Principia Mathematica to 56

Author: Alfred North Whitehead
Publisher: Cambridge University Press
ISBN: 9780521626064
Format: PDF, ePub, 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.

Intelligent Computer Mathematics

Author: Stephen M. Watt
Publisher: Springer
ISBN: 3319084348
Format: PDF, Kindle
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This book constitutes the joint refereed proceedings of Calculemus 2014, Digital Mathematics Libraries, DML 2014, Mathematical Knowledge Management, MKM 2014 and Systems and Projects, S&P 2014, held in Coimbra, Portugal, during July 7-11, 2014 as four tracks of CICM 2014, the Conferences on Intelligent Computer Mathematics. The 26 full papers and 9 Systems and Projects descriptions presented together with 5 invited talks were carefully reviewed and selected from a total of 55 submissions. The Calculemus track of CICM examines the integration of symbolic computation and mechanized reasoning. The Digital Mathematics Libraries track - evolved from the DML workshop series - features math-aware technologies, standards, algorithms and processes towards the fulfillment of the dream of a global DML. The Mathematical Knowledge Management track of CICM is concerned with all aspects of managing mathematical knowledge in the informal, semi-formal and formal settings. The Systems and Projects track presents short descriptions of existing systems or on-going projects in the areas of all the other tracks of the conference.

The Logic of Infinity

Author: Barnaby Sheppard
Publisher: Cambridge University Press
ISBN: 1107058317
Format: PDF, Mobi
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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 Theory of Logical Types Routledge Revivals

Author: Irving M. Copi
Publisher: Routledge
ISBN: 1136816143
Format: PDF, Docs
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This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it.

New Theory about Light and Colour

Author: Sir Isaac Newton
Publisher: Library of Alexandria
ISBN: 1465595619
Format: PDF, Mobi
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To perform my late promise to you, I shall without further ceremony acquaint you, that in the beginning of the Year 1666 (at which time I applyed my self to the grinding of Optick glasses of other figures than Spherical,) I procured me a Triangular glass-Prisme, to try therewith the celebrated Phænomena of Colours. And in order thereto having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Suns light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby; but after a while applying my self to consider them more circumspectly, I became surprised to see them in an oblong form; which, according to the received laws of Refraction, I expected should have been circular. They were terminated at the sides with streight lines, but at the ends, the decay of light was so gradual, that it was difficult to determine justly, what was their figure; yet they seemed semicircular. Comparing the length of this coloured Spectrum with its breadth, I found it about five times greater; a disproportion so extravagant, that it excited me to a more then ordinary curiosity of examining, from whence it might proceed. I could scarce think, that the various Thickness of the glass, or the termination with shadow or darkness, could have any Influence on light to produce such an effect; yet I thought it not amiss, first to examine those circumstances, and so tryed, what would happen by transmitting light through parts of the glass of divers thicknesses, or through holes in the window of divers bignesses, or by setting the Prisme without so, that the light might pass through it, and be refracted before it was terminated by the hole: But I found none of those circumstances material. The fashion of the colours was in all these cases the same.

Colours in the development of Wittgenstein s Philosophy

Author: Marcos Silva
Publisher: Springer
ISBN: 3319569198
Format: PDF, Kindle
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This book presents and discusses the varying and seminal role which colour plays in the development of Wittgenstein’s philosophy. Having once said that “Colours spur us to philosophize”, the theme of colour was one to which Wittgenstein returned constantly throughout his career. Ranging from his Notebooks, 1914-1916 and the Tractatus Logico-Philosophicus to the posthumously published Remarks on Colours and On Certainty, this book explores how both his view of philosophical problems generally and his view on colours specifically changed considerably over time. Paying particular attention to his so-called intermediary period, it takes a case-based approach to the presentation of colour in texts from this period, from Some Remarks on Logical Form and Philosophical Remarks to his Big Typescript.

1697 1722

Author: Isaac Newton
Publisher: Cambridge University Press
ISBN: 0521045916
Format: PDF, Mobi
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This last volume of Newton's mathematical papers presents the extant record of the investigations which he pursued during the last quarter of his life.