This Element explores the relationship between phenomenology and mathematics. Its focus is the mathematical thought of Edmund Husserl, founder of phenomenology, but other phenomenologists and phenomenologically-oriented mathematicians, including Weyl, Becker, Gödel, and Rota, are also discussed. After outlining the basic notions of Husserl's phenomenology, the author traces Husserl's journey from his early mathematical studies. Phenomenology's core concepts, such as intention and intuition, each contributed to the emergence of a phenomenological approach to mathematics. This Element examines the phenomenological conceptions of natural number, the continuum, geometry, formal systems, and the applicability of mathematics. It also situates the phenomenological approach in relation to other schools in the philosophy of mathematics-logicism, formalism, intuitionism, Platonism, the French epistemological school, and the philosophy of mathematical practice.
The cyberworld fast rolling in and impacting every aspect of human living on the globe today presents an enormous challenge to humankind. It is taken up by the media following current events through to all kinds of natural- and social-scientific discourses. Digitized technoscience develops at a breakneck pace in all areas accompanied by sociological analysis. What is missing is a philosophical response genuinely posing the basic ontological question: What is a digital being's peculiar mode of being? The present study offers a digital ontology that analyzes the dissolution of beings into bit-strings, driven by mathematized science. The mathematization of knowledge reaches back to Pythagoras, Plato and Aristotle, and continues with Descartes, Galileo, Newton, Leibniz. Western knowledge from its inception has always been driven by an unbridled will to efficient-causal power over all kinds of movement and change. This historical trajectory culminates in the universal Turing machine that enables efficient, automated, algorithmic control over the movement of digital beings through the cyberworld. The book fills in the ontological foundations underpinning this brave new cyberworld and interrogates them, especially by questioning the millennia-old conception of 1D-linear time. An alternative ontology of movement arises, based on a radically alternative conception of 3D-time.
The rapid advancement of technology has led to an explosion of speculative theories about what the future of humankind may look like. These "technological futurisms" have arisen from significant advances in the fields of nanotechnology, biotechnology and information technology and are drawing growing scrutiny from the philosophical and theological communities. This text seeks to contextualize the growing literature on the cultural, philosophical and religious implications of technological growth by considering technological futurisms such as transhumanism in the context of the long historical tradition of technological dreaming. Michael Burdett traces the latent religious sources of our contemporary technological imagination by looking at visionary approaches to technology and the future in seminal technological utopias and science fiction and draws on past theological responses to the technological future with Pierre Teilhard de Chardin and Jacques Ellul. Burdett’s argument arrives at a contemporary Christian response to transhumanism based around the themes of possibility and promise by turning to the works of Richard Kearney, Eberhard Jüngel and Jürgen Moltmann. Throughout, the author highlights points of correspondence and divergence between technological futurisms and the Judeo-Christian understanding of the future.
Theoretical physics and foundations of physics have not made much progress in the last few decades. Whether we are talking about unifying general relativity and quantum field theory (quantum gravity), explaining so-called dark energy and dark matter (cosmology), or the interpretation and implications of quantum mechanics and relativity, there is no consensus in sight. In addition, both enterprises are deeply puzzled about various facets of time including above all, time as experienced. The authors argue that, across the board, this impasse is the result of the "dynamical universe paradigm," the idea that reality is fundamentally made up of physical entities that evolve in time from some initial state according to dynamical laws. Thus, in the dynamical universe, the initial conditions plus the dynamical laws explain everything else going exclusively forward in time. In cosmology, for example, the initial conditions reside in the Big Bang and the dynamical law is supplied by general relativity. Accordingly, the present state of the universe is explained exclusively by its past. This book offers a completely new paradigm (called Relational Blockworld), whereby the past, present and future co-determine each other via "adynamical global constraints," such as the least action principle. Accordingly, the future is just as important for explaining the present as is the past. Most of the book is devoted to showing how Relational Blockworld resolves many of the current conundrums of both theoretical physics and foundations of physics, including the mystery of time as experienced and how that experience relates to the block universe.
We live today surrounded by countless digital gadgets and navigate through cyberspace as if it were the most natural thing in the world. This digital cast of being, however, comes from a long history of philosophical and mathematical thinking in which the Western will to productive power over movement has attained its consummation. This study traces the digital dissolution of beings from the Pythagoreans, Plato and Aristotle's ontology via Cartesian mathematical science through to our digitized economy and telecommunications. With an appendix reinterpreting quantum mechanical indeterminacy phenomenologically.
Burning Bodies interrogates the ideas that the authors of historical and theological texts in the medieval West associated with the burning alive of Christian heretics. Michael Barbezat traces these instances from the eleventh century until the advent of the internal crusades of the thirteenth century, depicting the exclusionary fires of hell and judicial execution, the purifying fire of post-mortem purgation, and the unifying fire of God's love that medieval authors used to describe processes of social inclusion and exclusion. Burning Bodies analyses how the accounts of burning heretics alive referenced, affirmed, and elaborated upon wider discourses of community and eschatology. Descriptions of burning supposed heretics alive were profoundly related to ideas of a redemptive Christian community based upon a divine, unifying love, and medieval understandings of what these burnings could have meant to contemporaries cannot be fully appreciated outside of this discourse of communal love. For them, human communities were bodies on fire. Medieval theologians and academics often described the corporate identity of the Christian world as a body joined together by the love of God. This love was like a fire, melting individuals together into one whole. Those who did not spiritually burn with God's love were destined to burn literally in the fires of Hell or Purgatory, and the fires of execution were often described as an earthly extension of these fires. Through this analysis, Barbezat demonstrates how presentations of heresy, and to some extent actual responses to perceived heretics, were shaped by long-standing images of biblical commentary and exegesis. He finds that this imagery is more than a literary curiosity; it is, in fact, a formative historical agent.
Heidegger's Philosophic Pedagogy examines how Martin Heidegger conceives and carries out the task of educating human beings in a life determined by philosophic questioning. Through an exposition of recently published lecture courses that Heidegger delivered in the years 1928-1935, his magnum opus, Being and Time, and other key texts, the author shows that the task of education is central to Heidegger's understanding of philosophy. A pedagogical intention is essential to Heidegger's discourse in all its forms: lecture course, treatise and public address. It determines the philosopher's relation to students, readers and the public generally and the task of education is here shown to have a broad scope. This book reveals a continuity between Heidegger's efforts to engender a 'living philosophizing' in students and his conception of the role of philosophy in politics, a role that is defined as a form of 'leadership'. Michael Ehrmantraut's study of the aims, necessity, character, method and limits of Heidegger's philosophic pedagogy thus opens up the political implications of Heidegger's thought as he himself understood them.
This Element explores the relationship between phenomenology and mathematics. Its focus is the mathematical thought of Edmund Husserl, founder of phenomenology, but other phenomenologists and phenomenologically-oriented mathematicians, including Weyl, Becker, Gödel, and Rota, are also discussed. After outlining the basic notions of Husserl's phenomenology, the author traces Husserl's journey from his early mathematical studies. Phenomenology's core concepts, such as intention and intuition, each contributed to the emergence of a phenomenological approach to mathematics. This Element examines the phenomenological conceptions of natural number, the continuum, geometry, formal systems, and the applicability of mathematics. It also situates the phenomenological approach in relation to other schools in the philosophy of mathematics-logicism, formalism, intuitionism, Platonism, the French epistemological school, and the philosophy of mathematical practice.
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