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.

Schnorr randomness is a notion of algorithmic randomness for real numbers closely related to Martin-Löf randomness. After its initial development in the 1970s the notion received considerably less attention than Martin-Löf randomness, but recently interest has increased in a range of randomness concepts. In this article, we explore the properties of Schnorr random reals, and in particular the c.e. Schnorr random reals. We show that there are c.e. reals that are Schnorr random but not Martin-Löf random, and provide a new (...) characterization of Schnorr random real numbers in terms of prefix-free machines. We prove that unlike Martin-Löf random c.e. reals, not all Schnorr random c.e. reals are Turing complete, though all are in high Turing degrees. We use the machine characterization to define a notion of "Schnorr reducibility" which allows us to calibrate the Schnorr complexity of reals. We define the class of "Schnorr trivial" reals, which are ones whose initial segment complexity is identical with the computable reals, and demonstrate that this class has non-computable members. (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.

Physical activity can prevent and treat multiple diseases. Exercise referral schemes have been used extensively as one healthcare pathway. Schemes typically involve the referral of an inactive individual, with a long term condition, for a time limited exercise programme. Evidence has shown limited benefit, yet the exploration of implementation is under researched. National guidance, in the United Kingdom, recommends that exercise referral schemes should not be commissioned unless behaviour change practices are implemented. Nonetheless, novel evaluations, which are sensitive to the (...) complex nature of behaviour change implementation, have not been undertaken. Therefore, this research sought to answer how, why, and in which circumstances behaviour change practices are implemented by exercise referral practitioners. Realist evaluation, a form of theory driven evaluation, was adopted to address the research question. Programme theory, the envisaged causal workings of implementation, was developed and tested to advance knowledge on how behaviour change practice can be achieved by exercise referral practitioners. An 8-month focused ethnography was used to develop programme theory. Subsequently, a survey was validated to empirically test programme theory. Adjudication between theory required an assessment of the fidelity to behaviour change practices. Therefore, vignettes were created and validated, which acted as a proxy to observations. The survey was then completed through online, and facilitated interviews, using a ‘think aloud’ methodology. The analysis showed that practice frameworks augment motivation when there is congruent practitioner characteristics and practice monitoring is utilised, whereas frameworks improve capability when faced with challenging attendees. Supportive leadership improves motivation when there is an organisational commitment to behaviour change and practitioners are passionate to empower attendees. Supportive leadership improves capability for implementation when a learning climate is created. Partnerships with medical professionals enhance implementation, through changes to motivation, when medical professionals commit and recognise the value of schemes, and partnerships enhance capability where medical professionals reinforce practice via congruent communication. On-going support enhances capability where practitioners are cognizant of their role and have lower behaviour change competencies, conversely, motivation is enhanced as practitioners become more capable. Exercise referral schemes risk being labelled ineffective without considering the implementation climate and fidelity to best practice guidance. This thesis provides portable and actionable findings, which could lead to a greater translation of behaviour change practices to applied settings in exercise referral and in other medically led community based self-management interventions. (shrink)

During the past few years significant progress has been made in our understanding of the structure and function of the proteins involved in eukaryotic DNA replication. Data from several laboratories suggest that, in contrast to prokaryotic DNA replication, two distinct DNA polymerases are required for eukaryotic DNA replication, i.e. DNA polymerase delta for the synthesis of the leading strand and DNA polymerase alpha for the lagging strand. Several accessory proteins analogous to prokaryotic replication factors have been identified and some of (...) these are specific for pol delta whereas others affect both DNA replicases. The replicases and their accessory proteins appear to be highly conserved in eukaryotes, as homologous proteins have been found in species ranging from humans to yeast. (shrink)

"With provocations on every page, this book is a philosophical feast. The specialist will find familiar ingredients assembled here in a perspicuous and compelling way, while the nonspecialist will discover a Husserl whose philosophy is made of flesh and blood." —Journal of the History of Philosophy In this thorough study of the full body of his writings, Donn Welton uncovers a Husserl very different from the established view. Arguing against established interpretations, The Other Husserl traces Husserl’s move from static (...) to genetic phenomenology and uses accounts of perception, discourse, subjectivity, and world to elaborate the scope of his systematic phenomenology. This serious reflection on the meaning of phenomenology is the first book in English to outline in full Husserl’s phenomenological method and to argue for its cogency. Welton’s stimulating interpretation highlights Husserl’s relevance for current philosophical debates. (shrink)

We investigate the initial segment complexity of random reals. Let K denote prefix-free Kolmogorov complexity. A natural measure of the relative randomness of two reals α and β is to compare complexity K and K. It is well-known that a real α is 1-random iff there is a constant c such that for all n, Kn−c. We ask the question, what else can be said about the initial segment complexity of random reals. Thus, we study the fine behaviour of K (...) for random α. Following work of Downey, Hirschfeldt and LaForte, we say that αK β iff there is a constant such that for all n, . We call the equivalence classes under this measure of relative randomness K-degrees. We give proofs that there is a random real α so that lim supn K−K=∞ where Ω is Chaitin's random real. One is based upon work of Solovay, and the other exploits a new idea. Further, based on this new idea, we prove there are uncountably many K-degrees of random reals by proving that μ=0. As a corollary to the proof we can prove there is no largest K-degree. Finally we prove that if n ≠ m then the initial segment complexities of the natural n- and m-random sets and Ω︀) are different. The techniques introduced in this paper have already found a number of other applications. (shrink)

INTRODUCTION Phenomenology as transcendental phenomenology is centered in a description of meaning interpreted in relationship to acts of consciousness. ...

This chapter, which deals with the notions of affectivity and engagement, explores the internal connection between basic affects to get at the emergence of affectivity. Additionally, it presents a discussion of motivation and the interplay of affectivity and engagement. Basic affects consist of needs, wants, and desires. Needs and then wants involve a kind of circumspective seeing in which ‘felt’ values are as much a part of objects as their utility. Intentions-in-action are rooted in basic affects. The basic types of (...) affects are each triadically structured with the moments of each type being dyadically organised. The affectivity circuit usually begins with what is not yet a profile coming to prominence out of a dark background. The circuit of engagement is inducted by a bodily drive seeking resolution. (shrink)

Can we deploy creative practices to critically address the fatal interlocking of global surveillance technologies, neo-colonial expansionism, environmental degradation and the lethal threat of drone warfare? Throughout the following conversation, Shona Illingworth and Anthony Downey examine these and other questions in relation to the recent publication of Topologies of Air (Sternberg Press and The Power Plant, 2022). Edited by Downey, the book includes discussion and documentation of two major bodies of work by Illingworth, including Topologies of Air (2021) (...) and Lesions in the Landscape (2015), alongside an extended series of essays that analyse the psychological and environmental impact of military, industrial and corporate transformations of airspace and outer space. Employing interdisciplinary research and collaborative processes, Illingworth’s practice, as detailed in the discussion below, uses creative methodologies to visualize and interrogate this proliferating exploitation of airspace. The conversation between Illingworth and Downey also outlines the work of the Airspace Tribunal, an ongoing series of public hearings that brings together diverse disciplines, methodologies, knowledge and lived experiences to propose a new human right that will counter the colonization of the sky and, in time, protect individuals, communities and ecologies from ever-increasing threats from above. (shrink)

We study for each computably bounded $\Pi ^0_1$ class P the set of degrees of c.e. paths in P. We show, amongst other results, that for every c.e. degree a there is a perfect $\Pi ^0_1$ class where all c.e. members have degree a. We also show that every $\Pi ^0_1$ set of c.e. indices is realized in some perfect $\Pi ^0_1$ class, and classify the sets of c.e. degrees which can be realized in some $\Pi ^0_1$ class as exactly (...) those with a computable representation. (shrink)

The recent first-time publication of works from Edmund Husserl’s later years, especially his Freiburg period, combined with new studies of his method and theories, has stimulated a remarkable shift in perceptions of the scope and significance of Husserl’s transcendental phenomenology. Informed by a deep reading of not just the works published during Husserl’s lifetime but also the countless lectures and manuscripts he wrote in his later years, the essays in The New Husserl provide an alternative approach to Husserl by examining (...) his work and his method as a whole and by probing issues, old and new, that occupied him during this exceptionally productive period. The noted Husserl specialist Klaus Held opens the book with two essays, published here in English for the first time, that provide an insightful and lucid introduction to Husserl’s central texts. Other prominent Husserl scholars treat his most important and lasting contributions to philosophy, such as the concept of intentionality, the theory of types, time-consciousness, consciousness and subjectivity, the phenomenological method, and the problem of generativity. By inviting readers to discover this "new Husserl," the present collection is likely to shape scholarly discussions of Husserl’s thought for some time to come. (shrink)

The Essential Husserl, the first anthology in English of Edmund Husserl's major writings, provides access to the scope of his philosophical studies, including selections from his key works: Logical Investigations, Ideas I and II, Formal and Transcendental Logic, Experience and Judgment, Cartesian Meditations, The Crisis of European Sciences and Transcendental Phenomenology, and On the Phenomenology of the Consciousness of Internal Time. The collection is an indispensable resource for anyone interested in twentieth-century philosophy.

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...) _\alpha ^0 $ orbit (from the proof). (shrink)

We show that Sacks' and Shoenfield's analogs of jump inversion fail for both tt- and wtt-reducibilities in a strong way. In particular we show that there is a ${\mathrm{\Delta }}_{2}^{0}$ set B > tt ∅′ such that there is no c.e. set A with A′ ≡ wtt B. We also show that there is a ${\mathrm{\Sigma }}_{2}^{0}$ set C > tt ∅′ such that there is no ${\mathrm{\Delta }}_{2}^{0}$ set D with D′ ≡ wtt C.

From Immanuel Kant to Postmodernism, this volume provides an unparalleled student resource: a wide-ranging collection of the essential works of more than 50 seminal thinkers in modern European philosophy.

Cenzer, D., R. Downey, C. Jockusch and R.A. Shore, Countable thin Π01 classes, Annals of Pure and Applied Logic 59 79–139. A Π01 class P {0, 1}ω is thin if every Π01 subclass of P is the intersection of P with some clopen set. Countable thin Π01 classes are constructed having arbitrary recursive Cantor- Bendixson rank. A thin Π01 class P is constructed with a unique nonisolated point A and furthermore A is of degree 0’. It is shown that (...) no set of degree ≥0” can be a member of any thin Π01 class. An r.e. degree d is constructed such that no set of degree d can be a member of any thin Π01 class. It is also shown that between any two distinct comparable r.e. degrees, there is a degree that contains a set which is of rank one in some thin Π01 class. It is shown that no maximal set can have rank one in any Π01 class, while there exist maximal sets of rank 2. The connection between Π01 classes, propositional theories and recursive Boolean algebras is explored, producing several corollaries to the results on Π01 classes. For example, call a recursive Boolean algebra thin if it has no proper nonprincipal recursive ideals. Then no thin recursive Boolean algebra can have a maximal ideal of degree ≥0”. (shrink)

Psychotherapy with the use of psychedelic substances, including psilocybin, lysergic acid diethylamide (LSD), ketamine, and 3,4-methylenedioxymethamphetamine (MDMA), has demonstrated promise in treatment of post-traumatic stress disorder (PTSD), anxiety, addiction, and treatment-resistant depression. Psychedelic-assisted psychotherapy (PP) represents a unique psychopharmacological model that leverages the profound effects of the psychedelic experience. That experience is characterized by strong dependency on two key factors: participant mindset and the therapeutic environment. As such, therapeutic models that utilize psychedelics reflect the need for careful design that promotes (...) an open, flexible, trusting mindset and a supportive setting. To meet this need, the PP model is increasingly supplemented by auxiliary methods, including meditation, relaxation, visualization or spiritual practices. We suggest virtual reality (VR) as a full-spectrum tool able to capitalize on and catalyze the innately therapeutic aspects of the psychedelic experience, such as detachment from familiar reality, alteration of self-experience, augmentation of sensory perception and induction of mystical-type experiences. This is facilitated by VR’s evidenced capacity to: aid relaxation and reduce anxiety; buffer from external stimuli; promote a mindful presence; train the mind to achieve altered states of consciousness (ASC); evoke mystical states; enhance therapeutic alliance and encourage self-efficacy. While these unique VR features appear promising, VR’s potential role in PP remains speculative due to lack of empirical evidence on the combined use of VR and PP. Given the increased commercial interest in this synergy there is an urgent need to evaluate this approach. We suggest specific VR models and their role within PP protocols to inspire future direction in scientific research, and provide a list of potential disadvantages, side effects and limitations that need to be carefully considered. These include sensory overstimulation, cyber-sickness, triggering memories of past traumatic events as well as distracting from the inner experience or strongly influencing its contents. A balanced, evidence-based approach may provide continuity across all phases of treatment, support transition into and out of an ASC, deepen acute ASC experiences including mystical states and enrich the psychotherapeutic process of integration. We conclude that the potential application of VR in modulating psychedelic-assisted psychotherapy demands further exploration and an evidence-based approach to both design and implementation. (shrink)

We study the relationship between a computably enumerable real and its presentations. A set A presents a computably enumerable real α if A is a computably enumerable prefix-free set of strings such that equation image. Note that equation image is precisely the measure of the set of reals that have a string in A as an initial segment. So we will simply abbreviate equation image by μ. It is known that whenever A so presents α then A ≤wttα, where ≤wtt (...) denotes weak truth table reducibility, and that the wtt-degrees of presentations form an ideal ℐ in the computably enumerable wtt-degrees. We prove that any such ideal is equation image, and conversely that if ℐ is any nonempty equation image ideal in the computably enumerable wtt-degrees then there is a computable enumerable real α such that ℐ = ℐ. We also prove a kind of Rice Theorem for these ideals, namely that if the index set of such a equation image ideal is not empty or equal to ω then it is equation image-complete. (shrink)

The survey contains a detailed discussion of methods and results in the new emerging area of online “punctual” structure theory. We also state several open problems.

The concept of the body is one of the most recent, and hotly contested areas of inquiry among philosophers today.

WE CONTINUE TO BE SURPRISED that the only pieces of sustained philosophizing that Husserl published in the 15 years between Ideas I and Internal Time-Consciousness were three articles that appeared in Kaizo, a Japanese periodical, in 1923 and 1924. We also find well-written drafts of two other articles that were to follow in the series but were never completed and submitted. We are even more intrigued when we realize that in these texts Husserl takes up themes never touched in publications (...) before and not touched again until his very late work. While we know that his manuscripts contain continuous and extensive analyses of the essential forms of social and cultural life and of ethical normativity, the Kaizo articles build the only slender bridge actually published on these topics between his attack on "the new Weltanschauung philosophy" in his 1911 Logos article and the 1934-37 texts surrounding the The Crisis of European Sciences and Transcendental Philosophy; slender, indeed, when we think that the articles were published in Japan and that the second and third appeared only in Japanese translation. Yet our intrigue is coupled with anticipation, for we have long wondered what Husserl would say to the Japanese, a society highly developed and yet not Western, a culture that does not have its beginnings in the Greek conception of science and knowledge and which clearly poses the question of cultural diversity. And we have wondered how he could define ethical life in this context, how the analysis would proceed, and how the human and social sciences could play a role in the account that he gives. (shrink)

A subspace V of an infinite dimensional fully effective vector space V ∞ is called decidable if V is r.e. and there exists an r.e. W such that $V \oplus W = V_\infty$ . These subspaces of V ∞ are natural analogues of recursive subsets of ω. The set of r.e. subspaces forms a lattice L(V ∞ ) and the set of decidable subspaces forms a lower semilattice S(V ∞ ). We analyse S(V ∞ ) and its relationship with L(V (...) ∞ ). We show: Proposition. Let U, V, W ∈ L(V ∞ ) where U is infinite dimensional and $U \oplus V = W$ . Then there exists a decidable subspace D such that U |oplus D = W. Corollary. Any r.e. subspace can be expressed as the direct sum of two decidable subspaces. These results allow us to show: Proposition. The first order theory of the lower semilattice of decidable subspaces, Th(S(V ∞ )), is undecidable. This contrasts sharply with the result for recursive sets. Finally we examine various generalizations of our results. In particular we analyse S * (V ∞ ), that is, S(V ∞ ) modulo finite dimensional subspaces. We show S * (V ∞ ) is not a lattice. (shrink)

We show that for every nontrivial r.e. wtt-degree a, there are r.e. wtt-degrees b and c incomparable to a such that the infimum of a and b exists but the infimum of a and c fails to exist. This shows in particular that there are no strongly noncappable r.e. wtt-degrees, in contrast to the situation in the r.e. Turing degrees.

We show the existence of noncomputable oracles which are low for Demuth randomness, answering a question in [15]. We fully characterize lowness for Demuth randomness using an appropriate notion of traceability. Central to this characterization is a partial relativization of Demuth randomness, which may be more natural than the fully relativized version. We also show that an oracle is low for weak Demuth randomness if and only if it is computable.

The question I am asking in this paper is whether Husserl adequately distinguished between the intentionality of speech acts, or what he called judgments, and that of perceptual acts. ...I am asking ... whether there is a change in H's theory of perception...

This essay situates itself on the ground of a very powerful but as yet unanswered critique of Husserl’s theory of intentionality and language proposed by Ernst Tugendhat. After suggesting the necessity of a dialogue between linguistic analysis and phenomenology, Tugendhat turns a critical eye toward Husserl. In the first section we reproduce his attack. Then in the second section we attempt to give a response to his critique from within the boundaries he has superimposed upon the discussion. In the third (...) and fourth sections, however, we attempt to enliven the problem by introducing several historical considerations which have been overlooked by Tugendhat and by taking the first steps toward reclaiming the productivity of language for genetic analysis. It is only when one makes this turn that Husserl’s notion of intentionality finds its solvency. (shrink)

We describe new results in parametrized complexity theory. In particular, we prove a number of concrete hardness results for W[P], the top level of the hardness hierarchy introduced by Downey and Fellows in a series of earlier papers. We also study the parametrized complexity of analogues of PSPACE via certain natural problems concerning k-move games. Finally, we examine several aspects of the structural complexity of W [P] and related classes. For instance, we show that W[P] can be characterized in (...) terms of the DTIME ) and NP. (shrink)

We develop a theory of LOGSPACE structures and apply it to construct a number of examples of Abelian Groups which have LOGSPACE presentations. We show that all computable torsion Abelian groups have LOGSPACE presentations and we show that the groups ${\mathbb {Z}, Z(p^{\infty})}$ , and the additive group of the rationals have LOGSPACE presentations over a standard universe such as the tally representation and the binary representation of the natural numbers. We also study the effective categoricity of such groups. For (...) example, we give conditions are given under which two isomorphic LOGSPACE structures will have a linear space isomorphism. (shrink)