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.

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

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

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

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

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)

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.

ABSTRACT In the second decade of the twentieth century a new subject appeared in American high schools, aimed at providing citizens with an understanding of the essential nature of scientific thinking. “General science,” as it was called, was developed and promoted by an emerging class of professional educators who sought to offer a version of science that they believed would both excite public interest and prove useful in the everyday lives of the masses of students streaming into the rapidly expanding (...) institution of secondary education. It was to be a course with real utility that would transcend the boundaries of the specialized, abstract disciplinary subjects like chemistry and physics—subjects with identities tied to the practices and standards of the colleges and universities, which had long exerted control over the content of secondary schooling. This essay recounts the origins of general science and, in particular, examines how the intellectual and material environment of the city of Chicago at the turn of the century influenced the course that was produced and widely adopted in school programs across the United States. (shrink)

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)

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)

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).

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 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)

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

As a preliminary to the modern theory of measurement with which this paper is chiefly concerned, it is desirable to review a few of the characteristics and implications of classical physics to illustrate the far reaching changes that have taken place in our conception of nature as the result of the development of quantum mechanics.

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

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)

From unemployment to Brexit to climate change, capitalism is in trouble and ill-prepared to cope with the challenges of the coming decades. How did we get here? While contemporary economists and policymakers tend to ignore the political and social dimensions of capitalism, some of the great economists of the past - Adam Smith, Friedrich List, John Maynard Keynes, Joseph Schumpeter, Karl Polanyi and Albert Hirschman - did not make the same mistake. Leveraging their insights, sociologists John L. Campbell (...) and John A. Hall trace the historical development of capitalism as a social, political, and economic system throughout the twentieth and early twenty-first centuries. They draw comparisons across eras and around the globe to show that there is no inevitable logic of capitalism. Rather, capitalism's performance depends on the strength of nation-states, the social cohesion of capitalist societies, and the stability of the international system - three things that are in short supply today. (shrink)

Hastings Center Report, Volume 52, Issue 2, Page 14-20, March‐April 2022.

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)

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.