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.

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)

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

Presenting an analytical and critical study of the contemporary adult educator, Paulo Freire, this book deals with all aspects of his thought, placing at the centre of consideration his educational philosophy.

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.

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

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)

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..

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’s morning. You sit down at your desk, cup of coffee in hand, and prepare to begin your day. First, you turn on your computer. Once it is running, you check your e-mail. Having decided it is all spam, you trash it. You close the window on your e-mail program, but leave the program running so that it will periodically check the mail server to see whether you have new mail. If it finds new mail it will alert you by (...) playing a musical tone. Next you start your word processor. You have in mind to write a paper in moral philosophy about whether people who send spam deserve capital punishment. So you open a new window and type several paragraphs of text into it. You like what you wrote, so you save it, creating a file. Later, you have more thoughts about spam and capital punishment, so you open the file again and make some changes. Then it is time to go to class. You turn off your word processor, but leave your computer running so that your email program can collect your e-mail. This mundane sequence of events can seem philosophically puzzling when we think about it carefully. While in your word processor, you opened several windows, entered text into them, and created files. What sorts of things are these files, windows, and text? It might seem that windows are easy to understand. You can, after all, see windows. That is the whole point of them. You see a window by seeing a pattern on the surface of your monitor. Isn’t the window identical with that physical pattern? But that is too quick. First, you can turn your monitor off. The window is still open. You can type text into it, and if you turn the monitor back on you can verify that you made that change. Second, you can drag another window in front of the original window. The original window disappears from view, but it still exists. Things may be happening in it that you cannot see. For example, if it is an e-mail window, new messages may be listed in it as they are 1 downloaded.. (shrink)

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

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.

This paper is concerned with Wittgenstein's early doctrine of the independence of elementary propositions. Using the notion of a free generator for a logical calculus–a concept we claim was anticipated by Wittgenstein–we show precisely why certain difficulties associated with his doctrine cannot be overcome. We then show that Russell's version of logical atomism–with independent particulars instead of elementary propositions–avoids the same difficulties.

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)

Perkins, John L With his regular programmes on radio and television, newspaper columns and commentary, Waleed Aly has become Australia's favourite Muslim celebrity. He is intelligent, articulate and provides incisive analysis of political and social issues. Given this, it might have been expected that he could have applied the same quality of analysis in his book, People Like Us: How Arrogance is Dividing Islam and the West (2007); however this is not the case.

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

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)

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)

Axioms for the continuum, or smooth real line R. These include the usual axioms for a commutative ring with unit expressed in terms of two operations + and i , and two distinguished elements 0 ≠ 1. In addition we stipulate that R is a local ring, i.e., the following axiom: ∃y x i y = 1 ∨ ∃y (1 – x) i y = 1. Axioms for the strict order relation < on R. These are: 1. a < b (...) and b < c implies a < c. 2. ¬(a < a) 3. a < b implies a + c < b + c for any c. ≤ 4. a < b and 0 < c implies acbc.. (shrink)

This essay presents analogies between the development of historical writing and of physical science during the early modern period. Its necessarily spotty coverage runs from the mid sixteenth century to the beginning of the eighteenth. The analogies include arising from practical concerns; preferring material documents and experimental inquiries over texts; making use of mathematical auxiliary sciences; distinguishing between primary and secondary elements; establishing new fundamental principles; undermining the traditional world system; and devising methods to control rapidly multiplying knowledge. A history (...) of learning that meets today's standards of historical scholarship should identify and exploit such parallels, not only because of scholarly interest and responsibility, but also because an understanding of the historical importance of linkages between distant branches of learning may help redress the increasing imbalance in resources among the natural sciences, the social sciences, and the humanities in our higher schools and universities. (shrink)

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

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)

It has long been asserted that the evolutionary path to spoken language was paved by manual–gestural behaviors, a claim that has been revitalized in response to recent research on mirror neurons. Renewed interest in the relationship between manual and vocal behavior draws attention to its development. Here, the pointing and vocalization of 16.5-month-old infants are reported as a function of the context in which they occurred. When infants operated in a referential mode, the frequency of simultaneous vocalization and pointing exceeded (...) the frequency of vocalization-only and pointing-only responses by a wide margin. In a non-communicative context, combinatorial effects persisted, but in weaker form. Manual–vocal signals thus appear to express the operation of an integrated system, arguably adaptive in the young from evolutionary times to the present. It was speculated, based on reported evidence, that manual behavior increases the frequency and complexity of vocal behaviors in modern infants. There may be merit in the claim that manual behavior facilitated the evolution of language because it helped make available, early in development, behaviors that under selection pressures in later ontogenetic stages elaborated into speech. (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)

Stuart Russell [14] describes rational agents as --œthose that do the right thing--�. The problem of designing a rational agent then becomes the problem of figuring out what the right thing is. There are two approaches to the latter problem, depending upon the kind of agent we want to build. On the one hand, anthropomorphic agents are those that can help human beings rather directly in their intellectual endeavors. These endeavors consist of decision making and data processing. An agent that (...) can help humans in these enterprises must make decisions and draw conclusions that are rational by human standards of rationality. Anthropomorphic agents can be contrasted with goal-oriented agents --” those that can carry out certain narrowly-defined tasks in the world. Here the objective is to get the job done, and it makes little difference how the agent achieves its design goal. (shrink)