Philosophy of mathematics and mathematical practice in the seventeenth century

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. The Seventeenth Century Saw More Dramatic Advances In Mathematical Theory And Practice Than Any Other Era Before Or Since. With The Recovery Of Many Of The Classical Greek Mathematical Texts, New Techniques Were Introduced, And Within 100 Years, Analytic Geometry, The Geometry Of Indivisibles, The Arithmetic Of Infinites, And The Calculus Had Been Developed. Philosophy Of Mathematics And Mathematical Practice In The Seventeenth Century Have Often Been Studied. Independently Of One Another. In This Groundbreaking Work, Paolo Mancosu Offers The First Comprehensive Account Of The Rich Interaction Between The Two Fields. Beginning With The Renaissance Debates On The Certainty Of Mathematics, Mancosu Leads The Reader Through The Foundational Issues Raised By The Emergence Of These New Mathematical Techniques, Including The Influence Of The Aristotelian Conception Of Science In Cavalieri And Guldin, The Foundational Relevance Of. Descartes's Geometrie, The Relationship Between Empiricist Epistemology And Infinitistic Theorems In Geometry, And The Debates Concerning The Foundations Of The Leibnizian Calculus. In The Process, Mancosu Draws A Sophisticated Picture Of The Subtle Dependencies Between Technical Development And Philosophical Reflection In Seventeenth-century Mathematics. Philosophers Of Mathematics And Historians Of Philosophy And Mathematics Will Welcome This Much Needed Study. 1. Philosophy Of Mathematics And Mathematical Practice In The Early Seventeenth Century -- 2. Cavalieri's Geometry Of Indivisibles And Guldin's Centers Of Gravity -- 3. Descartes' Geometrie -- 4. Problem Of Continuity -- 5. Paradoxes Of The Infinite -- 6. Leibniz's Differential Calculus And Its Opponents -- Appendix: Giuseppe Biancani's De Mathematicarum Natura: Translated By Gjula Klima. Paolo Mancosu. Includes Bibliographical References And Index.

the Seventeenth Century Saw Dramatic Advances In Mathematical Theory And Practice Than Any Era Before Or Since. With The Recovery Of Many Of The Classical Greek Mathematical Texts, New Techniques Were Introduced, And Within 100 Years, Analytic Geometry, The Geometry Of Indivisibles, The Arithmetic Of Infinites, And The Calculus Had Been Developed. Although Many Technical Studies Have Been Devoted To These Innovations, Paolo Mancosu Provides The First Comprehensive Account Of The Relationship Between Mathematical Advances Of The Seventeenth Century And The Philosophy Of Mathematics Of The Period. Beginning With The Renaissance Debates On The Certainty Of Mathematics, Mancosu Leads The Reader Through The Foundational Issues Raised By The Emergence Of These New Mathematical Techniques, Including The Influence Of The Aristotelian Conception Of Science In Cavalieri And Guldin, The Foundational Relevance Of Descartes' geometrie, The Relationship Between Empiricist Epistemology And Infinitistic Theorems In Geometry, And The Debates Concerning The Foundations Of The Leibnizian Calculus In The Process Mancosu Draws A Sophisticated Picture Of The Subtle Dependencies Between Technical Development And Philosophical Reflection In Seventeenth Century Mathematics.

This book provides the first comprehensive account of the relationship between philosophy of mathematics and the mathematical practice of the seventeenth century - the most eventful period of mathematical development in history. Starting with the Renaissance debates on the certainty of mathematics, the author leads the readers through the foundational issues raised by the emergence of new mathematical techniques including the influence of the Aristotelian conception of science in Cavalieri and Guldin. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical developments and philosophical reflection in seventeenth century mathematics The 17th century saw a dramatic development in mathematical theory and practice. This is an account of the foundational issues raised in the relationship between mathematical advances of the period and the philosophy of mathematics