Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements (...) the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index. (shrink)

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the (...) realm of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if for all Y ∈ Q there exists X ∈ P such that X is Turing reducible to Y. A weak degree is an equivalence class of mass problems under mutual weak reducibility. Let [Formula: see text] be the lattice of weak degrees of mass problems associated with nonempty [Formula: see text] subsets of the Cantor (...) space. The lattice [Formula: see text] has been studied in previous publications. The purpose of this paper is to show that [Formula: see text] partakes of hyperarithmeticity. We exhibit a family of specific, natural degrees in [Formula: see text] which are indexed by the ordinal numbers less than [Formula: see text] and which correspond to the hyperarithmetical hierarchy. Namely, for each [Formula: see text], let hα be the weak degree of 0, the αth Turing jump of 0. If p is the weak degree of any mass problem P, let p* be the weak degree of the mass problem P* = {Y | ∃X ⊆ BLR )} where BLR is the set of functions which are boundedly limit recursive in X. Let 1 be the top degree in [Formula: see text]. We prove that all of the weak degrees [Formula: see text], [Formula: see text], are distinct and belong to [Formula: see text]. In addition, we prove that certain index sets associated with [Formula: see text] are [Formula: see text] complete. (shrink)

In Making Science, Cole shows how social variables and cognitive variables interact in the evaluation of frontier knowledge.

Considerable controversy has recently arisen regarding the patenting of medical and surgical processes in the United States. One such patent, viz. for a "chevron" incision used in ophthalmologic surgery, has especially occasioned heated response including a major, condemnatory ethics policy statement from the American Medical Association as well as federal legislation denying patent protection for most uses of a patented medical or surgical procedure. This article identifies and discusses the major legal, ethical and public policy considerations offered by proponents and (...) opponents of such patents. The existing literature divides up into those who favor such patents essentially without qualification, and those who condemn and wish to outlaw them. We advance a compromise position where administrative and legislative action is called for to provide more specific guidelines regarding the patentability of such processes by the Patent and Trademark Office. Our position, in sum, will be that too much is at stake in this complicated area for either the blanket prohibition, or wholesale, uncritical acceptance, of the patenting of medical and surgical processes or techniques. (shrink)

Stephen Pinker sets out over a dozen arguments in The language instinct (Morrow, New York, 1994) for his widely shared view that natural language is inadequate as a medium for thought. Thus he argues we must suppose that the primary medium of thought and inference is an innate propositional representation system, mentalese. I reply to the various arguments and so defend the view that some thought essentially involves natural language. I argue mentalese doesn't solve any of the problems Pinker (...) cites for the view that we think in natural language. So I don't think I think the way he thinks I think. (shrink)

From roughly 1965 to 1995, Columbia University's Department of Sociology was a leading center for social study of science, both nationally and internationally. It was often referred to as the Merton School or Columbia School, and four scholars paved its way : Robert K. Merton, Harriet Zuckerman, Stephen Cole, and Jonathan Cole. The goal of the Columbia School was to create and legitimate a new sociological specialty focusing on the scientific community and the growth of scientific knowledge (...) and they did this by exploring the norms, values, and structure of science. The core values of the scientific and university system and the norms attached to them consisted of deeply held beliefs as well as principles that determined how individuals would act. They were organizing principles designed to support the institution in meeting its goals and mission. They influenced the types of social structures that developed to carry out the activities of scientists. Edited by Jonathan R. Cole, this collection of individually and co-authored papers and essays by Cole represents some of the work produced by Cole and his close collaborators over the past 50 years. the essays are contextualized with an introduction by Cole. The pieces in this volume represent the major concerns on the Columbia School, whose focus of attention was not on the production of individual pieces of knowledge, but on the social systems that made that production possible. (shrink)

This paper examines ideas which underpin the 'New Literacy Studies', including Street's critique of the 'autonomous model' of literacy. Through a re-examination of the work of Scribner and Cole, the implication that literacy is not related to cognitive development is questioned. Gee's critique of linguistic prescription is discussed. Drawing on action research perspectives, which argue that educational theory concerns the identification of educational problems and values, an approach to literacy for education is proposed.

This book puts forward a radical, unorthodox thesis with respect to the Anthropocene, the philosophy of Deleuze/Guattari and education. This book analyses the Anthropocene for its unconscious drives and develops a parallel mode of education and social change.

The French writer, philosopher, and mystic Simone Weil (1909-1943) was one of the most original spiritual personalities of the 20th century. Now Coles presents a brilliant portrait of the beloved and controversial figure who was a spiritual influence on T.S. Eliot, Flannery O'Connor, Adrienne Rich, and Albert Camus.

In Return to Reason, Stephen Toulmin argues that the potential for reason to improve our lives has been hampered by a serious imbalance in our pursuit of ...

The Hedgehog, the Fox, and the Magister's Pox is a controversial discourse, rich with facts and observations gathered by one of the most erudite minds of our ...

Stephen Toulmin argues that the potential for reason to improve our lives has been hampered by a serious imbalance in our pursuit of knowledge. The centuries-old dominance of rationality has diminished the value of reasonableness. Toulmin issues a powerful call to redress the balance between rationality and reasonableness.

I argue that God’s holiness as conceived in Hebrew Scripture grounds human obligations to obey divine commands. To disobey the commands of a holy God would disrespect a basic good, which we have decisive reason to avoid doing. God’s holiness may be a somewhat obscure property––though I propose transcendence and perfect morality as necessary conditions––but His omniscience and perfect morality guarantee that He would not command human beings to do things that His holiness would not ground His authority to command. (...) I conclude by replying to objections. (shrink)

I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed (...) by human activity in a manner similar to the constitutive construction of the US Supreme Court by certain legal and political activities. Finally, I outline some of the philosophical merits of metaphysical interpretations of mathematical theories of this type. (shrink)

"Biophilia" is the term coined by Edward O. Wilson to describe what he believes is humanity's innate affinity for the natural world. In his landmark book Biophilia, he examined how our tendency to focus on life and lifelike processes might be a biologically based need, integral to our development as individuals and as a species. That idea has caught the imagination of diverse thinkers. The Biophilia Hypothesis brings together the views of some of the most creative scientists of our time, (...) each attempting to amplify and refine the concept of biophilia. The variety of perspectives -- psychological, biological, cultural, symbolic, and aesthetic -- frame the theoretical issues by presenting empirical evidence that supports or refutes the hypothesis. Numerous examples illustrate the idea that biophilia and its converse, biophobia, have a genetic component: fear, and even full-blown phobias of snakes and spiders are quick to develop with very little negative reinforcement, while more threatening modern artifacts -- knives, guns, automobiles -- rarely elicit such a response people find trees that are climbable and have a broad, umbrella-like canopy more attractive than trees without these characteristics people would rather look at water, green vegetation, or flowers than built structures of glass and concrete The biophilia hypothesis, if substantiated, provides a powerful argument for the conservation of biological diversity. More important, it implies serious consequences for our well-being as society becomes further estranged from the natural world. Relentless environmental destruction could have a significant impact on our quality of life, not just materially but psychologically and even spiritually. (shrink)

What does it mean to think of philosophy in the condition of modernism, in which its relation to its past and future has become a relevant problem? This book argues that the writings of Wittgenstein, Heidegger, and Kierkegaard are best understood as responsive (each in their own way) to such questions. Through detailed analysis of these authors' most influential texts, Stephen Mulhall reorients our sense of the philosophical work each text aims to accomplish, engendering a critical dialogue between them (...) from which the elements of a new conception of philosophy might emerge. (shrink)

Thomas Aquinas, one of the "founding fathers" of just war theory, offers an account of virtuous warfare in practice. The author argues that Aquinas's approach to warfare, with its emphasis on justice and charity, is helpful in providing a coherent moral account of war to which Christians can subscribe. Particular attention is given to the role of charity, since this virtue is the distinguishing characteristic of the Christian soldier. Charity compels him to soldier justly, and by fighting justly, he is (...) elevated by God to friendship with God. Notable features of this approach are its emphasis on the criteria for judging whether a war is just and its relativizing of the criteria for proper combat behavior. (shrink)

Transnational corporations have become actors with significant political power and authority which should entail responsibility and liability, specifically direct liability for complicity in human rights violations. Holding TNCs liable for human rights violations is complicated by the discontinuity between the fragmented legal/political structure of the TNC and its integrated strategic reality and the international state system which privileges sovereignty and non-intervention over the protection of individual rights. However, the post-Westphalian transition—the emergence of multiple authorities, increasing ambiguity of borders and jurisdiction (...) and blurring of the line between the public and private spheres—should facilitate imposing direct responsibility on transnational firms. Mechanisms for imposing direct responsibility on TNCs are considered including voluntary agreements and international law. However, I conclude that a hybrid public-private regime which relies on non-hierarchical compliance mechanisms is likely to be both more effective and consistent with the structure of the emerging transnational order. (shrink)