Mathematics : History & Philosophy

The Hindu–Arabic numeral system (1, 2, 3,...) is one of mankind's greatest achievements and one of its most commonly used inventions. How did it originate? Those who have written about the numeral system have hypothesized that it originated in India; however, there is little evidence to support this claim. This book provides considerable evidence to show that the Hindu–Arabic numeral system, despite its commonly accepted name, has its origins in the Chinese rod numeral system. This system was widely used in China from antiquity till the 16th century. It was used by officials, astronomers, traders and others to perform addition, subtraction, multiplication, division and other arithmetic operations, and also used by mathematicians to develop arithmetic and algebra. Based on this system, numerous mathematical treatises were written. more...

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Despite his tragic death at the age of 26, Frank Ramsey (1903 - 1930) remains one of the most intriguing minds of the twentieth century. His thought had a profound influence on both Ludwig Wittgenstein and Bertrand Russell, and many strands of contemporary analytic philosophy find their origin in Ramsey's ideas. Frank Ramsey: Truth and Success provides a much-needed introduction to the work of this undervalued thinker, and makes an important and profound contribution to our understanding of Ramsey's work and his place in twentieth century philosophy. It will be of interest to all students of logic, metaphysics and the history of philosophy. more...

Price: $95.00

This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume. - ;Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number. theory, analysis, logic and set theory--with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics. - more...

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Hermann Gramann, Gymnasiallehrer in Stettin und bekannt als Begrnder der n-dimensionalen Vektoralgebra, erwarb sich auch in der Physik und der Sprachforschung bleibende Verdienste. Gesttzt auf die Dialektik Schleiermachers entwickelte er in seinem Hauptwerk, der Ausdehnungslehre, mit philosophischer Methode eine vllig neue mathematische Disziplin. Zunchst von der Fachwelt abgelehnt, wurde sein Werk Jahrzehnte spter als wegweisend gefeiert. Die Biographie geht dem komplexen Geflecht innerer und uerer Einflsse nach, innerhalb derer Gramann sein Schpfertum entfaltete. more...

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Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality. Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world. Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly more...

Price: $195.00