Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

In Part 1 the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, (...) time, processes, knowledge and belief, obligation and permission. Accessible, authoritative, and assured, Modal Logics and Philosophy requires no more background than the completion of a standard introductory logic course. It will be welcomed not only by students looking for a bridge between introductory logic texts and the high-level technical literature but as a guide to, and exploration of, work at the forefront of logic and philosophy. (shrink)

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" (...) places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission. (shrink)

Robert I. Soare, Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets.Manuel Lerman, Robert I. Soare, $d$-Simple Sets, Small Sets, and Degree Classes.Peter Cholak, Automorphisms of the Lattice of Recursively Enumerable Sets.Leo Harrington, Robert I. Soare, The $\Delta^0_3$-Automorphism Method and Noninvariant Classes of Degrees.

First Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

Winner of the Gustave O. Arlt Award in the HumanitiesThree understandings of the nature of religion--religion as experience, symbolic meaning, and power--have dominated scholarly discussions, in succession, for the past hundred years. Proponents of each of these three approaches have tended to downplay, ignore, or actively criticize the others. But why should the three approaches be at odds? Religion as it is practiced involves experiences, meanings, and power, so students of religion should attend to all three. Furthermore, theorists of religion (...) should have an account that carefully conceptualizes all three aspects, without regarding any of them as more basic than the others.Visions of Religion provides just such an account. Stephen S. Bush examines influential proponents of the three visions, arguing that each approach offers substantial and lasting contributions to the study of religion, although each requires revision.Bush rehabilitates the concepts of experience and meaning, two categories that are much maligned these days. In doing so, he shows the extent to which these categories are implicated in matters of social power. As for power, the book argues that the analysis of power requires attention to meaning and experience.Visions of Religion accomplishes all this by articulating a social practical theory of religion that can account for all three aspects, even as it incorporates them into a single theoretical framework. (shrink)

From the myths of the ancient world to the Middle Ages to Darwin and beyond, Preece captures the most telling and fascinating accounts of humankind's ...

Anterior cingulate cortex {ACC} is a part of the brain's limbic system. Classically, this region has been related to affect, on the basis of lession studies in human and in animals. In the late 1980s, neuroimaging research indicated that ACC was active in many studies of cognition. The finding from EEG studies of a focal area of negativity in scalp electrodes following an error response led to the idea that ACC might be the brain's error detection and correction device.

Construed broadly as interpretation theory, hermeneutics could be understood to encompass all modes of interpretation (textual or otherwise), including any kind of literary criticism, from Aristotle's poetics to the New Criticism of the 1950s, as well as the French tradition of structuralism and even perhaps Derridean poststructural thought. Although Gadamer and Ricoeur both recognize the poetic work or, at least, lyric poetry, as belonging to a special class of literature, they do display somewhat different attitudes toward it. For Gadamer, one (...) of the hallmarks of the eminent text is its un‐translatability. That is, all literary works resist translation to one degree or another, but lyric poetry defies it altogether. In Part I of Truth and Method, Gadamer lays out the history of aesthetics and takes issue with the kind of “aesthetic consciousness” that takes the work of art as an object of study. (shrink)

Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possible worlds' has been a much debated issue in contemporary metaphysics. To propose the idea of a possible world that differs in some way from our actual world - for example a world where the grass is red or where no people exist - can help us to analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and of course, the notions of (...) possibility and necessity. This book examines the ways in which possible worlds have been used as a framework for considering problems in logic and argument analysis. The book begins with a non-technical introduction to the basic ideas of modal logic in terms of Kripke's possible worlds and then moves on to a discussion of 'possible for' and 'possible that'. The central chapters examine questions of meaning, epistemic possibility, temporal logic, metaphysics, and impossibility. Girle also investigates how the idea of a possible world can be put to use in different areas of philosophy, the problems it may raise, and the benefits that can be gained. (shrink)

Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possible worlds' has been a much debated issue in contemporary metaphysics. To propose the idea of a possible world that differs in some way from our actual world - for example a world where the grass is red or where no people exist - can help us to analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and of course, the notions of (...) possibility and necessity. This book examines the ways in which possible worlds have been used as a framework for considering problems in logic and argument analysis. The book begins with a non-technical introduction to the basic ideas of modal logic in terms of Kripke's possible worlds and then moves on to a discussion of 'possible for' and 'possible that'. The central chapters examine questions of meaning, epistemic possibility, temporal logic, metaphysics, and impossibility. Girle also investigates how the idea of a possible world can be put to use in different areas of philosophy, the problems it may raise, and the benefits that can be gained. (shrink)

We argue that the Soros account of reflexivity does not provide a clear-cut distinction between a social science such as economics and the physical sciences. It is pointed out that the participants who attempt to learn from refutations of conjectures in the Soros world are likely to be haunted by the Duhem–Quine problem of conjointness of hypotheses and unfocused refutation. On a more constructive note, we argue that models of inductive learning, in which participants form conjectures on the basis of (...) strictly limited information sets, can capture the basic thrust of the Soros position. The conjectures are in motion, as the participants attempt to avoid those that are systematically wrong, and there is something vague and uncertain about what can be learned from experience and refutations. The only notion of market efficiency in this world is one contingent on the strictly limited and varied information sets in play. Finally we present a mathematical model and numerical simulations that help justify the causal relationship between reflexivity and far-from-equilibrium dynamics postulated by Soros. (shrink)

In their book, Darwinism Evolving: Systems Dynamics and the Genealogy of Natural Selection, Depew and Weber (1995) argued for the need to address the relationship between self-organization and natural selection in evolutionary theory, and focused on seven “visions” for doing so. Recently, Batten et al. (2008) in a paper in this journal, entitled “Visions of evolution: self-organization proposes what natural selection disposes,” picked up the issue with the work of Depew and Weber as a starting point. While the efforts of (...) both sets of authors are to be commended, there are substantive errors in both the presentations of my work and of my work with colleagues (one of the “visions” discussed) that undermine theirs. My purpose here is to correct the errors in question, thereby removing the undermining effects and in so doing reassert the position my colleagues and I first advanced more than two decades ago, and that I still stand by and argue for today. The central points are as follows: (1) Self-organization or spontaneous ordering is a process of selection; (2) this selection process is governed by a “physical selection principle”; (3) this principle is the law of maximum entropy production; and (4) natural selection is a special case where the components are replicating. (shrink)

We construct a $\Delta^0_2$ degree which fails to be computably enumerable in any computably enumerable set strictly below $\emptyset'$.

We classify the asymptotic densities of the sets according to their level in the Ershov hierarchy. In particular, it is shown that for, a real is the density of an n‐c.e. set if and only if it is a difference of left‐ reals. Further, we show that the densities of the ω‐c.e. sets coincide with the densities of the sets, and there are ω‐c.e. sets whose density is not the density of an n‐c.e. set for any.

In their book, Darwinism Evolving: Systems Dynamics and the Genealogy of Natural Selection, Depew and Weber argued for the need to address the relationship between self-organization and natural selection in evolutionary theory, and focused on seven “visions” for doing so. Recently, Batten et al. in a paper in this journal, entitled “Visions of evolution: self-organization proposes what natural selection disposes,” picked up the issue with the work of Depew and Weber as a starting point. While the efforts of both sets (...) of authors are to be commended, there are substantive errors in both the presentations of my work and of my work with colleagues that undermine theirs. My purpose here is to correct the errors in question, thereby removing the undermining effects and in so doing reassert the position my colleagues and I first advanced more than two decades ago, and that I still stand by and argue for today. The central points are as follows: Self-organization or spontaneous ordering is a process of selection; this selection process is governed by a “physical selection principle”; this principle is the law of maximum entropy production; and natural selection is a special case where the components are replicating. (shrink)

The new edition of this widely used and respected textbook includes three new chapters on conditional logic. Other chapters have been revised and updated, making the second edition a fully comprehensive introduction to modal logics and their application. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, Modal Logics and Philosophy focuses on showing how useful modal logic can be as a tool for formal philosophical analysis. In Part 1, the reader is introduced to (...) some standard systems of modal logic and provided with a series of exercises that encourage proficiency in manipulating these logics. Girle emphasizes possible world semantics for modal logics and its formal method, Jeffrey-style truth-trees, in which standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, and obligation and permission. (shrink)

In this commentary on Stokoe’s article, ‘Moving forward with membership categorization analysis’, I take up the challenge to apply her keys for MCA to an extract of conversation recorded in a restaurant. The strengths of conversation analysis have not included – and indeed have not attempted to achieve – successful engagement with beyond-the-immediate-talk aspects of culture and the commonsense workings of society. The aim of the article is to explore what MCA might add to an analysis of a stretch of (...) talk using conversation analytic tools. It was found that a systematic application of the keys did indeed provide a richer account of what was going on. Whereas categories alone did not appear to provide more insights than commonsense can tell us, when the broader array of MCA tools and keys were applied, an enhanced analysis of the passage of talk emerged. An exploration of whether this can be extended as a method for a rigorous investigation of culture and society while still being grounded in participants’ mutual, moment-by-moment orientations to categories seems at the very least worth the serious attention of scholars interested in interaction. (shrink)

While there is a considerable body of research on law student identity construction based on interviews and transcripts of classroom talk, there is very little work based on student written texts. In this article two letters of advice written by beginning law students are analysed, using Ivanic and Camps’s framework, as an example of identity formation. Legal identity is argued to be formed by students’ attempts to accommodate a dynamic, partial, practitioner role of provider of advice to the traditional analytic (...) focus of the law student. The process of accommodation is evident in the language of the letters, which show disfluencies resulting from attempts to combine different roles into a coherent legal identity. Comparison with a professionally written letter suggests that, rather than seeking to shape a coherent position, lawyers are able simultaneously to hold incompatible perspectives, concealing the tensions by foregrounding some perspectives and backgrounding others. (shrink)

A common contemporary view is that the Bible and subsequent Christian thought authorize humans to exploit animals purely as means to human ends. This paper argues that Biblical and Christian thought have given rise to a more complex ethic of animal use informed by its pastoralist origins, Biblical pronouncements that permit different interpretations, and competing ideas and doctrines that arose during its development, and influenced by the rich and often contradictory features of ancient Hebrew and Greco-Roman traditions. The result is (...) not a uniform ethic but a tradition of unresolved debate. Differing interpretations of the Great Chain of Being and the conflict over animal experimentation demonstrate the colliding values inherent in the complex history of Biblical and Christian thought on animals. (shrink)

Contrary to conventional wisdom, the earlier Western tradition did not customarily deny souls per se to nonhuman animals; when it denied immortal souls to animals, it sometimes deemed that denial a reason for giving greater consideration to animals in their earthly existence. Nor has the Western tradition uniformly deemed animals intended for human use. Further, there was considerable opposition to the Cartesian view of animals as insentient machines, and—even among those who were convinced—it was not unknown for them to deem (...) it inappropriate to rely on that conviction in the treatment of animals. Moreover, Darwin's theory of evolution had neither a novel nor a positive impact on the way in which animals were to be regarded and treated. The study of the history of animal ethics needs to be rethought in a far more nuanced manner. (shrink)