Suicidal Thoughts is a compilation of some of the most moving and insightful writing accomplished on the topic of suicide. It presents the thoughts and experiences of fifteen writers who have contemplated suicide-some on a professional level, others on a personal level, and a few, both personally and professionally. Through this collection, the reader is able to bear witness to the struggle between life and death and to the devastating aftermath of suicide. Suicidal Thoughts provides readers with a better understanding (...) of the reasons why some individuals give serious consideration to killing themselves. (shrink)

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.

We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness notions (...) going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness based on definitions along the lines of Schnorr [117].These notions have complex interrelationships, and connections to classical notions from computability theory such as relative computability and enumerability. Computability figures in obvious ways in definitions of effective randomness, but there are also applications of notions related to randomness in computability theory. For instance, an exciting by-product of the program we describe is a more-or-less naturalrequirement-freesolution to Post's Problem, much along the lines of the Dekker deficiency set. (shrink)

The paper explores Aristotle’s notion of proairesis and its theoretical background, with the aim of presenting a novel interpretation of the concept, under five headings. These are: praxis and poiēsis are different aspects of human activity (energeia) rather than different kinds of it. End and means are correlative rather than complementary components of activity. Activity as praxis is continuous: there are no distinct, elementary, indivisible actions. Desire (orexis) and deliberation (bouleusis) are not distinct and complementary components of the mental process (...) that results in activity, but are the principles of proairesis. Since activity is identical with the individual’s entire and continuous lifespan, proairesis denotes a constant and perpetually present attitude of the human soul. (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)

Uses Sir Karl Popper’s philosophy of critical rationalism to examine the discussion of the UK ‘credit crunch’ as presented by the public record of the UK House of Commons Treasury Select Committee’s investigation. Identifies various philosophical doctrines that acted to shape that investigation and the testimony presented before it. Presents those doctrines as prejudicial to the advancement of knowledge, learning and rationality. Concludes that the philosophy of critical rationalism is relevant to the problems of modern society.

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.

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 answer a question of Jockusch by constructing a hyperimmune-free minimal degree below a 1-generic one. To do this we introduce a new forcing notion called arithmetical Sacks forcing. Some other applications are presented.

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)

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)

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)

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

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.

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.

The author focuses on Plato's reliance on images as a way of communicating abstract doctrinal points to his audience.

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 ...

A step-by-step guide to develop your idea from the first spark to the finished product, with charming illustrations recalling the whimsy and imagination of childhood.