Inescapable Dimension Research Articles

On New Notions of Algorithmic Dimension, Immunity, and Medvedev Degree

We prove various results connected together by the common thread of computability theory.First, we investigate a new notion of algorithmic dimension, the inescapable dimension, which lies between the effective Hausdorff and packing dimensions. We also study its generalizations, obtaining an embedding of the Turing degrees into notions of dimension.We then investigate a new notion of computability theoretic immunity that arose in the course of the previous study, that of a set of natural numbers with no co-enumerable subsets. We demonstrate how this notion of $\Pi ^0_1$ -immunity is connected to other immunity notions, and construct $\Pi ^0_1$ -immune reals throughout the high/low and Ershov hierarchies. We also study those degrees that cannot compute or cannot co-enumerate a $\Pi ^0_1$ -immune set.Finally, we discuss a recently discovered truth-table reduction for transforming a Kolmogorov–Loveland random input into a Martin-Löf random output by exploiting the fact that at least one half of such a KL-random is itself ML-random. We show that there is no better algorithm relying on this fact, in the sense that there is no positive, linear, or bounded truth-table reduction which does this. We also generalize these results to the problem of outputting randomness from infinitely many inputs, only some of which are random.Abstract prepared by David J. Webb.E-mail: dwebb@math.hawaii.eduURL: https://arxiv.org/pdf/2209.05659.pdf

From Diagnosis to Therapeutic Empathy: A Journey into Recognition

From Diagnosis to Therapeutic EmpathyA Journey into Recognition Francesca Brencio (bio) Conceptually, recognition claims a cardinal role in many prominent philosophical theories. Kant, in the Critique of Pure Reason, uses the German word Rekognition—a term that in many ways has no antecedent in prior tradition—to signify the identification, the grasping of, a unified meaning through thought (Kant, 1998). However, it is through Hegel that a substantial step in practical philosophy is taken, and recognition is put into dialogue with self-consciousness and freedom. Hegel uses the German word Anerkennung, in the period of Jena Realphilosophie, to mean the "real" actualization of freedom through a struggle which leads to two different levels of recognition: legal and moral—their forms constituted by love and the state (Hegel, 1996). Hegel's notion of recognition is peculiar as it endeavors to satisfy a threefold quest: First, it ensures the link between self-reflection and orientation toward the other; in other words, the reciprocal determination of the relation between self and intersubjectivity. Secondly, recognition guarantees the dynamism of the movement which proceeds from the negative toward the positive, as stated in the Preface to The Phenomenology of Spirit. Finally, it draws those systematic aspects which will be articulated into hierarchical levels corresponding to specific institutions (Honneth, 1996). Precisely in the fourth chapter of The Phenomenology of Spirit, we encounter a self who is a purposive agent struggling for recognition, and we see how the transition from desire (Begierde) to recognition becomes the central point for subjectivity and its social features. Conceived as a process, recognition is not a "static" concept, rather it is a "movement" which concerns both subjectivity and intersubjectivity: it unveils the self as never isolated but rather always embedded into a plural dimension in which the I-Thou relationship is the pre-condition of the We-ness of existence (Binswanger, 1993). The theoretical foundation of recognition shows us that recognition is a task which is accomplished by many struggles, whose ethical and epistemic aspects are closely linked, as opposed to being an automatic mechanism (Stanghellini, 2017). In the field of psychotherapy, this bond and the related struggles are pivotal. A person-centered approach is possible only if both the patient and the therapist can achieve a mutual and challenging recognition which implies not only the therapeutic relationship but also the construction of a therapeutic empathy centered on three main features: understanding, communicating and acting in a helpful therapeutic way (Howick, Bizzari, & Dambha-Miller, 2018). When we refer to recognition in the broad scenario [End Page 11] of mental health, we do not refer to the automatic and standardized pattern-recognition processes which take place into the diagnostic process. Instead, we refer to a complex and nuanced process which involves the individual subjects implicated into this process—the I–Thou relation and the meaning-making process. If we want to trace the roots of this process, we must go back to Freud, who claims that the recognition of alterity is an indiscernible part of our subjecthood: Freud paves the way to the reconciliation between the person and their own alterity (Freud, 1914). However, the journey from diagnosis to therapeutic empathy is complicated and infeasible if we depart from the issue of recognition. The quest (and struggle) for recognition calls into discussion both the very process of diagnosis and the epistemic models which ground the diagnostic classification systems, showing the limits of certain metaphysical views in understanding psychopathological phenomena (Zachar, 2014) as well as the need for reassessing those concepts and values at the core of therapeutic practices (Brencio & Bauer 2020). On the faint trail leading from diagnosis to therapeutic empathy, the contribution of Gilardi and Stanghellini is particularly illuminating and it shows how the struggle for recognition is a struggle in life, against life, by life (Ricoeur, 1977). It is not simply the description of a clinical case or a mere account of a conversation between a patient and his therapist; rather is it a philosophical dialogue embedded into the inescapable dimension of recognition. Lorenzo Gilardi received a diagnosis of schizophrenia, and he discusses with Giovanni Stanghellini what it means to be schizophrenic in terms of recognition. The dialectic...

Origins in History and Historiography: A Case Study of the First Swimmer at Bondi Beach

Abstract The search for origins is a hallmark of historical practice; origins are also fundamental to historical narratives, the predominant form by which historians present their interpretations of the past. Yet, paradoxically, history is ill-suited to studying firsts or origins. As the historian of culture and influential figure in historiography Jacob Burckhardt reminds us, single beginnings are rare phenomena. In this article, I investigate this paradox using swimming in the surf at the renowned Australian beach of Bondi as a case study. At one level, the history of swimming at Bondi is well known. Waverley Council built the Bondi Baths in the last quarter of the nineteenth century to protect bathers from dangerous surf and currents and to control how bathers revealed themselves in public. Over time, bathers became more proficient swimmers, and competitive individuals practiced the activity as a codified sport. Adventurous souls braved the surf and became surf swimmers and bodysurfers, and local authorities progressively relaxed the rules that defined how, and when, bathers presented their bodies in public. By the 1920s, Bondi was a bathing and swimming Mecca among Sydneysiders and other Australians. However, this history is strangely silent about the origins (and nature) of early swimming at Bondi. While scant primary sources partly explain the silence, it is also a function of the fact that history does not contain fully defined or fully formed subjects ready for analysis. Historians demarcate and position their subjects that they then configure into narratives. Each of these historiographical processes involves choices on the part of the historian that leaves inordinate space for alternative histories. In the search for Bondi’s first swimmer, I highlight these choices that, I argue, simultaneously direct attention to the speculative nature of origins and reaffirm them as an inescapable dimension of narrative form. In concluding this article, I identify the conditions under which historical narratives gain social acceptance and the philosophical value of analyzing origins.

New understandings of patients and carers as people - an ethical imperative

As the numbers of older persons (and with managed chronic diseases) increases rapidly, so will the number of people involved in caring, as the case of Mary illustrates. This is both a threat and a challenge to understanding and upholding the generally accepted ethical principle of respect for autonomy of patients. I will argue that we need to broaden the traditional ethical framework in addressing the connectivity between patients and their carers. We first need a new understanding of what it means to be elderly and dependent. Vulnerability is often understood as an inescapable dimension of life, but its meaning in healthcare is unclear. In gerontology, the concept of frailty is used. The degree of frailty reflects overall functional capacity, which is dependent on many factors, including social and psychological functioning and thus ‘self-management capabilities'. We will discuss the meaning of autonomy in the context of frailty, vulnerability and care dependency in elderly persons. In what way is Mary frail, vulnerable, dependent? Secondly, we need to understand the position of informal carers (Mary's stepson, niece, neigbours) who are partners in the (virtual) support team. These carers can be described as ‘dependency workers' (Kittay 1999) - they support someone who is dependent upon them, but this dependency in turn makes them vulnerable, and thus in need of ‘care for the carer'. Formal agencies, and related records, need to develop ways of identifying the needs of these ‘dependency workers' for respect and support. We need to remedy for the fact that informal carers are not only a resource and a team member but also persons with consequent needs and rights in their own respect. We will need to assess the accumulation of responsibilities many informal carers face (Mary's neighbours keeping an eye on her and at the same time caring for their own partner). Kittay EF (1999) Love's Labor - Essays on Women, Equality, and Dependency. New York, Routledge.

The Intercultural Horizons of Johann P. Arnason's Phenomenology of the World

The paper begins to elaborate an interpretative framework that takes account of the intercultural element of the human condition in-the-world. It situates itself within an emergent and diverse current of thought that emphasises the intercultural context of the recent ‘cultural turn’. Recent developments within phenomenological – and post-phenomenological – currents that emphasise cultural articulations of the world horizon, the ‘uncanniness of the alien’ or ‘the heterogeneity of the intercultural’ offer a range of important insights into this problematic. The paper turns to Johann P. Arnason's historical phenomenological investigations of the world horizon as a promising starting point. For Arnason, interculturality is an inescapable dimension of the world and the phenomenal field; he elaborates it along relational and interactive lines as part of his emphasis on the trans-subjective – that is, cultural – level of analysis. The paper reconstructs five overlapping approaches to the problematic of the intercultural in Arnason's thought.

Hypertext and the Teaching of Modernist Difficulty

T. S. Eliot (1963: 112), who famously declared in 1921 that poets in our civilization, as it exists at present, must be difficult, made difficulty a badge of modernist honor. The attitudes of academic criticism since then might be categorized according to their degree of acceptance or rejection of this premise. New Criticism, by and large, made a virtue of difficulty, measuring poetic achievement in terms of the poet's management of tension and paradox. Conversely, recent criticism has often looked askance at difficulty, suspecting that it may be a form of mystificatory elitism or an instance of dishonestly evasive impersonality. However one chooses to view the matter theoretically, difficulty is an inescapable dimension of modernist texts, especially those that exemplify high-modernist experimentation -- Eliot's The Waste Land, Pound's Cantos, Joyce's Ulysses, Barnes's Nightwood, Stein's Tender Buttons, Faulkner's The Sound and the Fury, Toomer's Cane, Dos Passos's U.S.A. trilogy -- in short, many of the most frequently taught works in the curriculum of twentieth-century literature. This essay proposes that hypertext is a practical, though partial, solution to the nearly insuperable problems associated with reading and teaching the difficult modernist text. Because my students and I have created and studied with a hypertext of Pound's Canto 81, my examples are drawn primarily from that poem. The hypertextual version of this Canto provides access not only to the poem's information but to Pound's working methods, his aims in writing this including history, and his presentation of the poem as covert and overt pedagogy.

The Cultural Anthropology of Time: A Critical Essay

Writing a review of the cultural anthropology of time is something like reading Borges's (19a) Book of Sand: as one opens this book, pages keep growing from it-it has no beginning or end. Borges's book could be taken as the spa ce of time: A page once seen is never seen again, and the book's harried possessors keep trying to escape its monstrous self-production by surrepti­ tiously selling or losing it. The diffuse, endlessly multiplying studies of sociocultural time reflect time's pervasiveness as an inescapable dimension of all aspects of social experience and practice. This apparently infinite complexity (1:200) seems