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.

When people speak of ‘the law of the jungle’, they usually mean unions restrained and ruthless competition, with everyone out solely for his own advantage. But the phrase was coined by Rudyard Kipling, in The Second Jungle Book , and he meant something very different. His law of the jungle is a law that wolves in a pack are supposed to obey. His poem says that ‘the strength of the Pack is the Wolf, and the strength of the Wolf is (...) the Pack’, and it states the basic principles of social co-operation. Its provisions are a judicious mixture of individualism and collectivism, prescribing graduated and qualified rights for fathers of families, mothers with cubs, and young wolves, which constitute an elementary system of welfare services. Of course, Kipling meant his poem to give moral instruction to human children, but he probably thought it was at least roughly correct as a description of the social behaviour of wolves and other wild animals. Was he right, or is the natural world the scene of unrestrained competition, of an individualistic struggle for existence? (shrink)

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 ...

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

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

A theory of rational choice is a theory of how an agent should, rationally, go about deciding what actions to perform at any given time. For example, I may want to decide whether to go to a movie this evening or stay home and read a book. The actions between which we want to choose are perfectly ordinary actions, and the presumption is that to make such a decision we should attend to the likely consequences of our decision. It is (...) assumed that these decisions must be made in the face of uncertainty regarding both the agent’s initial situation and the consequences of his actions. (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.

This is the first elementary book to employ the concept of infinitesimals.

Pollock argues that theories of ideal rationality are largely irrelevant to the decision making of real agents. Thinking about Acting aims to provide a theory of "real rationality.".

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 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)

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)

"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)

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q& R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability (...) calculus for prob(P/Q& R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q& R) 1 A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of "probable probabilities" that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, andprob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application. (shrink)

Princeton University Press, 984. This book is out of print, but can be downloaded as a pdf file (3.9 MB).

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.

Reliabilist theories propose to analyse epistemic justification in terms of reliability. This paper argues that if we pay attention to the details of probability theory we find that there is no concept of reliability that can possibly play the role required by reliabilist theories. A distinction is drawn between the general reliability of a process and the single case reliability of an individual belief, And it is argued that neither notion can serve the reliabilist adequately.

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)

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)

The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all (...) relevant reasons. (shrink)

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

John Wilson's work as moral educator is summarized and evaluated. His rationalist humanistic approach is based on a componential characterization of the morally educated person. Such a person consistently manifests a unity of reflection, feeling, belief, and acting under the logically structured rubrics of PHIL, EMP, GIG and KRAT, and exemplifying the formal features of 'moral opinion'. The rationale and conceptual status of the components is discussed, as is the view that the concept of education entails that teachers be (...) moral educators. This involves cultivating autonomous rationality with respect to the unconscious, motivation, day-to-day moral decision-making, and the emotions; in the latter case there are extensive applications in religious education. Finally, certain weaknesses and pre-eminent strengths of Wilson's position are indicated, and comparisons briefly made with the views of McPhail, Peters, Frankena and Kohlberg. (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)

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)

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)

David Marr provided a useful framework for theorizing about cognition within classical, AI-style cognitive science, in terms of three levels of description: the levels of (i) cognitive function, (ii) algorithm and (iii) physical implementation. We generalize this framework: (i) cognitive state transitions, (ii) mathematical/functional design and (iii) physical implementation or realization. Specifying the middle, design level to be the theory of dynamical systems yields a nonclassical, alternative framework that suits (but is not committed to) connectionism. We consider how a brain's (...) (or a network's) being a dynamical system might be the key both to its realizing various essential features of cognition — productivity, systematicity, structure-sensitive processing, syntax — and also to a non-classical solution of (frame-type) problems plaguing classical cognitive science. (shrink)