Since antiquity, opposed concepts such as the One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical thought. Yet they have also given rise to perplexing problems and conceptual paradoxes which continue to haunt scientists and philosophers. In _Oppositions and Paradoxes_, John L. Bell explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, Bell (...) not only motivates abstract conceptual thinking about the paradoxes at issue, but he also offers a compelling introduction to central ideas in such otherwise-difficult topics as non-Euclidean geometry, relativity, and quantum physics. These paradoxes are often as fun as they are flabbergasting. Consider, for example, the famous Tristram Shandy paradox: an immortal man composing an autobiography so slowly as to require a year of writing to describe each day of his life — he would, if he had infinite time, presumably never complete the work, although no individual part of it would remain unwritten. Or think of an office mailbox labelled “mail for those with no mailbox”—if this is a person’s mailbox, how can they possibly have “no mailbox”? These and many other paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty in many of our most basic concepts. (shrink)

This monograph is a follow up to the author's classic text Boolean-Valued Models and Independence Proofs in Set Theory, providing an exposition of some of the most important results in set theory obtained in the 20th century--the independence of the continuum hypothesis and the axiom of choice. Aimed at research students and academics in mathematics, mathematical logic, philosophy, and computer science, the text has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory, and (...) includes recent developments in the field. Numerous exercises, along with the enlarged and entirely updated background material, make this an ideal text for students in logic and set theory. (shrink)

In this paper a number of oppositions which have haunted mathematics and philosophy are described and analyzed. These include the Continuous and the Discrete, the One and the Many, the Finite and the Infinite, the Whole and the Part, and the Constant and the Variable.

Trait emotional intelligence (trait EI) covers a wide range of self-perceived skills and personality dispositions such as motivation, confidence, optimism, peer relations and coping with stress. In the last few years, there has been a growing awareness that social and emotional factors play an important part in students? academic success and it has been claimed that those with high scores on a trait EI measure perform better. This research investigated whether scores on a questionnaire measure of trait EI were related (...) to school performance in a sample of British pupils. Results showed that high performing students had higher trait EI scores than low performing students and that some aspects of trait EI (motivation and low impulsivity) as well as total trait EI were significant predictors of academic achievement after controlling for prior attainment at school. Therefore, initiatives to develop the emotional and social abilities of schoolchildren might be worthwhile and more effective than concentrating solely on teaching and curriculum activities. (shrink)

This volume of papers, arising from the Royal Institute of Philosophy Conference on Philosophy and Medical Welfare, includes contributions from doctors, nurses, and administrators in the field of health care as well as academics in the disciplines of philosophy, economics, and politics.

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics can be reproduced with this form of behaviour. In Part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model in L which it predicts. (...) In Part II of this paper we use M-space to show that QED can be reduced to two simple rules for a two-body interaction. (shrink)

The dissertation's primary task is to discern to what extent the investigations contained in Aristotle's Metaphysics conform to the model of science developed in the Posterior Analytics. It concludes that the Metaphysics substantially follows the model of the Analytics in studying the causes and attributes of a specific nature, although it makes significant departures especially in its conception of the principles of being and substance. ;Two introductory chapters discuss respectively Aristotle's conception of science in the Analytics and the problems one (...) is likely to face in attempting to apply this conception to the Metaphysics . Chapter 3 clarifies the meaning of the phrase "science of being qua being" by reference to the Posterior Analytics, and introduces the concept of pro&d13;v 3&d3;n equivocity. Chapter 4 considers the role of dialectic in metaphysics with particular reference to the principle of noncontradiction. Chapter 5 argues that the second part of Meta. 4.2 introduces a demonstrative science of the per se attributes of being and unity. ;Chapter 6 introduces the investigation into the principles and causes of being and reviews the aporias about the principles . Chapter 7 offers a hypothesis to explain Aristotle's identification of the science of being with first philosophy. The last two chapters argue that Aristotle is pursuing this investigation in the central books of Melaphysics, but his pursuit of the investigation there is incomplete. ;This interpretation provides an alternative to those of T. H. Irwin and Walter Leszl, who argue that metaphysics is a second-order discipline and not a science after the model of the Analytics. It finds explicit support in recent work by Robert Bolton and Alan Code, while widening the range of issues to include the attributes of being and the importance of first philosophy for understanding the nature of being. It supports many of the conclusions of Joseph Owens's, Urbain Dhondt's, and Frede and Patzig's work on the object of metaphysics. There are also substantial discussions of the contributions of G. E. L. Owen, J. G. Stevenson, Theodore Scaltsas, and John Thorp. (shrink)

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current (...) understanding of the profound nature of quantum concepts. First edition Hb (1987): 0-521-33495-0 First edition Pb (1988): 0-521-36869-3. (shrink)

We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. (Observe that the axiom of choice cannot be persistent in this sense since it implies the law of excluded middle.) We also establish the persistence of some (...) familiar results in the theory of (complete) Boolean algebras--notably, the proposition that every complete Boolean algebra is an absolute subretract. This (almost) resolves a question of Banaschewski and Bhutani as to whether the Sikorski extension theorem for Boolean algebras is persistent. (shrink)

We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. We also establish the persistence of some familiar results in the theory of Boolean algebras--notably, the proposition that every complete Boolean algebra is an absolute subretract. This (...) resolves a question of Banaschewski and Bhutani as to whether the Sikorski extension theorem for Boolean algebras is persistent. (shrink)

This new edition of the classic Contemporary Theories of Knowledge has been significantly updated to include analyses of the recent literature in epistemology.

The objective of this book is to produce a theory of rational decision making for realistically resource-bounded agents. My interest is not in “What should I do if I were an ideal agent?”, but rather, “What should I do given that I am who I am, with all my actual cognitive limitations?” The book has three parts. Part One addresses the question of where the values come from that agents use in rational decision making. The most comon view among philosophers (...) is that they are based on preferences, but I argue that this is computationally impossible. I propose an alternative theory somewhat reminiscent of Bentham, and explore how human beings actually arrive at values and how they use them in decision making. Part Two investigates the knowledge of probability that is required for decision-theoretic reasoning. I argue that subjective probability makes no sense as applied to realistic agents. I sketch a theory of objective probability to put in its place. Then I use that to define a variety of causal probability and argue that this is the kind of probability presupposed by rational decision making. So what is to be defended is a variety of causal decision theory. Part Three explores how these values and probabilities are to be used in decision making. In chapter eight, it is argued first that actions cannot be evaluated in terms of their expected values as ordinarily defined, because that does not take account of the fact that a cognizer may be unable to perform an action, and may even be unable to try to perform it. An alternative notion of “expected utility” is defined to be used in place of expected values. In chapter nine it is argued that individual actions cannot be the proper objects of decision-theoretic evaluation. We must instead choose plans, and select actions indirectly on the grounds that they are prescribed by the plans we adopt. However, our objective cannot be to find plans with maximal expected utilities. Plans cannot be meaningfully compared in that way. (shrink)

"A sequel to Pollock's How to Build a Person, this volume builds upon that theoretical groundwork for the implementation of rationality through artificial ...

Now in a new edition, this exceptionally successful survey text introduces the faith, belief, and practice of Islam from its earliest origins up to its contemporary resurgence. John L. Esposito, an internationally renowned expert on Islam, traces the development of this dynamic faith and its impact on world history and politics. The fourth edition features updated and expanded coverage of Islam and politics; more extensive treatment of early Islam; an enhanced art program; a new appendix; and a free 6-month (...) subscription to Oxford Islamic Studies Online edited by John L. Esposito. (shrink)

Probability is sometimes regarded as a universal panacea for epistemology. It has been supposed that the rationality of belief is almost entirely a matter of probabilities. Unfortunately, those philosophers who have thought about this most extensively have tended to be probability theorists first, and epistemologists only secondarily. In my estimation, this has tended to make them insensitive to the complexities exhibited by epistemic justification. In this paper I propose to turn the tables. I begin by laying out some rather simple (...) and uncontroversial features of the structure of epistemic justification, and then go on to ask what we can conclude about the connection between epistemology and probability in the light of those features. My conclusion is that probability plays no central role in epistemology. This is not to say that probability plays no role at all. In the course of the investigation, I defend a pair of probabilistic acceptance rules which enable us, under some circumstances, to arrive at justified belief on the basis of high probability. But these rules are of quite limited scope. The effect of there being such rules is merely that probability provides one source for justified belief, on a par with perception, memory, etc. There is no way probability can provide a universal cure for all our epistemological ills. (shrink)

In a number of recent papers I have been developing the theory of "nomic probability," which is supposed to be the kind of probability involved in statistical laws of nature. One of the main principles of this theory is an acceptance rule explicitly designed to handle the lottery paradox. This paper shows that the rule can also handle the paradox of the preface. The solution proceeds in part by pointing out a surprising connection between the paradox of the preface and (...) the gambler's fallacy. (shrink)

This exceptionally successful survey text introduces the teachings and practice of Islam from its earliest origins up to its contemporary practice. John L. Esposito, an internationally renowned expert on Islam, traces the development of Islam and its impact on world history and politics.Lucidly written and expansive in scope, Islam: The Straight Path, Updated Fifth Edition, provides keen insight into one of the world's least understood religions. It is ideally suited for use in courses on Islam, world religions, comparative religions, (...) and Middle East history and culture.A FREE 6-month subscription to Oxford Islamic Studies Online, edited by John L. Esposito, is included with the purchase of every new copy of this text. (shrink)

Counterexamples are constructed for the theory of rational choice that results from a direct application of classical decision theory to ordinary actions. These counterexamples turn on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. An alternative theory of rational choice is proposed that evaluates actions using a more complex measure, and then it is shown that this is equivalent to applying classical decision theory to "conditional (...) policies" rather than ordinary actions. (shrink)

In what seems to have been his last paper, Insight and Reflection (1954), Hermann Weyl provides an illuminating sketch of his intellectual development, and describes the principal influences—scientific and philosophical—exerted on him in the course of his career as a mathematician. Of the latter the most important in the earlier stages was Husserl’s phenomenology. In Weyl’s work of 1918-22 we find much evidence of the great influence Husserl’s ideas had on Weyl’s philosophical outlook—one need merely glance through the pages of (...) Space-Time-Matter or The Continuum to see it. Witness, for example, the following passages from the former. (shrink)

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.