Synthetic Philosophy of Contemporary Mathematics
Seiten
2012
Urbanomic (Verlag)
978-0-9567750-1-6 (ISBN)
Urbanomic (Verlag)
978-0-9567750-1-6 (ISBN)
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A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics.
The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830-1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the "real mathematics" of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Chatelet), Zalamea challenges philosophy's self-imposed ignorance of the "making of mathematics."
In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd.
Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics.
The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830-1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the "real mathematics" of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Chatelet), Zalamea challenges philosophy's self-imposed ignorance of the "making of mathematics."
In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd.
Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
Fernando Zalamea is Professor of Mathematics at the Universidad Nacional de Colombia.
IntroductionPart 1: The General Environment of Contemporary Mathematics: The Specificity of Modern and Contemporary Mathematics; Advanced Mathematics In the Tracts of Mathematical Philosophy; Toward a Synthetic Philosophy of Contemporary Mathematics;Part 2: Case Studies: Grothendieck; Eidal Mathematics; Quiddital Mathematics; Archeal Mathematics; Part 3: Synthetic Sketches: Fragments of a Transitory Ontology; Comparative Epistemology and Sheafification; Phenomenology of Mathematical Creativity; Mathematics and Cultural Circulation
| Erscheint lt. Verlag | 2.8.2019 |
|---|---|
| Übersetzer | Zachery Luke Fraser |
| Zusatzinfo | 6 b&w illus.; 12 Illustrations |
| Verlagsort | Falmouth |
| Sprache | englisch |
| Maße | 114 x 178 mm |
| Themenwelt | Geisteswissenschaften ► Philosophie |
| Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik | |
| ISBN-10 | 0-9567750-1-2 / 0956775012 |
| ISBN-13 | 978-0-9567750-1-6 / 9780956775016 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
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