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)

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)

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 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)

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)

The usual treatment of a dinner table utterance of ‘Can you pass the salt?’ is that it involves an indirect request to pass the salt as well as a direct question about the hearer’s ability to do so: an indirect speech act. These are held to involve two illocutionary forces and two illocutionary acts. Rod Bertolet has raised doubts about whether consideration of such examples warrants the postulation of indirect speech acts and illocutionary forces other than the literal ones. In (...) a recent article, Mary Kate McGowan, Shan Shan Tam, and Margaret Hall claim to show that these doubts are unfounded. The purpose of this paper is to show that they have not established this. (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 ...

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.

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)

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

Explains why the debate initiated by Stephen Lloyd Smith’s plea to jettison the so-called ‘Standard Account of Method’ ––the conventional wisdom of how research philosophy and methodology ought to be taught to management students––is of the utmost importance to the teaching of management studies in British universities. Identifies a fully-developed presentation of the SAM framework in a well-considered and widely-used textbook––‘Research Methods for Managers’ by John Gill and Phil Johnson––and demonstrates that the book’s argument is both logically and scholarly defective. (...) Identifies the SAM as a form of dogmatic rationalism; one that is oblivious to the possibility of applying deductive inference in the service of a critical rationalism. Outlines the logical role of deductive testing in empirical research and demonstrates that there need be no great divide between nomothetic and ideographic research problems once appropriate distinctions are drawn between different forms of explanation. Nonetheless, questions the relevance of these research problems to the concerns of practising managers by highlighting the contrast, as made by philosophers, between social science and social technology. Concludes that the continued presentation and defence of the SAM, as the conventional wisdom of how research philosophy and methodology ought to be taught to management students, is thoroughly lamentable. (shrink)

We examine the randomness and triviality of reals using notions arising from martingales and prefix-free machines.

We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.

We characterize the class of c.e. degrees that bound a critical triple as those degrees that compute a function that has no ω-c.e. approximation.

We construct the set of the title, answering a question of Cholak, Jockusch, and Slaman [1], and discuss its connections with the study of the proof-theoretic strength and effective content of versions of Ramsey's Theorem. In particular, our result implies that every ω-model of RCA 0 + SRT 2 2 must contain a nonlow set.

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)

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)

We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of${\rm{\Delta }}_2^0$functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees (Martin) and the array noncomputable degrees (Downey, Jockusch, and Stob). The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable antichain.

We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex (...) automorphism orbits.As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability. (shrink)

A problem is a multivalued function from a set of instances to a set of solutions. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness property if every computable instance of the problem admits a solution relative to which the property holds. For example, cone avoidance is the ability, given a noncomputable set A and a computable instance of a problem ${\mathsf {P}}$, to find a solution relative to which A (...) is still noncomputable.In this article, we compare relativized versions of computability-theoretic notions of preservation which have been studied in reverse mathematics, and prove that the ones which were not already separated by natural statements in the literature actually coincide. In particular, we prove that it is equivalent to admit avoidance of one cone, of $\omega $ cones, of one hyperimmunity or of one non- $\Sigma ^{0}_1$ definition. We also prove that the hierarchies of preservation of hyperimmunity and non- $\Sigma ^{0}_1$ definitions coincide. On the other hand, none of these notions coincide in a nonrelativized setting. (shrink)

We are engineers, and our view of consciousness is shaped by an engineering ambition: we would like to build a conscious machine. We begin by acknowledging that we may be a little disadvantaged, in that consciousness studies do not form part of the engineering curriculum, and so we may be starting from a position of considerable ignorance as regards the study of consciousness itself. In practice, however, this may not set us back very far; almost a decade ago, Crick wrote: (...) 'Everyone has a rough idea of what is meant by consciousness. It is better to avoid a precise definition of consciousness because of the dangers of premature definition. Until the problem is understood much better, any attempt at a formal definition is likely to be either misleading or overly restrictive, or both'. This seems to be as true now as it was then, although the identification of different aspects of consciousness by Block has certainly brought a degree of clarification. On the other hand, there is little doubt that consciousness does seem to be something to do with the operation of a sophisticated control system, and we can claim more familiarity with control systems than can most philosophers, so perhaps we can make up some ground there. (shrink)

In Plato on the Unity of the Virtues, Rod Jenks argues that while Plato makes several attempts to show how virtue is one, he deliberately fails to secure this because he thinks the way in which the virtues are both one and many is finally ineffable.

Generalized Darwinism (GD) claims to be a conceptual and theoretical framework for researching evolutionary change processes in organizations. This paper examines the claims of GD. It finds that in contrast to Darwin’s theory of evolution by natural selection proper, the GD framework is not an explanatory deductive argument form. What it is that GD actually generalizes and intends to explain thereby becomes somewhat moot. It is proposed that the so-called ‘generalization’ that the GD framework supplies might be best understood schematically. (...) Two general schemata that purport to distil commonalities between processes of organizational evolution and biological evolution are thereby identified. But in considering the applicability of the two schemata to organizational evolution, criticism reveals one to be problematic, whereas the other one, to which the GD programme collapses if the problematical schema is dispensed with, has been long associated with another so-called ‘evolutionary approach’ to the understanding of social change: Sir Karl Popper’s ‘evolutionary epistemology’. The paper concludes that if the research problem is to account for the evolutionary character of social and organizational change, then theorists need not commit to the GD framework. They may elect to use Popper’s evolutionary epistemology instead. (shrink)

This paper attempts to undermine Michael McKinsey’s Important objections to Kripke’s attempts to refute cluster versions of description theories of name reference. McKinsey argues that Kripke Ignores descriptions to which a clustser theorist might appeal In constructing his counterexamples, but that these same descriptions are what guide our intuitions In evaluating the examples. I argue that the descriptions McKinsey offers are question-begging, and thus of no help to a cluster theorist. In a second brief section, I offer an argument designed (...) to show that even If McKinsey*s descriptions were legitimate, the views Kripke endorses in "Naming and Necessity" would be supported rather than vitiated. (shrink)