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Author: Mark van Atten
Publisher: Springer
ISBN: 3319100319
Category : Philosophy
Languages : en
Pages : 336
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Book Description
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.
Author: Mark van Atten
Publisher: Springer
ISBN: 3319100319
Category : Philosophy
Languages : en
Pages : 336
Get Book Here
Book Description
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.
Author: Stefania Centrone
Publisher: Springer
ISBN: 9402411321
Category : Philosophy
Languages : en
Pages : 541
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Book Description
Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.
Author: Mirja Hartimo
Publisher: Cambridge University Press
ISBN: 1108997562
Category : Philosophy
Languages : en
Pages : 419
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Book Description
Husserl and Mathematics explains the development of Husserl's phenomenological method in the context of his engagement in modern mathematics and its foundations. Drawing on his correspondence and other written sources, Mirja Hartimo details Husserl's knowledge of a wide range of perspectives on the foundations of mathematics, including those of Hilbert, Brouwer and Weyl, as well as his awareness of the new developments in the subject during the 1930s. Hartimo examines how Husserl's philosophical views responded to these changes, and offers a pluralistic and open-ended picture of Husserl's phenomenology of mathematics. Her study shows Husserl's phenomenology to be a method capable of both shedding light on and internally criticizing scientific practices and concepts.
Author: Bharath Sriraman
Publisher: Springer Nature
ISBN: 3031408462
Category :
Languages : en
Pages : 3221
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Book Description
Author: Nicholas Rescher
Publisher: Springer Nature
ISBN: 3030484319
Category : Philosophy
Languages : en
Pages : 257
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Book Description
The book offers a reflection on the nature, scope, and limits of knowledge that have been at the focus of the author's work over decades. The essays collected in this volume expound and extend these efforts in exploring the outer fringes of understanding: the outer boundaries of conceivability, the limits of cognition, and the ramifications of ineffability and paradox. They join in exploring the lay of the land at the boundaries of knowledge. The first chapters address basic facts regarding the conceptualization of knowledge. This is followed by a study on how to deal with problems relating to the affirmation and considerations of truth. The final chapters scrutinize the limits of demonstration and the inherent impossibility of realizing an ideal systematization of our knowledge of totalities. The book affords novel perspectives regarding the thought of a widely appreciated philosopher. It is an original work aimed for readers interested in the theory of knowledge and philosophy of cognition.
Author: Burt Hopkins
Publisher: Routledge
ISBN: 1317591127
Category : Philosophy
Languages : en
Pages : 378
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Book Description
The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer.
Author: Katherine Laura Dunlop
Publisher: mentis Verlag GmbH
ISBN: 3957437903
Category : Philosophy
Languages : en
Pages : 273
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Book Description
G.W. Leibniz's legacy to philosophy is extraordinary for his vast body of work, for his originality and prescience, and for his influence. The aim of this volume is to provide a state-of-the-art exploration of Leibniz's philosophy and its legacy, especially in the period up to Kant.The essays collected here offer new insights into signature elements of Leibniz's thought – the theory of contingency, anti-materialism, the principle of sufficient reason, the metaphysics of substance, and his philosophy of mind – as well as the influence of predecessors such as Lull, Descartes, and Malebranche, the reckoning of his ideas in the works of Wolff and Kant, and the contributions of Clarke, Baumgarten, Meier, Du Châtelet, and others to the content, transmission, and reception of Leibnizian philosophy.
Author: Stephen Budiansky
Publisher: W. W. Norton & Company
ISBN: 1324005459
Category : Biography & Autobiography
Languages : en
Pages : 361
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Book Description
The first major biography written for a general audience of the logician and mathematician whose Incompleteness Theorems helped launch a modern scientific revolution. Nearly a hundred years after its publication, Kurt Gödel’s famous proof that every mathematical system must contain propositions that are true—yet never provable—continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life. Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of the Institute for Advanced Study in Princeton, NJ, where Gödel and Einstein both worked. Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.
Author: Yuk Hui
Publisher: Rowman & Littlefield
ISBN: 1786600544
Category : Philosophy
Languages : en
Pages : 337
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Book Description
This book employs recursivity and contingency as two principle concepts to investigate into the relation between nature and technology, machine and organism, system and freedom. It reconstructs a trajectory of thought from an Organic condition of thinking elaborated by Kant, passing by the philosophy of nature (Schelling and Hegel), to the 20th century Organicism (Bertalanffy, Needham, Whitehead, Wiener among others) and Organology (Bergson, Canguilhem, Simodnon, Stiegler), and questions the new condition of philosophizing in the time of algorithmic contingency, ecological and algorithmic catastrophes, which Heidegger calls the end of philosophy. The book centres on the following speculative question: if in the philosophical tradition, the concept of contingency is always related to the laws of nature, then in what way can we understand contingency in related to technical systems? The book situates the concept of recursivity as a break from the Cartesian mechanism and the drive of system construction; it elaborates on the necessity of contingency in such epistemological rupture where nature ends and system emerges. In this development, we see how German idealism is precursor to cybernetics, and the Anthropocene and Noosphere (Teilhard de Chardin) point toward the realization of a gigantic cybernetic system, which lead us back to the question of freedom. It questions the concept of absolute contingency (Meillassoux) and proposes a cosmotechnical pluralism. Engaging with modern and contemporary European philosophy as well as Chinese thought through the mediation of Needham, this book refers to cybernetics, mathematics, artificial intelligence and inhumanism.
Author: Julien Bernard
Publisher: Springer Nature
ISBN: 3030115275
Category : Science
Languages : en
Pages : 433
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Book Description
This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington). This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.
