Principia Mathematica to 56

Author: Alfred North Whitehead
Publisher: Cambridge University Press
ISBN: 9780521626064
Format: PDF, Mobi
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The great three-volume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

The Evolution of Principia Mathematica

Author: Bernard Linsky
Publisher: Cambridge University Press
ISBN: 1139497332
Format: PDF
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Originally published in 1910, Principia Mathematica led to the development of mathematical logic and computers and thus to information sciences. It became a model for modern analytic philosophy and remains an important work. In the late 1960s the Bertrand Russell Archives at McMaster University in Canada obtained Russell's papers, letters and library. These archives contained the manuscripts for the new Introduction and three Appendices that Russell added to the second edition in 1925. Also included was another manuscript, 'The Hierarchy of Propositions and Functions', which was divided up and re-used to create the final changes for the second edition. These documents provide fascinating insight, including Russell's attempts to work out the theorems in the flawed Appendix B, 'On Induction'. An extensive introduction describes the stages of the manuscript material on the way to print and analyzes the proposed changes in the context of the development of symbolic logic after 1910.

Mit den Worten rechnen

Author: Ulrike Ramming
Publisher: transcript Verlag
ISBN: 3839404436
Format: PDF, ePub, Mobi
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Dieses Buch versucht, dem Begriff »Medien« einen systematischen Ort im Kanon des Fachs Philosophie zu geben. Zu diesem Zweck entwickelt die Autorin einen Begriff von Medien, der diese weniger unter dem Aspekt der Informationsvermittlung betrachtet als vielmehr deren transformativen Charakter betont. Exemplarisch wird er an einer zeitgenössischen Konzeption von Schrift vorgeführt, die sich nicht auf die Dimension von verschrifteter Sprache beschränkt, sondern auch logische Notationen oder Computersoftware mit umfasst. Detaillierte Analysen zentraler Arbeiten von Derrida, Wittgenstein und Goodman weisen auf, dass Medien als die nicht hintergehbare Bedingung der Möglichkeit von Sinn- und Bedeutungsgebung anzusehen sind. Die philosophische Behandlung von Medien leitet somit in eine allgemeine Theorie der Medialität über, die die Weisen unserer Erschließung von Wirklichkeit zum Gegenstand hat.

Principia Mathematica

Author: Alfred North Whitehead
Publisher: Cambridge University Press
ISBN: 9780521067911
Format: PDF, Kindle
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Principia Mathematica was first published in 1910-13; this is the ninth impression of the second edition of 1925-7. The Principia has long been recognised as one of the intellectual landmarks of the century. It was the first book to show clearly the close relationship between mathematics and formal logic. Starting from a minimal number of axioms, Whitehead and Russell display the structure of both kinds of thought. No other book has had such an influence on the subsequent history of mathematical philosophy.

The Logic of Infinity

Author: Barnaby Sheppard
Publisher: Cambridge University Press
ISBN: 1107058317
Format: PDF, Kindle
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Few mathematical results capture the imagination like Georg Cantor's theory of infinity. Bridging the gap between technical accounts of mathematical foundations and popular accounts of logic, this book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.

The Geometry of Moduli Spaces of Sheaves

Author: Daniel Huybrechts
Publisher: Vieweg+Teubner Verlag
ISBN: 9783663116257
Format: PDF, ePub
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This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.