In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language (...) of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines. (shrink)

This book is dedicated to the life and work of the mathematician Joachim Lambek. The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist. In the 1960s, he began to work in category theory, categorical algebra, logic, proof (...) theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development, he introduced a novel and deeper algebraic framework for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists. (shrink)

From Aristotle to Thomas Jefferson, seminal thinkers have declared “common sense” essential for moral discernment and civilized living. Yet the story of commonsense philosophy is not well known today. In _America and the Political Philosophy of Common Sense_, Scott Segrest traces the history and explores the personal and social meaning of common sense as understood especially in American thought and as reflected specifically in the writings of three paradigmatic thinkers: John Witherspoon, James McCosh, and William James. The first two (...) represent Scottish Common Sense and the third, Pragmatism, the schools that together dominated American higher thought for nearly two centuries. Educated Americans of the founding period warmly received Scottish Common Sense, Segrest writes, because it reflected so well what they already thought, and he uncovers the basic elements of American common sense in examining the thought of Witherspoon, who introduced that philosophy to them. With McCosh, he shows the furthest development and limits of the philosophy, and with it of American common sense in its Scottish realist phase. With James, he shows other dimensions of common sense that Americans had long embraced but that had never been examined philosophically. Clearly, Segrest’s work is much more than an intellectual history. It is a study of the American mind and of common sense itself—its essential character and its human significance, both moral and political. It was common sense, he affirms, that underlay the Declaration of Independence and the founders’ ideas of right and obligation that are still with us today. Segrest suggests that understanding this foundation and James’s refreshing of it could be the key to maintaining America’s vital moral core against a growing alienation from common sense across the Western world. Stressing the urgency of understanding and preserving common sense, Segrest’s work sheds new light on an undervalued aspect of American thought and experience, helping us to perceive the ramifications of commonsense philosophy for dignified living. (shrink)

A theorem on the extendability of certain subsets of a Boolean algebra to ultrafilters which preserve countably many infinite meets (generalizing Rasiowa-Sikorski) is used to pinpoint the mechanism of the Barwise proof in a way which bypasses the set theoretical elaborations.

We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.

In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic , which is the linear fragment of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories / of an ambient *-autonomous category . Similar structures were first introduced by M. Barr in the late 1970’s in abstract duality theory and more recently in work on game semantics for linear logic. The paper has two goals: to discuss concrete models and (...) to present various completeness theorems.As concrete examples, we present a hypercoherence model, using Ehrhard’s hereditary/anti-hereditary objects, a Chu-space model, a double gluing model over our categorical framework, and a model based on iterated double gluing over a *-autonomous category.For the multiplicative fragment of. (shrink)

For more than 60 years, Jim Lambek has been a profoundly inspirational mathematician, with groundbreaking contributions to algebra, category theory, linguistics, theoretical physics, logic and proof theory. This Festschrift was put together on the occasion of his 90th birthday. The papers in it give a good picture of the multiple research areas where the impact of Jim Lambek's work can be felt. The volume includes contributions by prominent researchers and by their students, showing how Jim Lambek's ideas keep inspiring upcoming (...) generations of scholars. (shrink)

Complaining about humanitarian refugees is rarely an unequivocal activity for society members. Their talk appears dilemmatic: ‘sympathy talk’, comprising rhetorical displays of ‘care’, tolerance and aesthetic evaluations, is woven together with more pejorative messages. In this article we investigate how ‘sympathy talk’ functions as a discursive resource in talk-in-interaction when people give accounts of minority group individuals. A ‘synthetic’ discursive psychological approach was employed to analyse a corpus of 12 talkback radio calls to an evening ‘shock jock’ radio personality in (...) Adelaide, Australia, after the stabbing death of a Sudanese-Australian refugee. Analysis shows how host and callers dialogically negotiate and orientate to various sympathetic and humanitarian descriptions/evaluations. We contend that sympathetic talk advances the activity of conversation, softening complaints that could be made accountable as prejudiced. Sympathy talk also functions as a counter-argument to perceived punitive or ‘racist’ complaints. Moreover, this article proposes that such rhetoric shares an ideological thread that potentially undermines Sudanese refugees’ social positioning. Dialogue that deploys sympathetic formulations may be an element in the increasingly varied and subtle activity of ‘new racism’. We discuss how sympathetic accounts contain, within their semantic structure, their own antithesis for their deployment in anti-racist practice; for the development of counter discourses fundamental to the disruption of pervasive ideological representations and the construction of alternative refugee identities. (shrink)

Business Ethics, the Environment &Responsibility, EarlyView.

Dan Dennett and Jerry Fodor have recently offered diametrically opposed estimations of the relevance of the theory of natural selection to an adequate theory of intentionality. In this paper, I show, first, how this opposition can be traced largely to differences both in their respective understandings of what the theory of natural selection includes, and in their respective ‘pre-theoretic’ takes on the datum to be explained by a theory of intentionality. These differences, in turn, have been ‘pre-selected’ by contrasting outlooks (...) on the general nature of the explanatory enterprise. While no final adjudication of these large issues is attempted, I argue, second, that it is important to distinguish two rather different questions about the relevance of natural selection to the nature of intentionality, and that, having done so, one can see that, from standpoints purely internal to their respective projects, Dennett and Fodor each in his own way misconstrues the relevance of natural selection. (shrink)

Dan Dennett and Jerry Fodor have recently offered diametrically opposed estimations of the relevance of the theory of natural selection to an adequate theory of intentionality. In this paper, I show, first, how this opposition can be traced largely to differences both in their respective understandings of what the theory of natural selection includes, and in their respective ‘pre-theoretic’ takes on the datum to be explained by a theory of intentionality. These differences, in turn, have been ‘pre-selected’ by contrasting outlooks (...) on the general nature of the explanatory enterprise. While no final adjudication of these large issues is attempted, I argue, second, that it is important to distinguish two rather different questions about the relevance of natural selection to the nature of intentionality, and that, having done so, one can see that, from standpoints purely internal to their respective projects, Dennett and Fodor each in his own way misconstrues the relevance of natural selection. (shrink)

Can we succeed in giving consciousness a naturalistic explanation, that is, an explanation in “broadly physical terms”? This is the “problem of consciousness” which, along with other aspects of the mind-body problem, is explored by McGinn in a collection of eight independently written but related, sometimes overlapping papers, all but two previously published. The papers span a decade and divergent approaches. The resulting juxtaposition of two contrasting “resolutions” of the problem by the same author invites their comparison.

Knowing is something that we do not have much of a theory about., p. 365.)Interest has recently been shown in causal theories of perception, memory, inference, reference, truth, justification and belief, as well as in a more general “causal theory of knowledge” which would embrace and connect all of these concepts within a broad epistemological framework. The burden of this paper is that prospects are poor for an interesting and general enough causal theory of knowledge. A threat to generality arises (...) from the causal theory's difficulties with knowledge of general truths. A threat to interest arises when attempts to accommodate general truths lead to a weakening of the notion of “causal connection” appealed to, making dubious the explanatory force of such an appeal. (shrink)

This volume contains ten new essays on a priori knowledge by authors from Canada, the United States, Australia, & Europe Topics addressed include the nature, explanation, & indispensability of a priori knowledge, its connection with analytic truth, its place in mathematics, in logic, & in empirical theory, & the contribution of Kant & Quine to these topics. The focus is on twentieth-century contributions to these issues, but most essays also address earlier discussions at some length, & the essays that focus (...) on Kant also relate his views to more recent discussions. Contents: Introduction. A Rationalist Manifesto. Analyticity, Undeniability, & Truth. Analyticity & the A Priori. The Doubtful A Priori. Some Remarks on Indiscernibility. The Constitutive A Priori. Kant's A Priori Methods for Recognising Necessary Truths. EPR as A Priori Science. Gaps, Gluts, & Paradox. An Essay on Material Necessity. (shrink)

In everyday speech we seem to refer to such things as abstract objects, moral properties, or propositional attitudes that have been the target of metaphysical and/or epistemological objections. Many philosophers, while endorsing scepticism about some of these entities, have not wished to charge ordinary speakers with fundamental error, or recommend that the discourse be revised or eliminated. To this end a number of non-revisionary antirealist strategies have been employed, including expressivism, reductionism and hermeneutic fictionalism. But each of these theories faces (...) forceful objections. In particular, we argue, proponents of these strategies face a dilemma: either concedes that their theory is revisionary, or adopt an implausible account of speaker-meaning whereby the content of certain types of utterance is opaque to their speakers. In this paper we introduce a new type of antirealist strategy, which is thoroughly non-revisionary, and leaves speaker-meaning transparent to speakers. We draw on work on pragmatics in the philosophy of language to develop a theory we call ‘pragmatic antirealism’. The pragmatic antirealist holds that while the sentences of the discourses in question have metaphysically contentious truth conditions, ordinary utterances of them are pragmatically modified in context in such a way that speakers do not incur commitment to those truth conditions. After setting out the theory, we show how it might be developed for both mathematical and ethical discourse, before responding to some likely objections. (shrink)

We propose a causal model theory to explain asymmetries in judgments of the intentionality of a foreseen side-effect that is either negative or positive (Knobe, 2003). The theory is implemented as a Bayesian network relating types of mental states, actions, and consequences that integrates previous hypotheses. It appeals to two inferential routes to judgment about the intentionality of someone else's action: bottom-up from action to desire and top-down from character and disposition. Support for the theory comes from three experiments that (...) test the prediction that bottom-up inference should occur only when the actor's primary objective is known. The model fits intentionality judgments reasonably well with no free parameters. (shrink)