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Descartes's Mathematical Thought : Boston Studies in the Philosophy and History of Science - C. Sasaki

Descartes's Mathematical Thought

Boston Studies in the Philosophy and History of Science

By: C. Sasaki


Published: 30th November 2003
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Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.

From the reviews:

"The book is a study about the formation of Descartes's mathematical thought and its philosophical significance. ... The book is well documented as one can see also looking at the footnotes and the bibliography. There are also some interesting digressions as that concerning Jesuit mathematical education." (Raffaella Franci, Zentralblatt MATH, Vol. 1045 (20), 2004)

"This magnificent volume originates in a 1989 Ph.D. thesis from Princeton University. ... The author aims at a reconstruction of R. Descartes' early mathematical career, studying the formation of his mathematical thought and relating it to his methodological and philosophical ideas. ... The volume, containing a wealth of material, is made accessible by indexes of names, subjects and treatises." (Volker Peckhaus, Mathematical Reviews, 2005 d)

Prefacep. vii
List of Abbreviations and A Note on the Quotation and Translationp. xiv
Introduction: Rene Descartes and Modern European Mathematicsp. 1
The Formation of Descartes's Mathematical Thoughtp. 11
Descartes and Jesuit Mathematical Educationp. 13
Descartes and the Jesuit College of La Flechep. 13
The Curriculum at La Flechep. 16
Mathematical Studies in the Ratio Studiorump. 19
Motives for the Teaching of Mathematics in the Jesuit Collegesp. 30
The Mathematical Thought of Christoph Claviusp. 45
Descartes and Claviusp. 45
The Philosophy of Mathematics of Claviusp. 50
Pappus in the Works of Claviusp. 63
Diophantus in the Works of Claviusp. 72
Descartes's Mathematical Background before the Encounter with Beeckmanp. 84
The First Attempt at Reforming Mathematicsp. 95
"An Entirely New Science": The Idea for the Unification of Arithmetic and Geometryp. 95
The Mathematics in the Cogitationes privataep. 109
The Plan of a Book Titled Thesaurus mathematicusp. 109
The Mesolabe Compassp. 112
The Other Mathematical Instrumentsp. 121
The Interest in Figurate Numbers, the Extension of the Pythagorean Theorem and Other Resultsp. 127
The De Solidorum Elementisp. 132
A History of the Manuscriptp. 132
Solid Geometryp. 133
Figurate Numbersp. 138
The Date of the Original Manuscriptp. 145
Descartes's Mathematical and Philosophical Dream of 1619p. 149
The Mathematical Background of the Regulae Ad Directionem Ingeniip. 159
The Old Algebra: The First Fruit of "An Entirely New Science"p. 159
The Mathematics in the Regulae ad Directionem Ingeniip. 176
Pure Mathematics as the Paradigm for Certaintyp. 176
Algebra as the Method of Analysisp. 182
Mathesis Universalisp. 189
The Geometrie of 1637p. 205
The Pappus Problemp. 205
The Composition of the Geometriep. 225
Descartes's Place in the Formative Period of the Modern Analytic Traditionp. 235
Plagiarism Debates with Jean Beaugrand in 1637-1638p. 235
Descartes's Acquaintance with Viete before the Composition of the Geometriep. 245
The Beginning of the Traditon of Algebraic Analysis in Arabic Mathematics and the Ramean Restartp. 248
The Supposed Intermediary Adriaan van Roomenp. 260
From Viete to Descartesp. 270
Beyond Cartesian Mathematicsp. 274
Interim Consideration: Descartes and the Beginnings of Mathematicism in Modern Thoughtp. 281
The Concept of 'Mathesis Universalis' in Historical Perspectivep. 287
'Universal Mathematics' in Aristotlep. 289
Aristotle's Metaphysics and Posterior Analyticsp. 289
Greek Commentators: Alexander of Aphrodisias and Asclepius of Trallesp. 296
Medieval Commentators: Ibn Rushd (Averroes), Albertus Magnus, Thomas Aquinas, and the Scotist Antonius Andreaep. 301
Albertus Magnus and Thomas Aquinasp. 301
Ibn Rushd (Averroes) 's Commentary on the Metaphysicsp. 309
Albert and Thomas against the Oxford 'Platonists'p. 312
The Scotist Antonius Andreaep. 315
Renaissance Commentators: Agostino Nifo and Pedro da Fonsecap. 318
Agostino Nifop. 318
The Jesuit Commentator Pedro da Fonsecap. 321
The Status of Mathematics in the Aristotelian Scheme of Learningp. 326
'Mathesis Universalis' in the Sixteenth Centuryp. 333
Proclus Diadochus and Francesco Barozzip. 333
Adriaan van Roomenp. 342
'Mathesis Universalis' in the Seventeenth Centuryp. 359
Reviewing Descartes's Concept of 'Mathesis Universalis' from His Philosophy of Mathematicsp. 359
The Philosophy of Mathematics in the Regulae ad Directionem Ingeniip. 359
The Later Philosophy of Mathematics: Mathematical Truths as Creatures of Godp. 362
Descartes against the Skeptical Arguments on Mathematics: How Was the Philosophy of "Cogito, Ergo Sum" Discovered?p. 373
Difficulties of the Later Philosophy of Mathematics: The 'Cartesian Spiral'p. 386
The Disuse of the Concept of 'Mathesis Universalis' in the Later Writingsp. 391
'Mathesis Universalis' as the Discipline of Symbolic Algebra among Other Mathematiciansp. 394
The Leibnizian Synthesisp. 398
'Mathesis Universalis' Extendedp. 398
Leibniz's 'Logicist-Formalist' Philosophy of Mathematicsp. 405
Conclusion: Descartes and the Modern Scheme of Learningp. 419
Bibliographyp. 439
Indicesp. 468
Name Indexp. 468
Subject Indexp. 478
Treatise Indexp. 487
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781402017469
ISBN-10: 1402017464
Series: Boston Studies in the Philosophy and History of Science
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 496
Published: 30th November 2003
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 3.18
Weight (kg): 1.98