Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of dialectical (...) argument. On the basis of these nominal definitions, Aristotle develops his definitions of the essences of truth and falsehood--his "real" definitions of truth and falsehood. Aristotle's methodical exposition of his essential definitions of truth and falsehood in the Metaphysics serves as a well-developed example of how his philosophical inquiry starts with nominal definitions and ends with real definitions. Wheeler also argues for the novel claim that Aristotle defines the most fundamental kind of truth in terms of accurate measurement. Aristotle's metrical conception of truth serves as the theoretical basis for specifying the truth conditions of various assertions, for identifying the sorts of beings implicated in these truth conditions, and for explaining the nature of approximate truth and falsehood. Far from offering us a minimal account of truth, Wheeler shows how Aristotle offers us a sophisticated and metrical theory of truth. (shrink)

Isaac Newton was indisputably one of the greatest scientists in history. His achievements in mathematics and physics marked the culmination of the movement that brought modern science into being. Richard Westfall's biography captures in engaging detail both his private life and scientific career, presenting a complex picture of Newton the man, and as scientist, philosopher, theologian, alchemist, public figure, President of the Royal Society, and Warden of the Royal Mint. An abridged version of his magisterial study Never at Rest, (...) this concise biography makes Westfall's highly acclaimed portrait of Newton newly accessible to general readers. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Isaac Newton was born on 25 December 1642 in the hamlet of Colsterworth, Lincolnshire, about six miles south of Grantham. The posthumous and only son of Isaac Newton, père, he found himself deposited with grandparents at the age of three when his mother married a second time; he remained with the grandparents for eight years until the death of his stepfather. After successfully resisting his mother's intention that he manage the considerable estate she had inherited from the two husbands, Newton (...) graduated from the grammar school in Grantham and enrolled in Trinity College, Cambridge, in June 1661. Trinity was Newton's home for the following 35 years. He received his B.A. in 1665 and his M.A. three years later. Meanwhile he had been elected to a fellowship in the college, and in 1669, upon the resignation of Isaac Barrow, he was appointed Lucasian Professor of Mathematics. Newton did not strain himself with teaching. During his nearly 30 years as a fellow of Trinity he tutored only three students, all of them wealthy fellow commoners; he formed no perceptible bond with any of them. As Lucasian Professor, he lectured once a week during one term each year, at least early in his tenure. There is testimony that frequently no one attended the lectures, and even later, when he was famous and a connection with him was potentially valuable, only two men claimed to have heard them. He ceased to lecture altogether after 1687, and may have stopped before that. (shrink)

How do we know and understand who we really are as human beings? The concept of 'the self' is central to many strands of psychology and philosophy. This book tackles the problem of how to define persons and selves and discusses the ways in which different disciplines, such as biology, sociology and philosophy, have dealt with this topic. Richard S. Hallam examines the notion that the idea of the self as some sort of entity is a human construction and, (...) in effect, a virtual reality. At the same time, this virtual self is intimately related to the reality of ourselves as biological organisms. Aiming to integrate a constructionist understanding of self with the universalizing assumptions that are needed in natural science approaches, this text is unique in its attempt to create a dialogue across academic disciplines, while retaining a consistent perspective on the problem of relating nature to culture. (shrink)

Conflicts of interest have been reduced to financial conflicts. The National Institutes of Health’s new rules for managing conflicts of interest in medical research, the first major change to the regulations in over 15 years, address only financial ties. Although several commentators urged that the regulations also cover non-financial interests, the Department of Health and Human Services declined to do so. Similarly, the Institute of Medicine’s influential 2009 Conflict of Interest Report focuses almost exclusively on financial conflicts. Institutional policies at (...) academic medical centers and guidance from professional bodies and medical journals also primarily emphasize financial ties. Even broadly worded rules are applied more readily to financial ties than non-financial interests, such as the regulations that restrict institutional review board members with conflicting interests from participating in protocol reviews. (shrink)

Studies the politics of Heidegger in terms of "thrownness" or "existential contingency". Attempts to think through Heidegger's philosophy in a manner that parallels his own dialogue with other key western thinkers.

While it seems to be evident that the vision of the eternal return of the same is the solution to the riddle mentioned in "On the vision and the riddle," exactly what constitutes the riddle is anything but clear. Li ke all good riddles the solution demands a paradigm shift. Nietzsche's riddle is solved by a radical rethinking of the concept of time, from a straight line to a circle. I give a detailed account of how Nietzsche's riddle is formulated (...) in such a way tha t the eternal return of the same is the only possible solution. (shrink)

Athletics, body imagery and spectacle : Greco-Roman practices, discourses and ideologies -- The politics of representation : English sport as an object and project of modernity -- "Staging" (capitalist/colonial) modernity : international exhibitions and Olympics -- German modernism, anti-modernism and the critical theory of sport -- A savage sorting of "winners" and "losers" : modernization, development, sport, and the challenge of slums.