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)

The Meaning of Life and the Great Philosophers reveals how great philosophers of the past sought to answer the question of the meaning of life. This edited collection includes thirty-five chapters which each focus on a major figure, from Confucius to Rorty, and that imaginatively engage with the topic from their perspective. This volume also contains a Postscript on the historical origins and original significance of the phrase 'the meaning of life'.

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.

The problem that Tallis attempts to address in Freedom: An Impossible Reality is that science appears to describe the entire world deterministically and that this seems to leave no room for free will. In the face of this threat, Tallis defends the existence of free will by arguing that science does not explain our intentional awareness of the world; and it is our intentional awareness that makes both science and free will possible. Against Tallis, it is here argued that his (...) argument is vulnerable to two criticisms. Firstly, his characterisation of science as apparently deterministic is inaccurate. Secondly, he has not solved the problem he has set himself but rather recast it, so that his conclusion leaves us having to account for free will, not in a deterministic universe, but either as a product of chance or as a miracle. It is here suggested that when we set aside the illusory threat of scientific determinism, we also set aside the temptation of free will. That done, we may better focus upon agent’s freedom of action – as discussed by philosophers such as Hobbes, Locke and Hume – the rational capability of an agent to act upon their wishes, given the constraints under which they find themselves. (shrink)

Consciousness and the Great Philosophers addresses the question of how the great philosophers of the past might have reacted to the contemporary problem of consciousness. Each of the thirty two chapters within this edited collection focuses on a major philosophical figure from the history of philosophy, from Anscombe to Xuanzang, and imaginatively engages with the problem from their perspective. Written by leading experts in the field this exciting and engaging book explores the relevance of the history of philosophy to contemporary (...) debates and therefore is essential reading for students and scholars studying the history of philosophy, contemporary philosophy of mind and consciousness, or both. ". (shrink)

Against Tartaglia, I argue (1) that life is not necessarily meaningless but it is absurd. It is absurd because our possible disappointment at death is not a disappointment we shall ever actually experience but it is a disappointment we yet fear, now, in life. (2) Tartaglia's idea is that life is meaningless whether we realise it or not but we are better able to realise it when we are bored. Against Tartaglia, it might be argued that the idea is itself (...) a symptom of boredom, ie part of boredom itself. He has isolated meaninglessness in life but not the meaninglessness of life. (shrink)

'Roman England': R.G. Collingwood's Correspondence with Harold Bruff, compiled and introduced by Stephen Leach.

Leach asks, what would Collingwood have thought of archaeological theory, a sub-discipline of archaeology that has developed since the 1960s? He argues that Collingwood would have welcomed it for it has developed out of respect for the principle that in any investigation, in examining the evidence, one must always have some question in mind. Nonetheless, although Collingwood would have welcomed recent developments in archaeological theory, and would have urged metaphysicians to take notice of such developments, he is not himself (...) an archaeological theorist: he is, primarily, a metaphysician. (shrink)

Moore argues as follows: (1) "Metaphysics is the most general attempt to make sense of things." (1) (2) "Because of its generality, metaphysics is the one branch of philosophy that is not the philosophy of this or that specific area of human thought or experience. It is 'pure' philosophy." (8) (3) It is "a fundamentally creative exercise." (17) Against Moore, I argue that it is rather philosophy that is the most general attempt to make sense of things. Alternatively, and in (...) my view preferably, Moore might have argued as follows: (1) 'Pure' philosophy is the most general attempt to make sense of things. (2) Because of its generality, it is not concerned with this or that area of human thought or experience. (3) It is a fundamentally uncreative exercise. (shrink)

On January 11 1951 Chadbourne Gilpatric met with Wittgenstein to offer him, on behalf of the Rockefeller Foundation, funding for any forthcoming publications. Wittgenstein politely declined the offer as he did not believe his health would permit him to bring any projects to completion. The meeting is referred to in a letter from Wittgenstein to Norman Malcolm and is also recalled by O.K. Bouwsma. Bouwsma learned of it from conversations with Wittgenstein and by Gilpatric. However, it is also recounted in (...) Gilpatric’s diary. Gilpatric’s account comprises the fullest account of the meeting. It has remained unedited, until now, and is here transcribed for the first time. Five years later on February 1 1956 Gilpatric submitted a report, entitled ‘Logician and Mystic’, to the Rockefeller Foundation This report adds detail to his original account and summarises the Rockefeller’s financial support of the posthumous publication of Wittgenstein’s work. It also sketches Gilpatric’s view of Wittgenstein’s work. (shrink)

The author examines Williams' appraisal of Collingwood both in his eponymous essay on Collingwood, in the posthumously published Sense of the Past , and elsewhere in his work. The similarities and differences between their philosophies are explored: in particular, with regard to the relationship between philosophy and history and the relationship between the study of history and our present-day moral attitudes. It is argued that, despite Williams usually being classified as an analytic philosopher and Collingwood being classified as an idealist, (...) there is substantial common ground between them. Williams was aware of this and made clear his sympathy for Collingwood; but, nonetheless, the relationship between Williams and Collingwood has not previously been explored in any detail. After establishing the common ground between these philosophers, and the areas of disagreement, the author suggests that both may have something to gain from the other. (shrink)

In Philosophy in a Technological World Tartaglia argues that humanity can decide its own future, or at least try to, but that this distinctive...

For Richard Rorty the autonomy of philosophy and the idea of an ahistorical criterion of truth are ideas that stand or fall together. This article challenges that assumption. However, before proceeding to this criticism, it is necessary in this section of the article to provide some rudimentary exposition of Rorty's position.Richard Rorty wished to subjugate philosophy to history. He announced this position in Philosophy and the Mirror of Nature (1979), and his opinion on this matter did not change substantially in (...) any subsequent work. He argued that although it might be interesting to read the great philosophical texts of the past as having something to say to us directly (as proposed by Ryle and Austin), or .. (shrink)

The roots of Rorty’s mature philosophy are explored in a discussion of his early philosophical papers and reviews. His lifelong interest in metaphilosophy is traced to the influence of Richard McKeon. The crucial influence of Sellars, Wittgenstein, Heidegger, and Kuhn are also explored, as is his long-standing interest in pragmatism. It is explained how Rorty took something from all of these influences so as, cautiously, to arrive at an entirely new metaphilosophical position of his own.

This article examines the distinction that Russell drew between his work as a philosopher and his work as a journalist. It explains why, when warning against the threat posed by a nuclear arms race, Russell thought it better to write as a journalist (speaking on behalf of common sense) rather than as a philosopher. It is argued that to put aside philosophy in favour of common sense is, in this instance, a mistake.

An introduction to the role of U. T. Place in the development of modern physicalism.Export citation.

ABSTRACT A commitment to receive input from stakeholders is often obligatory in the crafting of environmental policies. This requirement is presumed to satisfy certain conditions of democracy. In this article, by drawing from pragmatism, we examine the logic of participation and prerequisites of the meaningful game of asking for and giving reasons. We elaborate the nature and significance of three components—the game, the pleadings, and the reasons. We conclude by offering the conditions under which the stakeholder game might be considered (...) legitimate. (shrink)

In Philosophy in a Technological World Tartaglia argues that humanity can decide its own future, or at least try to, but that this distinctive...

Is philosophy continuous with science or does it have a distinctive domain of inquiry that differs from that of the special sciences? Collingwood claimed that philosophy has a distinctive subject matter and a distinctive method. Its distinctive subject matter is what he called the “absolute presuppositions” that govern the special sciences and its method consists in making these presuppositions explicit by showing that they are entailed by the questions asked in the special sciences. In this chapter the editors seek to (...) provide a guide to the diverging interpretations of Collingwood’s claim that metaphysics is not the study of pure being but of the presuppositions that govern knowledge of reality. They argue that a reassessment of his contribution to philosophical methodology is timely in the light of the recent revival of interest in second-order questions concerning the role and character of philosophical analysis. (shrink)

This book discusses Collingwood's conception of the role and character of philosophical analysis. It explores questions, such as, is there anything distinctive about the activity of philosophizing? If so, what distinguishes philosophy from other forms of inquiry? What is the relation between philosophy and science and between philosophy and history? For much of the twentieth century, philosophers philosophized with little self-awareness; Collingwood was exceptional in the attention he paid to the activity of philosophizing. This book will be of interest both (...) to those who are interested in Collingwood’s philosophy and, more generally, to all who are interested in the question ‘what is philosophy?’. (shrink)

De-Signing Design: Cartographies of Theory and Practice throws new light on the terrain between theory and practice in transdisciplinary discourses of design and art. The collection brings together a selection of essays on spatiality, difference, cultural aesthetics, and identity in the expanded field of place-making and being.