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)

A central issue in epistemology concerns the connection between truth and justification. The burden of our paper is to explain this connection. Reliabilism, defended by Goldman, assumes that the connection is one of reliability. We argue that this assumption is too strong. We argue that foundational theories, such as those articulated by Pollock and Chisholm fail to elucidate the connection. We consider the potentiality of coherence theories to explain the truth connection by means of higher level convictions about probabilities, which (...) we call doxastic ascent, and defend such a theory. Our defense appeals to the work of Reid and contemporary cognitive psychology in order to account for the psychological reality of higher level evaluations. (shrink)

Disney's computer‐animated musical film, Moana tells the tale of Moana, the daughter of Tui, the chief of a Polynesian island, Motunui. Bound by the legendary tradition of her ancestors, Moana is expected to follow her lineage and take over as chief when she grows up. As the authors dig beneath the surface level of the story, they find a metaphorical and philosophical level to Moana's journey. The story of Moana has layers. First, it is literally a tale of Moana's voyage (...) outside beyond the reef so that she can restore the heart of Te Fiti and save the people of Motunui. She closes this tale with a happy ending as she simultaneously lives the life that she freely chooses, becomes the leader of her people (by saving them) as her parents wanted, and honors her tradition insofar as she restores her ancestors' tradition of wayfinding. (shrink)

Bringing together leading international scholars within the fields of social and political theory and philosophy, this book explores how we should understand work and its role(s) in our lives and wider society. -/- What challenges are posed by work in our changing economy and the new economic forms that are beginning to emerge, and how can we best address these challenges? In what ways do patterns of working, as well as work technologies, shape people’s lives within and outside work, in (...) particular their life opportunities and their social and natural environment? How might we organize—or seek to reorganize—workplaces so that the experience of work better reflects our shared ethical ideals and normative principles? This volume examines these vital questions in a comprehensive and systematic manner in order to provide much needed theoretical insight and practical guidance in reflecting on the nature, problems, and possibilities of work currently. -/- This book will be of interest to undergraduate and postgraduate students and established academics in the areas of contemporary political theory and philosophy, social theory, legal philosophy, labour studies, the sociology of work, practical ethics, critical theory, and political activism. (shrink)

Psychological-epistemic accounts take scientific progress to consist in the development of some psychological-epistemic attitude. Disagreements over what the relevant attitude is – true belief, knowledge, or understanding – divide proponents of thesemantic,epistemic,andnoeticaccounts of scientific progress, respectively. Proponents of all such accounts face a common challenge. On the face of it, only individuals have psychological attitudes. However, as I argue in what follows, increases in individual true belief, knowledge, and understanding are neither necessary nor sufficient for scientific progress. Rather than being (...) fatal to the semantic, epistemic, and noetic accounts, this objection shows that these accounts are most plausible when they take the psychological states relevant to scientific progress to be states of communities, rather than individuals. I draw on recent work in social epistemology to develop two ways in which communities can be the bearers of irreducible psychological-epistemic states. Each way yields a strategy by which proponents of one of the psychological-epistemic accounts might attempt to account for the social dimensions of scientific progress. While I present serious reasons for concern about the first strategy, I argue that the second strategy, at least, offers a promising path forward for a psychological-epistemic account of scientific progress. (shrink)

When Wet’suwet’en matriarch Freda Huson declared that ‘reconciliation is dead’ and called on supporters to ‘Shut Down Canada’, activists responded with a nationwide series of blockades and occupations. Many commenters, even those sympathetic to the Wet’suwet’en, rushed to defend the idea of reconciliation. Such responses fail to take the contributions this movement offers to decolonial thought seriously. Drawing on interviews with movement participants, I explore what participants mean by reconciliation and what they intend by declaring it dead, showing how participants (...) reject forms of decolonization that center the needs of the settler state. I also explore Land Back as an emerging, grassroots alternative to reconciliation that centers the resurgence of Indigenous governance systems in place of the settler state. Finally I explore settlers’ place within this project and considers its relation to the resurgence school of thought. (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)