Explains how our innate pattern-making abilities allow us to perform mathematical reasoning.

Classical logic, beginning with the work of Aristotle, has developed into a powerful and rigorous mathematical theory with many applications in mathematics and ...

"[Goodbye, Descartes] is certain to attract attention and controversy..a fascinating journey to the edges of logical thinking and beyond." -Publishers Weekly Critical Acclaim for Keith Devlin's Previous Book Mathematics: The Science of Patterns "A book such as this belongs in the personal library of everyone interested in learning about some of the most subtle and profound works of the human spirit." -American Scientist "Devlin's very attractive book is a well-written attempt to explain mathematics to educated nonmathematicians. the (...) basic ideas are presented in a clear, concise, and easily understood manner. Highly recommended." -Choice "[Devlin] has found an interesting way of exhibiting how mathematics is unified. the author's presentation is a tour de force." -Mathematical Reviews A Selection of the Newbridge Library of Science and Reader's Subscription. (shrink)

"[Goodbye, Descartes] is certain to attract attention and controversy..a fascinating journey to the edges of logical thinking and beyond." -Publishers Weekly Critical Acclaim for Keith Devlin's Previous Book Mathematics: The Science of Patterns "A book such as this belongs in the personal library of everyone interested in learning about some of the most subtle and profound works of the human spirit." -American Scientist "Devlin's very attractive book is a well-written attempt to explain mathematics to educated nonmathematicians. the (...) basic ideas are presented in a clear, concise, and easily understood manner. Highly recommended." -Choice "[Devlin] has found an interesting way of exhibiting how mathematics is unified. the author's presentation is a tour de force." -Mathematical Reviews A Selection of the Newbridge Library of Science and Reader's Subscription. (shrink)

Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given (...) axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking. (shrink)

In [2], Prikry showed that if κ is a weakly inaccessible cardinal which carries a Rowbottom filter, then there is a Boolean extension of V (the universe), having the same cardinals as V, in which cf(κ) = ω. In this note, we obtain necessary and sufficient conditions which a filter D on κ must possess in order that this may be done.

Various equivalents and weakenings of the combinatorial principle $\diamond$ are considered. The paper contains both absolute results and consistency results. Also included is a new characterisation of the notion of a stationary subset of ω 1.

I argue that the role played by infons in the kind of mathematical theory of information being developed by several workers affiliated to CSLI is analogous to that of the various number systems in mathematics. In particular, I present a mathematical construction of infons in terms of representations and informational equivalences between them. The main theme of the paper arose from an electronic mail exchange with Pat Hayes of Xeroxparc. The exposition derives from a talk I gave at theTheories of (...) Partial Information conference held at the University of Texas at Austin, January 1990. (shrink)

Various equivalents and weakenings of the combinatorial principle $\diamond$ are considered. The paper contains both absolute results and consistency results. Also included is a new characterisation of the notion of a stationary subset of $\omega_1$.

For most of the 1980s, Jon Barwise focused much of his research in the area of natural language semantics. This article surveys his research publications in that area.Most, but not all, of those publications were in the area of situation semantics, a new approach to natural language semantics Barwise developed jointly with his colleague John Perry in the first half of the 1980s. That work was both blessed, and cursed, by becoming closely identified in academic circles with the award of (...) a $23 million gift to Stanford from the System Development Foundation for the establishment in 1983 of its Center for the Study of Language and Information. The development of situation semantics, and in due course its underlying mathematical foundation Situation Theory, carried out for the most part within the framework of CSLI's STASS research group, was actually a relatively small part of the overall research program at CSLI. But because Barwise and Perry were leading figures at CSLI, were centrally involved in securing the SDF gift, and were respectively the first and second directors of CSLI, a general impression sprung up that the two of them had been awarded millions of dollars to develop situation semantics.A major consequence of this false impression was that from the theory's early days, a great deal of interest was shown in the project. With so many accomplished scholars pouring over the work while the ink was still wet on the manuscript pages, Barwise and Perry were able to take advantage of a broad range of helpful criticism. This meant that they were able to develop the new theory much more rapidly than would otherwise have been the case. (shrink)

We consider various strengthenings of the combinatorial principle ⋄ + which are provable from V = L, and give applications in set theory.

For most of the 1980s, Jon Barwise focused much of his research in the area of natural language semantics. This article surveys his research publications in that area.Most, but not all, of those publications were in the area of situation semantics, a new approach to natural language semantics Barwise developed jointly with his colleague John Perry in the first half of the 1980s. That work was both blessed, and cursed, by becoming closely identified in academic circles with the award of (...) a $23 million gift to Stanford from the System Development Foundation for the establishment in 1983 of its Center for the Study of Language and Information. The development of situation semantics, and in due course its underlying mathematical foundation Situation Theory, carried out for the most part within the framework of CSLI's STASS research group, was actually a relatively small part of the overall research program at CSLI. But because Barwise and Perry were leading figures at CSLI, were centrally involved in securing the SDF gift, and were respectively the first and second directors of CSLI, a general impression sprung up that the two of them had been awarded millions of dollars to develop situation semantics.A major consequence of this false impression was that from the theory's early days, a great deal of interest was shown in the project. With so many accomplished scholars pouring over the work while the ink was still wet on the manuscript pages, Barwise and Perry were able to take advantage of a broad range of helpful criticism. This meant that they were able to develop the new theory much more rapidly than would otherwise have been the case. (shrink)

Recently, new life has been breathed into the ancient philosophical topic of skepticism. The subject of some of the best and most provocative work in contemporary philosophy, skepticism has been addressed not only by top epistemologists but also by several of the world's finest philosophers who are most known for their work in other areas of the discipline. Skepticism: A Contemporary Reader brings together the most important recent contributions to the discussion of skepticism. Covering major approaches to the skeptical problem, (...) it features essays by Anthony Brueckner, Keith DeRose, Fred Dretske, Graeme Forbes, Christopher Hill, David Lewis, Thomas Nagel, Robert Nozick, Hilary Putnam, Ernest Sosa, Gail Stine, Barry Stroud, Peter Unger, and Ted Warfield. The book opens with a thorough introduction that outlines the skeptical problem, explains the dominant responses to skepticism, and discusses the strengths, weaknesses, and unresolved issues of each response, providing undergraduate students and nonphilosophers with the background and context necessary to understand the essays. Skepticism: A Contemporary Reader serves as an ideal text for courses in epistemology and skepticism and will also appeal to professional philosophers and interested general readers. (shrink)

Boys, Boyz, Bois concerns questions of ethics, gender and race in popular American images, national discourse and cultural production by and about black men. The book proposes an ethics of masculinity, as ethnics refers to a system of morality and valuation and as ethics refers to a care of the self and ethical subject formation. The texts of analysis include recent films by black/African American filmmakers, gansta rap and hip-hop and black star persona: texts ranging from Blaxploitation and New Black (...) Cinema to contemporary music video to autobiography and the public image of Sidney Poitier. The book is a significant contribution to cultural studies and gender studies and critical race theory. What is distinctive about the book is the question of ethics as a question of race and gender. (shrink)

This paper constructs a theory according to which an intention is not a mental state but an action at a certain developmental stage. I model intention on organic life, and thus intention stands to action as tadpole stands to frog. I then argue for this theory by showing how it overcomes three problems: intending while merely preparing, not taking any steps, and the action is impossible. The problems vanish when we see that not all actions are mature. Just as some (...) frogs are immature frogs, some actions are immature actions. (shrink)

This paper brings together two positions that for the most part have been developed and defended independently of one another: contextualism about knowledge attributions and the knowledge account of assertion.

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.