation, efficiency and implementation costs, with final decisions left to managers at the top of the internal hierarchy. Main tensions arise between commercial and substantial arguments. The editorial process is closely connected to commercial practices of creating business value, and the very specific terms in which business value is understood, such as reputation considerations and the urge to increase efficiency. Journals independent of large commercial publishers tend to have less hierarchically structured processes, report more flexibility to implement innovations, and to a greater extent decouple commercial and editorial perspectives.ConclusionOur study demonstrates that peer review innovations are partly to be understood in light of commercial considerations related to reputation, efficiency and implementations costs. These arguments extend beyond previously studied topics in publishing economics, including publishers’ choice for business or publication models and reach into the very heart of the editorial and peer review process. (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)

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)

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)

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)

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 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)

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)

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)

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 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 is a much-revised edition of the 1941 text; the most significant changes are as follows: sections ## 21-30 are revised into seven and the discussions on validity, truth-functional implication, truth, etc., are revised in form to bring them in line with more modern approaches; the third chapter, except for the terminological changes which pervade the text is essentially unchanged from the original; the last chapter on quantificational inference is much-revised in all but the first few sections. The tone of (...) the book is now very much closer to his Methods of Logic, but the last chapter of the latter covers far more of glimpses ahead than does the corresponding one here.—P. J. M. (shrink)

Peer review of journal submissions has become one of the most important pillars of quality management in academic publishing. Because of growing concerns with the quality and effectiveness of the system, a host of enthusiastic innovators has proposed and experimented with new procedures and technologies. However, little is known about whether these innovations manage to convince other journal editors. This paper will address open questions regarding the implementation of new review procedures, the occurrence rate of various peer review procedures and (...) their distribution over scientific disciplines or academic publishers, as well as the motivations for editors or publishers to engage in novel review procedures. It shows that in spite of enthusiastic innovation, the adoption of new peer review procedures is in fact very slow, with the exception of text similarity scanners. For now, peer review innovations appear to be restricted to specific niches in academic publishing. Analysing these niches, the article concludes with a reflection on the circumstances in which innovations might be more widely implemented. (shrink)

Following publication of this article [1] it was brought to our attention that we omitted to provide credit for Table 1. While the content of the table and the systematization of blinding in review have been referenced in the text as coming from [2], the credit line for Table 1 should have been added as follows: “Reproduced with permission from [2] licensed under a CC BY-NC-ND 3.0 License”. The original publication of this article has been corrected accordingly.

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)