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

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.

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

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)

Georges Sorel's reputation as a proponent of violence has helped to link his ideas to fascist and totalitarian thought. Much of the literature on Sorel as developed this theme, at the expense of what Sorel himself stated as his primary purpose, "the discovery of the historical genesis of morals." How, Sorel asked, in the light of the development of modern industry and the vast powers of the modern state the individual can possess a sense of self-worth and at the same (...) time help to sustain a cultural vitality similar to the great societies of antiquity? How is it possible to avoid the utter resignation and nihilistic relativism of modern existence? In his writings Sorel outlined a sociology of virtue that combined the importance of family love as the basis of community feelings with acceptance of the basis of individual vitality as constant industrial struggle against nature. Sorel's solution is different from Marx's: in place of the ida of transcended alienation, Sorel envisions an agonal striving against nature's unceasing resistance to our efforts. The Feuerbachian unity of nature that, for Marx, had been alienated under capitalism, Sorel regarded as being inherently fragmented by scientific procedures themselves, as well as by the industrial processes that correspond to those scientific procedures. For Sorel, the struggle against nature is the struggle that enables man to overcome himself, to strive against his own inclination to passivity, sloth, and licentiousness. The Marxist concept of totality so necessary to the vision of a communist society is rejected, in favor of a pragmatic, pluralist view of nature that parallels the social pluralism of a regime of workers' syndicates. The primary function of Sorel's famous "myth of the general strike" is to link the workers' constant struggles against capitalist employers to the never-ending struggle against nature. The feelings engendered by such a strubble constitute the true core of socialism; without such feelings, socialism is doomed to the same decay that Sorel and Marx foresaw for capitalist civilization. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1981. (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)

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

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)

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)

In this paper the view is developed that classes should not be understood as individuals, but, rather, as "classes as many" of individuals. To correlate classes with individuals "labelling" and "colabelling" functions are introduced and sets identified with a certain subdomain of the classes on which the labelling and colabelling functions are mutually inverse. A minimal axiomatization of the resulting system is formulated and some of its extensions are related to various systems of set theory, including nonwellfounded set theories.

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.

The objective of the OSCAR Project is twofold. On the one hand, it is to construct a general theory of rational cognition. On the other hand, it is to construct an artificial rational agent (an "artilect") implementing that theory. This is a joint project in philosophy and AI.

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.

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

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)