Primal emergence -- Out of the dreamtime -- The quickening of chemistry -- Ecology emergent -- Intimate ark : sex and emergence -- Social order in nature : between conflict and cooperation -- Self within world -- From self to sage -- From self to no-self to all-self -- Anti-sage : from cult to empire -- Into Indra's net.

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

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

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

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)

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.

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.

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, 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 and he would, if he had infinite time, presumably never complete the work, although no individual part of it would remain unwritten. Or imagine an English professor who time-travels back to 1599 to offer a printing of Hamlet to Shakespeare, so as to help the Bard overcome writer's block and author the play which will centuries later inspire an English professor to travel back in time. 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 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.

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)

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

Perkins, John L The atrocity of September 11 led me to become an atheist. A boundary had been crossed, I thought, and religions could no longer be regarded as benign. As the buildings crashed to the ground in New York, this conclusion seemed obvious. Yet a decade and a half later, it seems remarkable how few people have been able to reach the same conclusion.

It has long been claimed that Homo sapiens is the only species that has language, but only recently has it been recognized that humans also have an unusual pattern of growth and development. Social mammals have two stages of pre-adult development: infancy and juvenility. Humans have two additional prolonged and pronounced life history stages: childhood, an interval of four years extending between infancy and the juvenile period that follows, and adolescence, a stage of about eight years that stretches from juvenility (...) to adulthood. We begin by reviewing the primary biological and linguistic changes occurring in each of the four pre-adult ontogenetic stages in human life history. Then we attempt to trace the evolution of childhood and juvenility in our hominin ancestors. We propose that several different forms of selection applied in infancy and childhood; and that, in adolescence, elaborated vocal behaviors played a role in courtship and intrasexual competition, enhancing fitness and ultimately integrating performative and pragmatic skills with linguistic knowledge in a broad faculty of language. A theoretical consequence of our proposal is that fossil evidence of the uniquely human stages may be used, with other findings, to date the emergence of language. If important aspects of language cannot appear until sexual maturity, as we propose, then a second consequence is that the development of language requires the whole of modern human ontogeny. Our life history model thus offers new ways of investigating, and thinking about, the evolution, development, and ultimately the nature of human language. (shrink)

An argument is self-defeating when it contains defeaters for some of its own defeasible lines. It is shown that the obvious rules for defeat among arguments do not handle self-defeating arguments correctly. It turns out that they constitute a pervasive phenomenon that threatens to cripple defeasible reasoning, leading to almost all defeasible reasoning being defeated by unexpected interactions with self-defeating arguments. This leads to some important changes in the general theory of defeasible reasoning.

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

subsets X of A for which ∃x (x ∈ A). The set of functions from A to B is denoted by BA.

Examples growing out of the Newcomb problem have convinced many people that decision theory should proceed in terms of some kind of causal probability. I endorse this view and define and investigate a variety of causal probability. My definition is related to Skyrms' definition, but proceeds in terms of objective probabilities rather than subjective probabilities and avoids taking causal dependence as a primitive concept.

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)

Princeton University Press, 1982. This book is out of print, but can be downloaded as a pdf file (5 MB).

is a presentation of mathematics in terms of the fundamental concepts of transformation, and composition of transformations. While the importance of these concepts had long been recognized in algebra (for example, by Galois through the idea of a group of permutations) and in geometry (for example, by Klein in his Erlanger Programm), the truly universal role they play in mathematics did not really begin to be appreciated until the rise of abstract algebra in the 1930s. In abstract algebra the idea (...) of transformation of structure (homomorphism) was central from the beginning, and it soon became apparent to algebraists that its most important concepts and constructions were in fact formulable in terms of that idea alone. Thus emerged the view that the essence of a mathematical structure is to be sought not in its internal constitution, but rather in the nature of its relationships with other structures of the same kind, as manifested through the network of transformations. This idea has achieved its fullest expression in category theory, an axiomatic framework within which the notions of transformation (as morphism or arrow) and composition (and also structure, as object) are fundamental, that is, are not defined in terms of anything else. (shrink)

In the Newcomb problem, the standard arguments for taking either one box or both boxes adduce what seem to be relevant considerations, but they are not complete arguments, and attempts to complete the arguments rely upon incorrect principles of rational decision making. It is argued that by considering how the predictor is making his prediction, we can generate a more complete argument, and this in turn supports a form of causal decision theory.

Falk claims that human language took a step forward when infants lost their ability to cling and were placed on the ground, increasing their fears, which mothers assuaged prosodically. This claim, which is unsupported by anthropological and psychological evidence, would have done little for the syllabic and segmental structure of language, and ignores infants' own contribution to the process.

As a high school student, I rediscovered Hume’s problem of induction on my own. For a while, I was horrified. I thought, “We cannot know anything!” After a couple of weeks I calmed down and reasoned that there had to be something wrong with my thinking, and that led me quickly to the realization that good reasons need not be deductive, and to the discovery of defeasible reasoning. From there it was a short jump to a more general interest in (...) how rational cognition works. I am interested in rational cognition in general. Epistemology is one constituent of rational cognition, practical cognition (rational decision making) another. Much of the work on rational cognition begins with the supposition that only ideal agents can be truly rational. Real agents have limited powers of reasoning and limited memory capacity. It is often supposed that such resource-bounded agents can only approximate rationality, and that as philosophers we should confine our attention to ideal agents. If one wishes, one can of course define “rationality” in this way, but this has never been what interested me. We come to philosophy wondering what we should believe, what we should do, and how we should go about deciding these matters. These are questions about ourselves, with all of our cognitive limitations. For example, it is often claimed that ideal agents, with unlimited cognitive powers, should believe all of the logical consequences of their beliefs. But we, as real resource-bounded agents, cannot do that, so that is not something we should do. What I want to know is how I, as a real agent, should go about deciding what to believe and what to do. Thus my topic is real rationality as opposed to ideal rationality. In the realm of practical decision making, I have explored this distinction at great length in my recent book (2006). Here I will focus on its implications for epistemology. For many years epistemology was derailed by the Gettier problem.. (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..

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)