The practice of personal autonomy is a dynamic event that consists of a vital interplay between the self, socio-cultural reality, meaning, and being epistemically responsible. Autonomy is not static, something that we simply possess by virtue of a status as 'rational beings'. Therefore, in this dissertation, I examine the traditional notion of autonomy as it has been developed by Kant and subsequently influenced the current debate between 'liberals' and 'communitarians'. Primarily from the standpoint of the critiques developed by Charles Taylor, (...) I argue that the fundamental disagreement between these two camps is over the concept of the self. While this landscape stands divided, some middle ground can be found in the work of Joseph Raz, who postulated the need for a combination of individual abilities and an autonomy-supporting environment as necessary conditions for practicing personal autonomy. His characterization of 'personal autonomy', distinct from Kantian autonomy, forms the underlying paradigm for this work. (shrink)

Experiential evidence shows that pain is associated with common meanings. These include a meaning of threat or danger, which is experienced as immediately distressing or unpleasant; cognitive meanings, which are focused on the long-term consequences of having chronic pain; and existential meanings such as hopelessness, which are more about the person with chronic pain than the pain itself. This interdisciplinary book - the second in the three-volume Meanings of Pain series edited by Dr Simon van Rysewyk - aims to better (...) understand pain by describing experiences of pain and the meanings these experiences hold for the people living through them. The lived experiences of pain described here involve various types of chronic pain, including spinal pain, labour pain, rheumatic pain, diabetic peripheral neuropathic pain, fibromyalgia, complex regional pain syndrome, endometriosis-associated pain, and cancer-related pain. Two chapters provide narrative descriptions of pain, recounted and interpreted by people with pain. Language is important to understanding the meaning of pain since it is the primary tool human beings use to manipulate meaning. As discussed in the book, linguistic meaning may hold clues to understanding some pain-related experiences, including the stigmatisation of people with pain, the dynamics of patient-clinician communication, and other issues, such as relationships between pain, public policy and the law, and attempts to develop a taxonomy of pain that is meaningful for patients. Clinical implications are described in each chapter. This book is intended for people with pain, their family members or caregivers, clinicians, researchers, advocates, and policy makers. (shrink)

Ideal rule utilitarianism says that a moral code C is correct if its acceptance maximizes utility; and that right action is compliance with C. But what if we cannot accept C? Rawls and L. Whitt suggest that C is correct if accepting C maximizes among codes we can accept; and that right action is compliance with C. But what if merely reinforcing a code we can't accept would maximize? G. Trianosky suggests that C is correct if reinforcing it maximizes; and (...) that right action is action that has the effect of reinforcing compliance with C. I object to this and argue that C is correct if both accepting and reinforcing C would maximize and if C is reinforcible; and that right action consists in coming as close as possible to perfect acceptance of and compliance with C. (shrink)

John Martin Fischer and Anthony L. Brueckner have argued that a person’s death is, in many cases, bad for him, whereas a person’s prenatal non-existence is not bad for him. Their suggestion relies on the idea that death deprives the person of pleasant experiences that it is rational for him to care about, whereas prenatal non-existence only deprives him of pleasant experiences that it is not rational for him to care about. Jens Johansson has objected to this justification of (...) ‘The Asymmetry’ between the badness of death and pre-natal non-existence on the grounds that what it is actually rational for us to care about is irrelevant to the question of whether the event is bad for us. Taylor Cyr has recently argued that Jens Johansson’s objection to Fischer’s and Brueckner’s position relies on an incoherent example, and is thus unsuccessful. I argue that Cyr’s attempt to defend Fischer and Brueckner in fact illustrates that their position is incoherent, and that Johansson’s objection therefore succeeds. (shrink)

Pain and pleasure affect us all. Knowing this with empathy, and acting upon it, civilises us. Without such empathy, pain can become a means of domination and injustice. Moreover, pain is expressed and responded to in all social contexts, and the word “pain” has diverse meanings, depending on the associated activities. To observe various ways in which we say that it hurts, and the many meanings of pain, I follow ordinary-language philosophy, particularly Ludwig Wittgenstein and John L Austin, and (...) I consider a range of social and historical contexts, from the closest intimacy, everyday chatter, the clinic, and beyond, to the domain of public policy and human rights. This addresses our verbal expressions of pain, their lived contexts and effects, within relationships and among social groups, altering mutual obligations, eliciting actions and reactions, and thence creating moral, legal and political norms. My aim, then, is to consider the social and political implications of ordinary performative pain-talk, in particular regarding the relationship between pain and justice, public policy, human rights and law.Clinical Implications: Clinicians’ roles in disability assessment and pain management are often affected by extrinsic concerns such as financial incentives and the risks of substance abuse. This chapter addresses those complex issues, illustrating how they have arisen in particular historical circumstances, and with political and economic causes and consequences. While unable to provide ready-to-hand clinical solutions, a pragmatic ordinary-language approach to conversations and disagreements about pain helps to chart the grounds on which these matters are debated. (shrink)

This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides 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.

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

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of (...) Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal. (shrink)

The usual meaning of the word continuous is “unbroken” or “uninterrupted”: thus a continuous entity —a continuum—has no “gaps.” We commonly suppose that space and time are continuous, and certain philosophers have maintained that all natural processes occur continuously: witness, for example, Leibniz's famous apothegm natura non facit saltus—“nature makes no jump.” In mathematics the word is used in the same general sense, but has had to be furnished with increasingly precise definitions. So, for instance, in the later 18th century (...) continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function. With the abandonment of infinitesimals in the 19th century this definition came to be replaced by one employing the more precise concept of limit. (shrink)

"The Third Edition of Philosophical Foundations of Adult Education presents seven theoretical approaches to adult education: liberal, progressive, behaviorist, humanist, radical/critical, analytic, and postmodem. The book gives the historical grounding as well as the basic principles for each approach. In this edition each chapter has been revised and brought up to date. The chapter on radical adult education incorporates recent developments in radical education, phenomenology, feminist educational theory, and critical social theory. The book contains an entirely new chapter on postmodem (...) adult education.". (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 ...

This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory, an important form of type theory (...) based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined. (shrink)

The principle of set theory known as the Axiom of Choice has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid's axiom of parallels which was introduced more than two thousand years ago” (Fraenkel, Bar-Hillel & Levy 1973, §II.4). The fulsomeness of this description might lead those unfamiliar with the axiom to expect it to be as startling as, say, the Principle of the Constancy of (...) the Velocity of Light or the Heisenberg Uncertainty Principle. But in fact the Axiom of Choice as it is usually stated appears humdrum, even self-evident. For it amounts to nothing more than the claim that, given any collection of mutually disjoint nonempty sets, it is possible to assemble a new set — a transversal or choice set — containing exactly one element from each member of the given collection. Nevertheless, this seemingly innocuous principle has far-reaching mathematical consequences — many indispensable, some startling — and has come to figure prominently in discussions on the foundations of mathematics. It (or its equivalents) have been employed in countless mathematical papers, and a number of monographs have been exclusively devoted to it. (shrink)

Hermann Weyl, one of the twentieth century's greatest mathematicians, was unusual in possessing acute literary and philosophical sensibilities—sensibilities to which he gave full expression in his writings. In this paper I use quotations from these writings to provide a sketch of Weyl's philosophical orientation, following which I attempt to elucidate his views on the mathematical continuum, bringing out the central role he assigned to intuition.

Princeton University Press, 1974. This book is out of print, but can be downloaded as a pdf file (5 MB).

5.5. Every topos is linguistic: the equivalence theorem.

Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some (...) classical first-order logic and would like to learn about other logics important to their philosophical work. (shrink)

(1984). Weather foreasting and the development of meteorological theory at the Paris Observatory, 1853–1878. Annals of Science: Vol. 41, No. 4, pp. 359-382.

IN THEIR WELL-KNOWN PAPER, Kochen and Specker (1967) introduce the concept of partial Boolean algebra (pBa) and show that certain (finitely generated) partial Boolean algebras arising in quantum theory fail to possess morphisms to any Boolean algebra (we call such pBa's intractable in the sequel). In this note we begin by discussing partial..

Traditionally, expressions in formal systems have been regarded as signifying finite inscriptions which are—at least in principle—capable of actually being written out in primitive notation. However, the fact that (first-order) formulas may be identified with natural numbers (via "Gödel numbering") and hence with finite sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is called (...) an infinitary language : in this article I discuss those infinitary languages which can be obtained in a straightforward manner from first-order languages by allowing conjunctions, disjunctions and, possibly, quantifier sequences, to be of infinite length. In the course of the discussion it will be seen that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter. Accordingly, the infinitary languages that do in fact possess these features merit special attention. (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.

This essay is an attempt to sketch the evolution of type theory from its beginnings early in the last century to the present day. Central to the development of the type concept has been its close relationship with set theory to begin with and later its even more intimate relationship with category theory. Since it is effectively impossible to describe these relationships (especially in regard to the latter) with any pretensions to completeness within the space of a comparatively short article, (...) I have elected to offer detailed technical presentations of just a few important instances. (shrink)

In their writings on Africa and colonialism, John and Jean Comaroff have explored some of the fundamental questions of social science, delving into the nature of history and human agency, culture and consciousness, ritual and representation. How are human differences constructed and institutionalized, transformed and (sometimes) resisted? How do local cultures articulate with global forms? How is the power of some people over others built, sustained, eroded, and negated?These essays work toward an "imaginative sociology," demonstrating the techniques by which (...) social science may capture the contexts that human beings construct and inhabit. In the introduction the authors offer their most complete statement to date on historical anthropology. Standing apart from the traditional disciplines of social history and modernist social science, their work is dedicated to discovering how human worlds are made and signified, forgotten and remade. (shrink)

We investigate Hilbert’s varepsilon -calculus in the context of intuitionistic type theories, that is, within certain systems of intuitionistic higher-order logic. We determine the additional deductive strength conferred on an intuitionistic type theory by the adjunction of closed varepsilon -terms. We extend the usual topos semantics for type theories to the varepsilon -operator and prove a completeness theorem. The paper also contains a discussion of the concept of “partially defined‘ varepsilon -term. MSC: 03B15, 03B20, 03G30.

The centrality of the whole/part relation in mathematics is demonstrated through the presentation and analysis of examples from algebra, geometry, functional analysis,logic, topology and category theory.

In this book Pollock deals with the subject of probabilistic reasoning, making general philosophical sense of objective probabilities and exploring their ...

then E has a subset which is the domain of a model of Peano's axioms for the natural numbers. (This result is proved explicitly, using classical reasoning, in section 3 of [1].) My purpose in this note is to strengthen this result in two directions: first, the premise will be weakened so as to require only that the map ν be defined on the family of (Kuratowski) finite subsets of the set E, and secondly, the argument will be constructive, i.e., (...) will involve no use of the law of excluded middle. To be precise, we will prove, in constructive (or intuitionistic) set theory3, the following.. (shrink)

Pollock describes an exciting theory of rationality and its partial implementation in OSCAR, a computer system whose descendants will literally be persons.

The years 1850–80 saw great advances in electrical technology in France. Innovations and inventions in this field came mainly but not exclusively from the artisan/craftsman sector, with some contribution from men from a more academic science research environment. By the end of the period inventors were more likely to have undergone some formal training in science, although there were still contributions from those who had not attended courses at the Grandes Écoles or the faculties of science but had benefited from (...) lower level classes. However, from whatever sector the innovations came, they were likely to have been, at some stage, submitted to the Academy for its judgement and approval. Thus the Academy was still playing something of its pre-revolutionary role and having an influence on the pace of electrical innovation in France. (shrink)