Using the framework of categorical logic, this paper analyzes and streamlines Gabbay's semantical proof of the Craig interpolation theorem for intuitionistic predicate logic. In the process, an apparently new and interesting fact about the relation of coherent and intuitionistic logic is found.

Let C be a small Barr-exact category, Reg the category of all regular functors from C to the category of small sets. A form of M. Barr's full embedding theorem states that the evaluation functor e : C →[Reg, Set ] is full and faithful. We prove that the essential image of e consists of the functors that preserve all small products and filtered colimits. The concept of κ-Barr-exact category is introduced, for κ any infinite regular cardinal, and the natural (...) generalization to κ-Barr-exact categories of the above result is proved. The treatment combines methods of model theory and category theory. Some applications to module categories are given. (shrink)

We use a fundamental theorem of Vaught, called the covering theorem in [V] (cf. theorem 0.1 below) as well as a generalization of it (cf. Theorem $0.1^\ast$ below) to derive several known and a few new results related to the logic $L_{\omega_1\omega}$. Among others, we prove that if every countable model in a $PC_{\omega_1\omega}$ class has only countably many automorphisms, then the class has either $\leq\aleph_0$ or exactly $2^{\aleph_0}$ nonisomorphic countable members (cf. Theorem $4.3^\ast$) and that the class of countable (...) saturated structures of a sufficiently large countable similarity type is not $PC_{\omega_1\omega}$ among countable structures (cf. Theorem 5.2). We also give a simple proof of the Lachlan-Sacks theorem on bounds of Morley ranks ($\s 7$). (shrink)

We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied by Baldwin–Eklof–Trlifaj are stable (...) and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosický. (shrink)

This book defends a form of ethical intuitionism, according to which (i) there are objective moral truths; (ii) we know some of these truths through a kind of immediate, intellectual awareness, or "intuition"; and (iii) our knowledge of moral truths gives us reasons for action independent of our desires. The author rebuts all the major objections to this theory and shows that the alternative theories about the nature of ethics all face grave difficulties.

The first edition of The Scientific Background to Modern Philosophy took the dialogue of science and philosophy from Aristotle through to Newton. This second edition adds eight chapters, taking the dialogue through the Enlightenment and up to Darwin. This anthology is an attempt to help bridge the gap between the history of science and the history of philosophy.

Part I: The representation of life -- Can life be given a real definition? -- The representation of the living individual -- The representation of the life-form itself -- Part II: Naive action theory -- Types of practical explanation -- Naive explanation of action -- Action and time -- Part III: Practical generality -- Two tendencies in practical philosophy -- Practices and dispositions as sources of the goodness of individual actions -- Practice and disposition as sources of individual action.

Virtually all philosophers agree that for a belief to be epistemically justified, it must satisfy certain conditions. Perhaps it must be supported by evidence. Or perhaps it must be reliably formed. Or perhaps there are some other "good-making" features it must have. But does a belief's justification also require some sort of awareness of its good-making features? The answer to this question has been hotly contested in contemporary epistemology, creating a deep divide among its practitioners. Internalists, who tend to focus (...) on scientific or theoretical beliefs as the ideal, insist that such awareness is required for justification. Externalists, who think children's ordinary beliefs in obvious facts are paradigm cases of justified belief, say it isn't required. Michael Bergmann's book offers a decisive refutation of internalism and a sustained defense of externalism. (shrink)

At the University of Sheffield during 2011 and 2012, a leading group of philosophers, psychologists, and others gathered to explore the nature and significance of implicit bias. The two volumes of Implicit Bias and Philosophy emerge from these workshops. Each volume philosophically examines core areas of psychological research on implicit bias as well as the ramifications of implicit bias for core areas of philosophy. Volume I: Metaphysics and Epistemology is comprised of two parts: “The Nature of Implicit Attitudes, Implicit Bias, (...) and Stereotype Threat,” and “Skepticism, Social Knowledge, and Rationality.” The first part contains chapters examining the relationship between implicit attitudes and “dual process” models of the mind; the role of affect in the formation and change of implicit associations; the unity (or disunity) of implicit attitudes; whether implicit biases are mental states at all; and whether performances on stereotype-relevant tasks are automatic and unconscious or intentional and strategic. The second part contains chapters examining implicit bias and skepticism; the effects of implicit bias on scientific research; the accessibility of social stereotypes in epistemic environments; the effects of implicit bias on the self-perception of members of stigmatized social groups as rational agents; the role of gender stereotypes in philosophy; and the role of heuristics in biased reasoning. (shrink)

Versions and extensions of intuitionistic and modal logic involving biHeyting and bimodal operators, the axiom of constant domains and Barcan's formula, are formulated as structured categories. Representation theorems for the resulting concepts are proved. Essentially stronger versions, requiring new methods of proof, of known completeness theorems are consequences. A new type of completeness result, with a topos theoretic character, is given for theories satisfying a condition considered by Lawvere . The completeness theorems are used to conclude results asserting that certain (...) logics are conservatively interpretable in others. (shrink)

Externalist theories of justification create the possibility of cases in which everything appears to one relevantly similar with respect to two propositions, yet one proposition is justified while the other is not. Internalists find this difficult to accept, because it seems irrational in such a case to affirm one proposition and not the other. The underlying internalist intuition supports a specific internalist theory, Phenomenal Conservatism, on which epistemic justification is conferred by appearances.

In this engaging and spirited text, Michael Lynch argues that truth does matter, in both our personal and political lives. He explains that the growing cynicism over truth stems in large part from our confusion over what truth is.

Causation: A Realist Approach Traditional empiricist accounts of causation and laws of nature have been reductionist in the sense of entailing that given a complete specification of the non-causal properties of and relations among particulars, it is therefore logically determined both what laws there are and what events are causally related. It is argued here, however, that reductionist accounts of causation and of laws of nature are exposed to decisive objections, and thus that the time has come for empiricists to (...) break with that tradition. -/- The basic goal of this book, therefore, is to set out and defend realistic accounts of those concepts. In the case of causal relations, for example, Tooley maintains that causation is basically a matter of theoretical relations between states of affairs that underlie and explain relative frequencies. He also argues that such an approach avoids the objections that tell against reductionist accounts and that it does so without making causal relations epistemologically inaccessible. (shrink)

Dignity plays a central role in current thinking about law and human rights, but there is sharp disagreement about its meaning. Combining conceptual precision with a broad historical background, Michael Rosen puts these controversies in context and offers a novel, constructive proposal. “Penetrating and sprightly...Rosen rightly emphasizes the centrality of Catholicism in the modern history of human dignity. His command of the history is impressive...Rosen is a wonderful guide to the recent German constitutional thinking about human dignity...[Rosen] is in (...) general an urbane and witty companion, achieving his aim of accessibly written philosophy.” —Samuel Moyn, The Nation “[An] elegant, interesting and lucid exploration of the concept of dignity...Drawing on classical, liberal and Catholic traditions, Rosen hopes to rehabilitate dignity to its rightful place near the centre of moral thought...Rosen's admirable book deserves wide attention from political theorists, jurisprudes and political philosophers.” —Simon Blackburn, Times Higher Education “Dignity deserves to be widely read, not only for its intrinsic interest, but also as a corrective to the habit of discussing such topics in abstraction from their social context. Whether or not one agrees with Rosen's arguments, there can be no doubt he has widened our horizons.” —Rae Langton, Times Literary Supplement. (shrink)

Michael G. Titelbaum presents a new Bayesian framework for modeling rational degrees of belief—the first of its kind to represent rational requirements on agents who undergo certainty loss.

edition (unseen), $12.95. traditions, bringing into being new modes of understanding. Paper Anthropology, and particularly ethnography, is torn between two quests, one to capture the diversity of social life and the other to discover universal principles structuring that diversity. Jackson examines these quests within the context of ethnographic fieldwork, focusing on the relationship between ethnographers and the people they study. He is concerned with defining the anthropological project as something more than the projection of the anthropologist's traditions and concerns onto (...) an alien culture. Rather, he would have the project open a genuine dialogue between people from different cultures or Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

A listing is given of the published writings of the logician and philosopher Hao Wang , which includes all items known to the authors, including writings in Chinese and translations into other languages.

Abstract: Kant declares the judgment of beauty to be neither ‘objective’ nor ‘merely subjective’. This essay takes up the question of what this might mean and whether it can be taken seriously. It is often supposed that Kant's denials of ‘objectivity’ to the judgment of beauty express a rejection of realism about beauty. I suggest that Kant's thought is not to be understood in these terms—that it does not properly belong in the arena of debates about the constituents of ‘reality’—motivating (...) the suggestion by first considering a pair of opposing views on the question of whether Kant can be understood to develop a real alternative to realism about beauty at all. (shrink)

In this paper, I propose a new way of defining sport that I call a ‘core-periphery’ model. According to a core-periphery model, sport comes in degrees – what I refer to as ‘sport-likeness’ – and the aim of the philosopher of sport is to chart those dimensions along which an activity can be more or less a sport. By introducing the concept of sport-likeness, the core-periphery model complicates the picture of what is or is not a sport and encourages philosophers (...) interested in defining sport to engage with the social sciences in exploring the extension of the term sport in common usage. In this paper I present the results of a small survey about attitudes to sport, and use it to illustrate how a core-periphery definition of sport would proceed. (shrink)

A listing is given of the published writings of the logician and philosopher Hao Wang (1921—1995), which includes all items known to the authors, including writings in Chinese and translations into other languages.