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)

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)

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)

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)

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

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.

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)

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.

A Brief History of Time: From the Big Bang to Black Holes is a popular-science book on cosmology (the study of the origin and evolution of the universe) by British physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for readers who have no prior knowledge of the universe and people who are interested in learning.

A comprehensive reassessment of the concept of mimesis in the history of ancient Greek aesthetics and philosophy of art, with particular attention to Plato, Aristotle, Hellenistic philosophy, and neoplatonism. There is also a wide-ranging review of arguments pro and contra the idea of artistic mimesis from the Renaissance to modern literar theory. The book challenges standard accounts in numerous respects and builds a new dialectical model with which to make sense of the entire history of mimeticist thinking in aesthetics.

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 ...

Stephen Hetherington's prominent career within epistemology has been a series of distinctive, bold, varied and provocative arguments and ideas. Bringing together Hetherington's unique body of writing for the first time, this collection features previously published as well as new material that link his approaches to key issues including knowledge, justification, fallibility, scepticism and the Gettier Problem. Advancing our understanding of the systemic nature of Hetherington's thinking, Stephen Hetherington on Epistemology presents his distinctive perspective on some of philosophy's central (...) questions about knowledge - an inviting blend of forensic detail and 'big picture' proposals. (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)

This chapter talks about the war between the Formics, a seemingly malevolent species of aliens, and humans in the Ender's Game. The great tragedy of the violence that erupted from the Human/Formic war was the result of two deep misunderstandings. The Formics not only failed to grasp the capabilities of humanity, but humanity also deeply misunderstood the creatures that they would come to nickname “buggers.” These misunderstandings may have resulted from what is sometimes called “cultural incommensurability.” The chapter relates that (...) what is most important about Ender is not merely his ability to understand his “enemy,” but his ability to love them. He is able to harness the sympathies of the humans and change their minds about the buggers. Along with the Formic hive‐ queen, Ender now occupies the space in between the two conceptual schemes—a space he can never retreat from—and has begun translating their meanings. (shrink)

There is an imbalance of gender roles in everyone's favorite space saga, with the vast majority of characters played by males while the female parts are minimized at nearly every turn. But the underlying problem of womanhood in Star Wars might be even more insidious than Darth Sidious himself. This chapter explains why it is difficult to embrace a strong female identity anywhere, let alone in the midst of intergalactic war. It analyzes whether the women in Star Wars have what (...) it takes to bring feminism to the Force. While Princess Leia and Queen Amidala are instantly recognizable figures in popular culture, the question arises whether they represent women positively. While Leia and Padmé are typically recognized as the feminist icons of Star Wars, they are not all the films have to offer. The women of Star Wars offer just as much as any of the individual male characters. (shrink)

Defenders of pragmatic encroachment in epistemology (or what I call practicalism) need to address two main problems. First, the view seems to imply, absurdly, that knowledge can come and go quite easily—in particular, that it might come and go along with our variable practical interests. We can call this the stability problem. Second, there seems to be no fully satisfying way of explaining whose practical interests matter. We can call this the “whose stakes?” problem. I argue that both problems can (...) be addressed in roughly the same terms. More exactly, I argue that by first clarifying the whose stakes? problem an answer to the stability problem naturally falls out. (shrink)

Elizabeth Anscombe famously argued that "modern moral philosophy" centrally involved unsupported notions of obligation and culpability. Modern Moral Philosophy: From Grotius to Kant exhibits, for the first time, resources that modern moral philosophers had to respond to Anscombe's challenge, also enhancing our own philosophical grasp of morality and its foundations.