The book proposes that Foucault's archaeology is a direct response to the predicament for thought in modernity that he described in the closing chapters of The Order of Things, and that science and mathematics are fundamental to the possibility of this response. Centered around the figure of man, Foucault described thinking in modernity as split between empirical and transcendental forms of enquiry, neither of which is able to secure a foundation. To understand how Foucault responds to this situation, the book (...) sets out a series of key ideas in the work of Gaston Bachelard, Jean Cavaillès, and Michel Serres that pave the way for Foucault's account of the historical character of the formal conditions of knowledge. In this way, Foucault's conception of discourse, and above all of the historical a priori, can be understood against the background of what he calls the mathematical a priori. The book also provides an analysis of what Foucault calls ‘temporal dispersion’, tracing this idea back to his critique of Kant. Employing these ideas, the book goes on to provide a detailed commentary on Foucault's The Archaeology of Knowledge. (shrink)

Continuity and difference in Heidegger's sophist -- To think as mortals : Heidegger and the finitude of philosophical existence -- The contingency of freedom : Heidegger reading Kant -- Dimension and difference : from undifferentiatedness to singularity -- Heidegger and Weyl on the question of continuity -- The experience of language as such.

Volume one looks at the language of spirituality to deepen our understanding of the suicidal crisis. Spirituality remains the primary motivation for my work. However, two other significant influences have emerged in my research. The first is the intellectual tradition from the school of philosophy known as phenomenology. The second is only at an embryonic stage as a academic discourse. This is the social change, human rights movement that is becoming known as Mad Culture. The accompanying volume to this exegesis, (...) Thinking About Suicide, gives expression to the lived experience of suicidality as I have lived it and in my own words. Throughout Thinking About Suicide there is a theme of story-telling, a theme that continues here. Two distinct voices are used to tell the stories of Thinking About Suicide - a narrative voice that tells of my personal journey into and out of suicidality, and a commentary voice that reflects on that history. The aim of Thinking About Suicide is to encourage and contribute to a broad community conversation about suicide, so both these voices are in plain language to speak to that audience. In this exegesis, a third voice is heard, an academic voice telling academic 'stories'. These stories are told here through a selection of the academic papers that were written during the research and which represent the three central issues of my thesis and this exegesis: firstly, a phenomenology of the subjective, lived experience of suicidality; secondly, an anthropological or cultural critique of suicidology; and thirdly, a role for spirituality in understanding the suicidal crisis of the self. (shrink)

The present work determines the arithmetic complexity of the index sets of u.c.e. families which are learnable according to various criteria of algorithmic learning. Specifically, we prove that the index set of codes for families that are TxtFex\-learnable is \-complete and that the index set of TxtFex\-learnable and the index set of TxtFext\-learnable families are both \-complete.

In this highly personal book, one of Europe’s foremost contemporary philosophers confronts the theme of faith and religion. He argues that there is a substantial link between the history of Christian revelation and the history of nihilism, in particular as the latter appears in the work of Nietzsche and Heidegger, Vattimo’s philosophical specialty. Tracing the relation between his response to these two thinkers and his own life as a devout Catholic, Vattimo shows how his interpretation of Heidegger’s work and his (...) conceptions of “weak thought” and “weak ontology” can be seen as closely linked to a rediscovery of Christianity. Vattimo speaks here in the first person—a risk that results in a disarmingly open exploration of the themes of charity, truth, dogmatism, morality, and sin, viewed through the lens of his own life and his own return to Christianity. While deeply critical of institutionalized religion and the Church, Vattimo discovers in the Christian tradition a voice whose interpretation is still being played out around us. Shaped by his readings of Nietzsche and Heidegger, Vattimo’s decision to affirm his formation within the Christian tradition provides an original and engaging contribution to the contemporary debate on religion. At the center of this book is the enigma of belief. Freed by modernity from its Platonic subordination to knowledge, belief is recovered as a crucial and inevitable feature of our cultural and personal lives. “Do you believe?” Vattimo is asked. “I believe so,” he replies. (shrink)

Puts The Archaeology of Knowledge at the heart of Foucault's thoughtDavid Webb reveals the extent to which Foucault's approach to language in The Archaeology of Knowledge was influenced by the mathematical sciences, adopting a mode of thought indebted to thinkers in the scientific and epistemological traditions. By aligning his thought with the challenge to Kantian philosophy from mathematics and science in the late-19th and early-20th centuries, he shows how Foucault established his own perspective on the future of critical philosophy.

The aim of this paper is to question Derrida's approach to the theme of friendship and to set out an alternative reading drawn from the work of Foucault on the care of the self. Derrida's treatment of friendship as aporetic, though faithful to a long tradition of writing on friendship, depends on the use of a formal language that, I argue, exacerbates the difficulties inherent in the theme of friendship. Moreover, it is not clear that the experience of friendship always (...) displays the temporal form given to this aporetic structure. In contrast, Foucault's work suggests that friendship emerges from the complex system of relations that condition who we are and how we can act. Friends are those with whom we work on the historical conditions of our existence, and those with whom we share the practice of becoming who we are. (shrink)

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: [email protected]: https://arxiv.org/pdf/2209.05659.pdf. (shrink)

The conception of time presented in Aristotle’s Physics IV has been supremely influential in the philosophical tradition. However, I shall argue that it proves to be inadequate to resolve a question arising from Aristotle’s own ethics; namely, the relation of ethical action to eudaimonia. As one explores this issue, a sense of time begins to emerge that calls for a reconsideration of the concepts of magnitude or dimension (megethos) and continuity (suneches) that determine the account of time found in Physics (...) IV. This paper sets out the case for such a reconsideration and outlines the impact that it may have on the way we understand the temporal characteristics of eudaimonia. (shrink)