Mathematics And Logic in History And in Contemporary Thought

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ISBN: 9780202308500 | 0202308502
Cover: Nonspecific Binding
Copyright: 8/15/2006

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This book is not a conventional history of mathematics as such, a museum of documents and scientifi c curiosities. Instead, it identifi es this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought.

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I. The Meaning, Purpose and Methods of the History of Mathematics and of Logic page	9	(4)
II. Pre-Hellenic Mathematics	13	(7)
III. Greek Mathematics before Euclid	20	(40)
IV. The Logic of Aristotle	60	(16)
V. Euclid's Elements in Hellenistic culture	76	(27)
VI. Infinitesimal Methods in Classical Times: Archimedes	103	(14)
VII. Introduction to Higher Geometry: Apollonius and His Followers	117	(7)
VIII. Mathematics in the Roman World	124	(26)
IX. The Decline of Ancient Science	150	(6)
X. Mathematics and Logic in the Middle Ages	156	(12)
XI. The Mathematical Renaissance and the Algebraists	168	(10)
XII. Origins of Analytical Geometry and Cartesian Rationalism: Vico's Gnoseology	178	(14)
XIII. Modern Infinitesimal Analysis and the Philosophical Thought of its Constructors	192	(47)
XIV. From the Origins of Projective Geometry to the Development of the Erlanger Programme	239	(12)
XV. Criticism of Euclid's Postulate V: Non-Euclidean Geometries	251	(35)
XVI. Combinatorial Analysis and Calculus of Probability	286	(6)
XVII. Sets, Functions, Curves, Non-Archimedean Geometries	292	(23)
XVIII. Symbolic Logic and the Fundamentals of Arithmetic	315	(26)
XIX. Hypothetical-Deductive Systems, Non-Contra-dictoriness, Antinomies	341	(10)
XX. Problems of Contemporary Logic	351	(18)
Bibliography	369	(18)
Index	387

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Mathematics And Logic in History And in Contemporary Thought

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