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

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 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..

Imagine yourself sitting on your front porch, sipping your morning coffee and admiring the scene before you. You see trees, houses, people, automobiles; you see a cat running across the road, and a bee buzzing among the flowers. You see that the flowers are yellow, and blowing in the wind. You see that the people are moving about, many of them on bicycles. You see that the houses are painted different colors, mostly earth tones, and most are one-story but a (...) few are two-story. It is a beautiful morning. Thus the world interfaces with your mind through your senses. There is a strong intuition that we are not disconnected from the world. We and the other things we see around us are part of a continuous whole, and we have direct access to them through vision, touch, etc. However, the philosophical tradition tries to drive a wedge between us and the world by insisting that the information we get from perception is the result of inference from indirect evidence that is about how things look and feel to us. The philosophical problem of perception is then to explain what justifies these inferences. We will focus on visual perception. Figure one presents a crude diagram of the cognitive system of an agent capable of forming beliefs on the basis of visual perception. Cognition begins with the stimulation of the rods and cones on the retina. From that physical input, some kind of visual processing produces an introspectible visual image. In response to the production of the visual image, the cognizer forms beliefs about his or her surroundings. Some beliefs the perceptual beliefs are formed as direct responses to the visual input, and other beliefs are inferred from the perceptual beliefs. The perceptual beliefs are, at the very least, caused or causally influenced by having the image. This is signified by the dashed arrow marked with a large question mark. We will refer to this as the mystery link. Figure one makes it apparent that in order to fully understand how knowledge is based on perception, we need three different theories.. (shrink)

If we imagine a chess-board with alternate blue and red squares, then this is something in which the individual red and blue areas allow themselves to be distinguished from each other in juxtaposition, and something similar holds also if we imagine each of the squares divided into four smaller squares also alternating between these two colours. If, however, we were to continue with such divisions until we had exceeded the boundary of noticeability for the individual small squares which result, then (...) it would no longer be possible to apprehend the individual red and blue areas in their respective positions. But would we then see nothing at all? Not in the least; rather we would see the whole chessboard as violet, i.e. apprehend it as something that participates simultaneously in red and blue. (shrink)

"There is no attempt here to lay down as inviolable or to legislate certain ways of looking at things or ways of proceeding for philosophers of religion, only proposals for how to deal with a range of basic issues-proposals that I hope will ignite much fruitful discussion and which, in any case, I shall take as a basis for my own ongoing work in the field."-from the Preface Providing an original and systematic treatment of foundational issues in philosophy of religion, (...) J. L. Schellenberg's new book addresses the structure of religious and irreligious belief, the varieties of religious skepticism, and the nature of religion itself. From the author's searching analysis of faith emerges a novel understanding of propositional faith as requiring the absence of belief. Schellenberg asks what the aims of the field should be, setting out a series of principles for carrying out some of the most important of these aims. His account of justification considers not only belief but also other responses to religious claims and distinguishes the justification of responses, propositions, and persons. Throughout Prolegomena to a Philosophy of Religion, Schellenberg is laying the groundwork for an elaboration of his own vision while at the same time suggesting how philosophers might rethink assumptions guiding most of today's work in analytic philosophy of religion. (shrink)

ABSTRACT: It is characteristic of a continuum that it be “all of one piece”, in the sense of being inseparable into two (or more) disjoint nonempty parts. By taking “part” to mean open (or closed) subset of the space, one obtains the usual topological concept of connectedness . Thus a space S is defined to be connected if it cannot be partitioned into two disjoint nonempty open (or closed) subsets – or equivalently, given any partition of S into two open (...) (or closed) subsets, one of the members of the partition must be empty. This holds, for example, for the space R of real numbers and for all of its open or closed intervals. Now a truly radical condition results from taking the idea of being “all of one piece” literally, that is, if it is taken to mean inseparability into any disjoint nonempty parts, or subsets, whatsoever . A space S satisfying this condition is called cohesive or indecomposable. While the law of excluded middle of classical logic reduces indecomposable spaces to the trivial empty space and one-point spaces, the use of intuitionistic logic makes it possible not only for nontrivial cohesive spaces to exist, but for every connected space to be cohesive.In this paper I describe the philosophical background to cohesiveness as well as some of the ways in which the idea is modelled in contemporary mathematics. (shrink)

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)

This chapter traces the historical and conceptual development of the idea of the continuum and the allied concept of real number. Particular attention is paid to the idea of infinitesimal, which played a key role in the development of the calculus during the seventeenth and eighteenth centuries, and which has undergone a revival in the later twentieth century.

For this second edition, the editors have returned to Austin's original lecture notes, amending the printed text where it seemed necessary.

John Bintliff et alii Le Tanagra Project : recherches dans une cité antique de Béotie et son territoire (2000-2002) p.541-606 Cet article présente les résultats préliminaires du Leiden-Ljubljana Field Project dans la cité antique de Tanagra, en Béotie orientale, et dans ses environs immédiats. Les travaux ont débuté en 1999, avec une vaste équipe de chercheurs et d'étudiants des Pays-Bas, de Belgique, de Slovénie et de Grèce, sous la direction de John Bintliff et Bozidar Slapsak et la sous-direction (...) de Kostas Sbonias. Les différents spécialistes présentent ici leur travail en détail, développant les rapports des deux premières campagnes publiés dans Pharos, le périodique annuel de l'Institut néerlandais d'Athènes. (shrink)

Some aspects of the theory of Boolean algebras and distributive lattices–in particular, the Stone Representation Theorems and the properties of filters and ideals–are analyzed in a constructive setting.

This chapter relates a broadly chronological story of the developments over the last 50 years that have sought to reshape the science curriculum in English schools by introducing aspects of the history of science and nature of science. The chapter highlights key curriculum projects by outlining the contexts in which they developed and summarising their rationales as set out in their publications. It also provides signposts to some of the reports of research and scholarship that have evaluated these initiatives. The (...) chapter shows how the first national curriculum in 1989 was influenced by earlier initiatives as it made teaching about the nature of science mandatory for all. This requirement faded into the background after a few years and then re-emerged with a new rationale as ‘how science works’ in 2004. The chapter ends by looking to the future with a discussion of a new course which contrasts with earlier traditions by focussing the teaching and learning on the history and philosophy of science rather than using ideas from these disciplines to teach about science. (shrink)

A rational agent has beliefs reflecting the state of its environment, and likes or dislikes Its situation. When it finds the world not entirely to Its liking, it tries to change that. We can, accordingly, evaluate a system of cognition in terms of its probable success in bringing about situations that are to the agent's liking. In doing this we are viewing practical reasoning from “the design stance.” It is argued that a considerable amount of the structure of rationality can (...) be elicited as providing the only apporant solutions to various logical and feasibility problems that arise in the course of trying to design a rational agent that satisfies this design specification. (shrink)

The strategy of this paper is to throw light on rational cognition and epistemic justification by examining irrationality. Epistemic irrationality is possible because we are reflexive cognizers, able to reason about and redirect some aspects of our own cognition. One consequence of this is that one cannot give a theory of epistemic rationality or epistemic justification without simultaneously giving a theory of practical rationality. A further consequence is that practical irrationality can affect our epistemic cognition. I argue that practical irrationality (...) derives from a general difficulty we have in overriding built-in shortcut modules aimed at making cognition more efficient, and all epistemic irrationality can be traced to this same source. A consequence of this account is that a theory of rationality is a descriptive theory, describing contingent features of a cognitive architecture, and it forms the core of a general theory of “voluntary” cognition — those aspects of cognition that are under voluntary control. It also follows that most of the so-called “rules for rationality” that philosophers have proposed are really just rules describing default (non- reflexive) cognition. It can be perfectly rational for a reflexive cognizer to break these rules. The “normativity” of rationality is a reflection of a built-in feature of reflexive cognition — when we detect violations of rationality, we have a tendency to desire to correct them. This is just another part of the descriptive theory of rationality. Although theories of rationality are descriptive, the structure of reflexive cognition gives philosophers, as human cognizers, privileged access to certain aspects of rational cognition. Philosophical theories of rationality are really scientific theories, based on inference to the best explanation, that take contingent introspective data as the evidence to be explained. (shrink)

This book examines the revival of antique philosophy in the Renaissance as a literary preoccupation informed by wit.