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.

As a natural example of a 1-random real, Chaitin proposed the halting probability Ω of a universal prefix-free machine. We can relativize this example by considering a universal prefix-free oracle machine U. Let [Formula: see text] be the halting probability of UA; this gives a natural uniform way of producing an A-random real for every A ∈ 2ω. It is this operator which is our primary object of study. We can draw an analogy between the jump operator from computability theory (...) and this Omega operator. But unlike the jump, which is invariant under the choice of an effective enumeration of the partial computable functions, [Formula: see text] can be vastly different for different choices of U. Even for a fixed U, there are oracles A =* B such that [Formula: see text] and [Formula: see text] are 1-random relative to each other. We prove this and many other interesting properties of Omega operators. We investigate these operators from the perspective of analysis, computability theory, and of course, algorithmic randomness. (shrink)

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)

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.

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)

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.

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)

Current models for regulation of parent‐specific gene expression in plants have been based on a small number of imprinted genes in Arabidopsis. These present repression as the default state, with expression requiring targeted activation. In general, repression is associated with maintenance methylation of cytosines, while no role has been found in Arabidopsis imprinting for de novo methylation—unlike the case in mammals. A recent paper1 both reinforces and challenges the model drawn from Arabidopsis. Methylation patterns of two imprinted loci in maize (...) were tracked from gametes to offspring, enabling an exploration of the timing of imprinting. For one gene, fie1, the results were as expected: parent‐specific methylation patterns were inherited from the three types of gamete: egg, central cell and sperm. The behaviour of fie2, however, was a surprise: no alleles were methylated in the gametes, although paternally contributed fie2 is methylated and silent in the endosperm, indicating that, in some cases, plant imprinting requires de novo DNA methylation. This work significantly broadens our understanding of plant imprinting and points to a greater diversity in imprinting mechanisms than has previously been appreciated. BioEssays 28: 1167–1171, 2006. © 2006 Wiley Periodicals, Inc. (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)

Philosophical arguments stemming from the public health ethics arena suggest that public health interventions ought to be subject to normative inquiry that considers relational values, including concepts such as solidarity, reciprocity and health equity. As yet, however, the extent to which ‘public’ values influence the ‘autonomous’ decisions of the public remains largely unexplored. Drawing on interviews with 50 men in Vancouver, Canada, this study employs a critical discourse analysis to examine participants’ decisions and motivations to voluntarily access HIV testing and/or (...) to accept a routine HIV test offer. Within a sub-set of interviews, a transactional discourse emerged in which the decision to test features an arrangement of ‘giving and receiving’. Discourses related to notions of solidarity emphasize considerations of justice and positions testing as a ‘public’ act. Lastly, ‘individualistic’ discourses focused on individual-level considerations, with less concern for the broader public ‘good’. These findings underscore how normative dimensions pertaining to men’s decisions to test are dialectically interrelated with the broader social and structural influences on individual and collective health-related behaviour, thereby suggesting a need to advance an explicit empirical-normative research agenda related to population and public health intervention research. (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)

Secondary English is a comprehensive introduction to the theory and practice of teaching English in secondary schools for pre-service teachers. Written by highly accomplished English teachers, the book's practical approach to language, literacy and literature, fosters the skills of assessment, unit planning and teaching strategies.

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

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)

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.

This paper revisits some recent contributions on ‘Why Management Theory Needs Popper’ to the journal Philosophy of Management. It proposes that those discussions provided an appraisal of the relevance of Popper’s falsification schema to management theory, but that they did not thereby bring to the fore all of the issues pertinent to a balanced and well-rounded understanding of Popper’s philosophy of critical rationalism. It is argued that such an understanding requires a discussion of what Popper himself declared to be the (...) real lynchpin of his thought: fallibilism and a critical approach. It is noted that this represents a rejection of the historical problem situation of philosophy — that knowledge claims need to be positively justified as true. It is argued that this rejection implies an anti-authoritarian, non-justificational philosophy based on the use of critical reason. Its application to several different objects of criticism is demonstrated and its ethical dimensions are explored. The relevance of critical rationalism to management studies and practice is assessed and an inherent limitation on the prospects of its adoption in management practice is identified. … the appeal to authorities is the death of knowledge… the growth of knowledge depends entirely upon disagreement. (shrink)