The purpose of this paper may be found in the following quotation. “Whenever an argument can be made to lead to a descending infinitude of natural numbers the hypothesis upon which the argument rests becomes untenable. This method of proof is called the method of infinite descent;.... It would be interesting and valuable to compare this method with the method of mathematical induction.”.

'Propositionalism' is the widely held view that all intentional mental relations-all intentional attitudes-are relations to propositions or something proposition-like. Paradigmatically, to think about the mountain is ipso facto to think that it is F, for some predicate 'F'. It seems, however, many intentional attitudes are not relations to propositions at all: Mary contemplates Jonah, adores New York, misses Athens, mourns her brother. I argue, following Brentano, Husserl, Church and Montague among others, that the way things seem is the way (...) they are, and that propositionalism must be abandoned. (shrink)

Modal counterpart theory identifies a thing’s possibly being F with its having a counterpart that is F at another possible world; temporal counterpart theory identifies a thing’s having been F or going to be F, with its having a counterpart that is F at another time. Benovsky, J. 2015. “Alethic Modalities, Temporal Modalities, and Representation.” Kriterion: Journal of Philosophy 29: 18–34 in this journal endorses modal counterpart theory but holds that temporal counterpart theory is untenable because it does not license (...) the ascription of the intuitively correct temporal properties to ordinary objects, and hence that we should understand ordinary objects, including persons, as transtemporal ‘worms’. I argue that the worm theory is problematic when it comes to accounting for what matters in survival and that temporal counterpart theory provides a plausible account of personal persistence. (shrink)

Modal counterpart theory identifies a thing’s possibly being F with its having a counterpart that is F at another possible world; temporal counterpart theory, the stage view, according to which people and other ordinary objects are instantaneous stages, identifies a thing’s having been F or going to be F, with its having a counterpart that is F at another time. Both counterpart theories invite what has been called ‘the argument from concern’ (Rosen, G. 1990. “Modal Fictionalism.” Mind 99 (395): 327–54). (...) Why should I be concerned about my counterparts at other possible worlds or other times? I care about how things might have gone for me—not how they go for other people at other possible worlds; I care about my prospects—not the way go for other people at other times. Jiri Benovsky has argued that while modal counterpart theory can be defended against this style of argument, temporal counterpart theory cannot (Benovsky, J. 2015. “Alethic Modalities, Temporal Modalities, and Representation.” Kriterion: Journal of Philosophy 29: 18–34). I argue that temporal counterpart theory, like modal counterpart theory, resists the argument from concern. (shrink)

Ashley Montagu, who first attacked the term "race" as a usable concept in his acclaimed work, Man's Most Dangerous Myth, offers here a devastating rebuttal to those who would claim any link between race and intelligence. In now classic essays, this thought-provoking volume critically examines the terms "race" and "IQ" and their applications in scientific discourse. The twenty-four contributors--including such eminent thinkers as Stephen Jay Gould, Richard Lewontin, Urie Bronfenbrenner, W.F. Bodmer, and Jerome Kagan--draw on fields that range from biology (...) and genetics to psychology, anthropology, and education. What emerges in piece after piece is a deep skepticism about the scientific validity of intelligence tests, especially as applied to evaluating innate intelligence, if only because scientists still cannot distinguish between genetic and environmental contributions to the development of the human mind. Five new essays have been included that specifically address the claims made in the recent, highly controversial book, The Bell Curve. Must reading for anyone interested in racism and education in America, Race and IQ is a brilliantly lucid exploration of the boundary line between race and intelligence. (shrink)

One of the goals of a certain brand of philosopher has been to give an account of language and linguistic phenomena by means of showing how sentences are to be translated into a "logically perspicuous notation" (or an "ideal language"—to use passe terminology). The usual reason given by such philosophers for this activity is that such a notational system will somehow illustrate the "logical form" of these sentences. There are many candidates for this notational system: (almost) ordinary first-order predicate logic (...) (see Quine [1960]), higher-order predicate logic (see Parsons [1968, 1970]), intensional logic (see Montague [1969, 1970a, 1970b, 1971]), and transformational grammar (see Harrnan [1971]), to mention some of the more popular ones. I do not propose to discuss the general question of the correctness of this approach to the philosophy of language, nor do I wish to adjudicate among the notational systems mentioned here. Rather, I want to focus on one problem which must be faced by all such systems—a problem that must be discussed before one decides upon a notational system and tries to demontrate that it in fact can account for all linguistic phenomena. The general problem is to determine what we shall allow as linguistic data; in this paper I shall restrict my attention to this general problem as it appears when we try to account for certain words with non-singular reference, in particular, the words that are classified by the count/ mass and sortal/non-sortal distinctions. (shrink)

Best known for reviving the tradition of classical liberalism, F. A. Hayek was also a prominent scholar of the philosopher John Stuart Mill. One of his greatest undertakings was a collection of Mill’s extensive correspondence with his longstanding friend and later companion and wife, Harriet Taylor-Mill. Hayek first published the Mill-Taylor correspondence in 1951, and his edition soon became required reading for any study of the nineteenth-century foundations of liberalism. This latest addition to the University of Chicago Press’s Collected (...) Works of F. A. Hayek series showcases the fascinating intersections between two of the most prominent thinkers from two successive centuries. Hayek situates Mill within the complex social and intellectual milieu of nineteenth-century Europe—as well as within twentieth-century debates on socialism and planning—and uncovers the influence of Taylor-Mill on Mill’s political economy. The volume features the Mill-Taylor correspondence and brings together for the first time Hayek’s related writings, which were widely credited with beginning a new era of Mill scholarship. (shrink)

This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around (...) 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality. (shrink)

Sound and Grammar: A Neo-Sapirian Theory of Language by Susan F. Schmerling offers an original overall linguistic theory based on the work of the early American linguist Edward Sapir, supplemented with ideas from the philosopher-logicians Kazimierz Ajdukiewicz and Richard Montague and the linguist Elisabeth Selkirk. The theory yields an improved understanding of interactions among different aspects of linguistic structure, resolving notorious issues directly inherited by current theory from (post- ) Bloomfieldian linguistics. In the theory presented here, syntax is a (...) filter on a phonological algebra, not a linguistic level; linguistic expressions are phonological structures, and syntax is semantically relevant relations among phonological structures. The book shows how Neo-Sapirian grammar sheds new light on syntax-phonology interactions in English, German, French, and Spanish. (shrink)

A process-oriented model of belief is presented which permits the representation of nested propositional attitudes within first-order logic. The model (NIM, for nested intensional model) is axiomatized, sense-based (via intensions), and sanctions inferences involving nested epistemic attitudes, with different agents and different times. Because NIM is grounded upon senses, it provides a framework in which agents may reason about the beliefs of another agent while remaining neutral with respect to the syntactic forms used to express the latter agent's beliefs. Moreover, (...) NIM provides agents with a conceptual map, interrelating the concepts of knowledge, belief, truth, and a number of cognate concepts, such as infers, retracts, and questions. The broad scope of NIM arises in part from the fact that its axioms are represented in a novel extension of first-order logic, -FOL (presented herein). -FOL simultaneously permits the representation of truth ascriptions, implicit self-reference, and arbitrarily embedded sentences within a first-order setting. Through the combined use of principles derived from Frege, Montague, and Kripke, together with context-sensitive semantic conventions, -FOL captures the logic of truth inferences, while avoiding the inconsistencies exhibited by Tarski. Applications of -FOL and NIM to interagent reasoning are described and the soundness and completeness of -FOL are established herein. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:John Gregory and the Invention of Professional Medical Ethics and the Profession of Medicine by Laurence B. McCullough, John Gregory’s Writings on Medical Ethics and Philosophy of Medicine ed. by Laurence B. McCullough, Medicine and Morals in the Enlightenment: John Gregory, Thomas Percival and Benjamin Rush by Lisbeth HaakonssenHeiner F. KlemmeLaurence B. McCullough. John Gregory and the Invention of Professional Medical Ethics and the Profession of Medicine. Dordrecht, (...) Boston, London: Kluwer Academic Publishers, 1998. Pp. xv + 347. Cloth, $140.00.Laurence B. McCullough, editor. John Gregory’s Writings on Medical Ethics and Philosophy of Medicine. Dordrecht, Boston, London: Kluwer Academic Publishers, 1998. Pp. xi + 254. Cloth, $105.00.Lisbeth Haakonssen. Medicine and Morals in the Enlightenment: John Gregory, Thomas Percival and Benjamin Rush. Amsterdam, Atlanta: Rodopi, 1997. Pp. x + 247. Paper, $20.50.The Scottish Enlightenment is widely appreciated for its contributions to philosophy, economics, sociology, law, chemistry, and medicine. The ideas and theories advanced by Hume, Smith, Millar, and Ferguson are still widely debated. John Gregory (1724–1773), important in his own time, is not as well known as some of his friends and colleagues. He was professor of medicine at the University of Edinburgh from 1766 to 1773, where he taught introductory lectures on the theory and practice of medicine. A set of extensive student notes from these lectures, entitled Observations on the Duties and Offices of a Physician, appeared anonymously in 1770. Two years later, Gregory himself published a revised version of his lectures under the title Lectures on the Duties and Qualifications of a Physician. These two books are said to mark the beginnings of professional medical ethics in the English-speaking world. They are also sometimes characterized as having anticipated bioethics.McCullough’s comprehensive John Gregory and the Invention of Professional Medical Ethics and the Profession of Medicine is the first modern intellectual biography of Gregory. Based on extensive research into eighteenth-century institutional context and the study of hitherto unknown manuscripts, he gives a full account of Gregory’s education at Edinburgh and Leiden, and his practice and teaching of medicine at Aberdeen, London, and Edinburgh. He stresses the importance of Gregory’s membership in the Aberdeen Philosophical Society and his close contact with Mrs. Montagu and her Circle for the understanding of his medical ethics. McCullough also shows that Bacon’s experimental method had a decisive influence on Gregory. Gregory took over Bacon’s three offices or ends of medicine: preservation of health, prolonging of life, and curing of diseases. In 1772, perhaps anticipating his premature death from hereditary gout, he added a fourth office, namely easing the pain of dying. Gregory referred mainly to Bacon (and Reid) in his Lectures to make clear how we can enlarge our medical knowledge by the method of experience and observation, pointing out that the progress of medicine had been seriously retarded by the way in which it was taught since Hippocrates. He also thought it was handicapped by the view that only professionals [End Page 535] should practice it, and claimed that even quacks have their advantages because their interest and reputation seldom suffer from the failure of the experiments necessary for the improvement of the medical profession.Gregory also argued that we should regard medicine not as a trade but as an art. In this context the principle of sympathy (or humanity) became important for him. Sympathy was the basis of the central duties in his Lectures. In a time of extreme instability of manners, when medicine was regarded more as a trade than an art, there was no physician-patient relationship based on the epistemological and moral authority of the physician. According to McCullough, it was Gregory who created “the physician-patient relationship as fiduciary. The virtues of the physician as fiduciary—openness to conviction, tenderness, and steadiness—provided for him the moral causes that would gather physicians together into a group worthy of the name, ‘profession,’ in its intellectual and moral senses” (265). The physician should no longer view his patients as moral strangers.McCullough claims that Gregory’s medical ethics is not just of historical interest, providing bioethics with its own history. It is also of... (shrink)

Since the pioneering work by Kripke and Montague, the term possible world has appeared in most theories of formal semantics for modal logics, natural languages, and knowledge-based systems. Yet that term obscures many questions about the relationships between the real world, various models of the world, and descriptions of those models in either formal languages or natural languages. Each step in that progression is an abstraction from the overwhelming complexity of the world. At the end, nothing is left but (...) a colorful metaphor for an undefined element of a set W called worlds, which are related by an undefined and undefinable primitive relation R called accessibility. For some purposes, the resulting abstraction has proved to be useful, but as a general theory of meaning, the abstraction omits too many significant features. So much information has been lost at each step that many philosophers, linguists, and psychologists have dismissed model-theoretic semantics as irrelevant to the study of meaning. This article examines the steps in the process of extractingthe pair (W,R) from the world and the way people talk about the world. It shows that the Kripke worlds can be reinterpreted as part of a Peircean semiotic theory, which can also include contributions from many other studies in cognitive science. Among them are Dunn’s semantics based on laws and facts, the lexical semantics preferred by manylinguists, psychological models of how the world is perceived, and philosophies of science that relate theories to the world. A full integration of all those sources is far beyond the scope of this article, but an outline of the approach suggests that Peirce’s vision is capable of relating and reconciling the competing sources. (shrink)

In 1974, a wonderful little book came out entitled Formal Philosophy: Selected Papers of Richard Montague, edited by Richmond H. Thomason. The book was a beautiful testimony to the fact that formal methods may indeed clarify, sharpen and solve philosophical problems, defusing airy philosophical intuitions in clear, crisp and concise ways while at the same time turning philosophical wonder into scientific inquiry.

This volume offers a collective study of the work of P. F. Strawson (1919-2006) and an exploration of its relevance for current philosophical debates. It is the first book since Strawson's death to cover the full range of his philosophy, with chapters by world-leading experts about his lasting contributions to the philosophy of language, metaphysics, epistemology, moral philosophy, and philosophical methodology. It aims to achieve a balance between exegesis of Strawson, critical engagement, and consideration of the reception and continuing value (...) of his work. It explores the intellectual relations between Strawson and some of his predecessors and contemporaries and it will be an indispensable source for scholars and students of twentieth-century philosophy and its influence in the twenty-first. With contributions by Anne Bezuidenhout, Ian Rumfitt, Paul Snowdon, Quassim Cassam, Michelle Montague, Hans-Johann Glock, Anil Gomes, Lilian Alweiss, Giuseppina D'Oro, A.P. Martinich, Paul Russell, Lucy Allais, and Victoria McGeer. (shrink)

The essays in this book analyze significant perspectives of the recent past in American philosophy; they represent some of the major trends of this period. Alfred North Whitehead is included with the recent American philosophers since his major philosophic ideas were fully developed in this country. There has been no attempt to deal comprehensively with this period. Several philosophers of equal importance who also deserve attention-C. l. Lewis, A. O. Love joy, W. F. Montague, R. B. Perry, F. J. (...) E. Woodbridge, and others have not been discussed. Most of the essays were published at various times in various journals. Though all of the perspectives are presented with sympathetic understanding, they are also critically evaluated. 2 AMERICAN PHILOSOPHY OF THE RECENT PAST But even more than individual philosophers and schools of philos ophy the larger background of contemporary American life has nour ished the empirical spirit. Science as the most pervasive climate of our intellectual and practical activity has enhanced the empirical attitude. The great development, in this country, of business and technological industry has encouraged the pragmatic, empirical outlook. Empiricism, however, is an ambiguous term, and its different meanings have different philosophic consequences. For some it means that only concrete personal experience can be accepted as reality; for others it means the succession of sense-impressions. The more recent usage, the one that has been dominant in American philosophy, identifies empiricism with objectively and socially verifiable pronounce ments, that is, with experimentalism, or confirmation through demon strable evidence. (shrink)

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis of (...) Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Löf, puts thesystem on par with the early efforts of Frege andWhitehead-Russell. This quite (...) recent work, however,has proved valuable not only in the philosophy andfoundations of mathematics, but has also foundpractical application in computer science, where thelanguage of constructivism serves as an implementableprogramming language, and within the philosophy oflanguage.\footnote{Nordstr\"{o}m et al. give an overview of the work in computerscience, whereas Ranta provides an impressiveconstructivist alternative to Montague Grammar usingthe richer type structure of Martin-L\"{o}f in placeof the simple classical type theory of Church.} Mypresentation will be carried out through a contrastwith standard metamathematical work.\footnote{Troelstra and van Dalen give an encyclopedictreatment of the metamathematics of constructivism.}In the course of the development I have occasion tooffer some novel considerations on thenature of proof and inference. (shrink)

Best known for reviving the tradition of classical liberalism, F. A. Hayek was also a prominent scholar of the philosopher John Stuart Mill. One of his greatest undertakings was a collection of Mill’s extensive correspondence with his longstanding friend and later companion and wife, Harriet Taylor-Mill. Hayek first published the Mill-Taylor correspondence in 1951, and his edition soon became required reading for any study of the nineteenth-century foundations of liberalism. This latest addition to the University of Chicago Press’s Collected (...) Works of F. A. Hayek series showcases the fascinating intersections between two of the most prominent thinkers from two successive centuries. Hayek situates Mill within the complex social and intellectual milieu of nineteenth-century Europe—as well as within twentieth-century debates on socialism and planning—and uncovers the influence of Taylor-Mill on Mill’s political economy. The volume features the Mill-Taylor correspondence and brings together for the first time Hayek’s related writings, which were widely credited with beginning a new era of Mill scholarship. (shrink)