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.

Michael Beaney has argued that Frege’s characterization of the senses of names as modes of presentation early in “On Sense and Reference” is problematic, but the problem disappears if we use the notion of modes of determination as that was deployed in the Begriffsschrift to characterize senses. It is argued that there is no philosophically interesting difference between the two notions, and no problem posed by modes of presentation that would be resolved by appeal to modes of determination.

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)

Introduction This book attempts to answer big questions about the meaning and purpose of life, as well as fate, free will and reincarnation, and all sorts ...

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)

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.

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.

Theories of revolution invoke human agency to commit the violence that revolution entails, yet theorists of revolution often denounce the general theory of human agency called rational choice because it does not explain macrosocial facts like revolution and also leaves out culture. Actually, however, rational choice is the major premise of any cogent explanation of revolution, and it includes culture as a factual premise. Rational-choice theory applied to explaining revolution dates back to Thucydides, whose method of explanation is sound and (...) whose theory of revolution is true. Thucydides explains the macrosocial fact of revolution by way of models whose elements are people doing what they hope will succeed, that is, acting on opinion alias culture. Theorists of revolution who make sense of it all rehearse Thucydides: they analyze the narrative history into strategic actions and reactions, explain these actions and reactions by rational choice, and document the explanation with direct and circumstantial evidence for hope of success, though they seldom own up on theory and method or preach what they practice. (shrink)

For a set A of non-negative integers, let D be the set of non-negative differences of elements of A. Clearly, if A is computable, then D is computably enumerable. We show that every simple set which contains 0 is the difference set of some computable set and that every computably enumerable set is computably isomorphic to the difference set of some computable set. Also, we prove that there is a computable set which is the difference set of the complement of (...) some computably enumerable set but not of any computably enumerable set. Finally, we show that every arithmetic set is in the Boolean algebra generated from the computable sets by the difference operator D and the Boolean operations. (shrink)

We solve a question of McLaughlin by showing that if A is a regressive co-simple isol, there is a co-simple regressive isol B such that the intersection type of A and B is trivial. The proof is a nonuniform 0 priority argument that can be viewed as the execution of a single strategy from a 0-argument. We establish some limit on the properties of such pairs by showing that if AxB has low degree, then the intersection type of A and (...) B cannot be trivial. (shrink)

Many of the figures in Thurnauer’s paintings who fix us with their gaze have been borrowed from the work of Manet, the artist who organized so many of his paintings around a face-to-face confrontation of viewer and work. The painting returns the viewer’s gaze with total impartiality, making us see our own motives and investments more than the illusion that the figure in the painting will accommodate them. Issues of language often surface literally in paintings by Thurnauer; written language appears (...) sometimes as part of the material fabric in which human figures move or recline. The textual elements are not superimposed on the figures but appear to exist in the world they inhabit, requiring the painter to relate figure to ground in a process of interlacing. When the viewer’s eye traverses the painting it falls under the magnetic influence of the text to the extent that viewing must succumb in some degree to the operations of reading with its specific rhythms and expectations. In these paintings, visual and verbal languages provide us with different maps of the same territory; and Thurnauer’s hybridized representations argue that the world can only be rendered through a dialogue, an interlocution of different forms, genres, media. We approach her work, not as viewers whose function is predicated through a gaze regulated according to the distorting demands of consumption or control, but as readers engaged in a critical activity seeing around the edges of historically produced versions of the self. (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)

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 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)

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)

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)

We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities introduced by the authors. We solve a question of Peter Cholakand the first author by proving the fundamental index sets associated with a computable set A, {e : W e ≤ q u A} for q∈ {m, T} are Σ4 0 complete. We also show hat FPT(≤ q n ), that is {e : W e computable and ≡ q n ?}, is Σ4 (...) 0 complete. We also look at computable presentability of these classes. (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)