Descartes’s Mathematical Thought

Boston Studies in the Philosophy and History of Science

Book 237
Springer Science & Business Media
Free sample

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.
Read more
Collapse
Loading...

Additional Information

Publisher
Springer Science & Business Media
Read more
Collapse
Published on
Mar 9, 2013
Read more
Collapse
Pages
496
Read more
Collapse
ISBN
9789401712255
Read more
Collapse
Read more
Collapse
Best For
Read more
Collapse
Language
English
Read more
Collapse
Genres
History / General
Mathematics / General
Mathematics / History & Philosophy
Philosophy / History & Surveys / General
Science / Philosophy & Social Aspects
Read more
Collapse
Content Protection
This content is DRM protected.
Read more
Collapse

Reading information

Smartphones and Tablets

Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.

Laptops and Computers

You can read books purchased on Google Play using your computer's web browser.

eReaders and other devices

To read on e-ink devices like the Sony eReader or Barnes & Noble Nook, you'll need to download a file and transfer it to your device. Please follow the detailed Help center instructions to transfer the files to supported eReaders.
two main (interacting) ways. They constitute that with which exploration into problems or questions is carried out. But they also constitute that which is exchanged between scholars or, in other terms, that which is shaped by one (or by some) for use by others. In these various dimensions, texts obviously depend on the means and technologies available for producing, reproducing, using and organizing writings. In this regard, the contribution of a history of text is essential in helping us approach the various historical contexts from which our sources originate. However, there is more to it. While shaping texts as texts, the practitioners of the sciences may create new textual resources that intimately relate to the research carried on. One may think, for instance, of the process of introduction of formulas in mathematical texts. This aspect opens up a wholerangeofextremelyinterestingquestionstowhichwewillreturnatalaterpoint.But practitioners of the sciences also rely on texts produced by themselves or others, which they bring into play in various ways. More generally, they make use of textual resources of every kind that is available to them, reshaping them, restricting, or enlarging them. Among these, one can think of ways of naming, syntax of statements or grammatical analysis, literary techniques, modes of shaping texts or parts of text, genres of text and so on.Inthissense,thepractitionersdependon,anddrawon,the“textualcultures”available to the social and professional groups to which they belong.
. . . that departed from the traditional dry-as-dust mathematics textbook. (M. Kline, from the Preface to the paperback edition of Kline 1972) Also for this reason, I have taken the trouble to make a great number of drawings. (Brieskom & Knorrer, Plane algebraic curves, p. ii) . . . I should like to bring up again for emphasis . . . points, in which my exposition differs especially from the customary presentation in the text books: 1. Illustration of abstract considerations by means of figures. 2. Emphasis upon its relation to neighboring fields, such as calculus of dif ferences and interpolation . . . 3. Emphasis upon historical growth. It seems to me extremely important that precisely the prospective teacher should take account of all of these. (F. Klein 1908, Eng\. ed. p. 236) Traditionally, a rigorous first course in Analysis progresses (more or less) in the following order: limits, sets, '* continuous '* derivatives '* integration. mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass . ;::: Leibniz 1675 Fermat 1638 In this book, with the four chapters Chapter I. Introduction to Analysis of the Infinite Chapter II. Differential and Integral Calculus Chapter III. Foundations of Classical Analysis Chapter IV. Calculus in Several Variables, we attempt to restore the historical order, and begin in Chapter I with Cardano, Descartes, Newton, and Euler's famous Introductio.
two main (interacting) ways. They constitute that with which exploration into problems or questions is carried out. But they also constitute that which is exchanged between scholars or, in other terms, that which is shaped by one (or by some) for use by others. In these various dimensions, texts obviously depend on the means and technologies available for producing, reproducing, using and organizing writings. In this regard, the contribution of a history of text is essential in helping us approach the various historical contexts from which our sources originate. However, there is more to it. While shaping texts as texts, the practitioners of the sciences may create new textual resources that intimately relate to the research carried on. One may think, for instance, of the process of introduction of formulas in mathematical texts. This aspect opens up a wholerangeofextremelyinterestingquestionstowhichwewillreturnatalaterpoint.But practitioners of the sciences also rely on texts produced by themselves or others, which they bring into play in various ways. More generally, they make use of textual resources of every kind that is available to them, reshaping them, restricting, or enlarging them. Among these, one can think of ways of naming, syntax of statements or grammatical analysis, literary techniques, modes of shaping texts or parts of text, genres of text and so on.Inthissense,thepractitionersdependon,anddrawon,the“textualcultures”available to the social and professional groups to which they belong.
The broad range of interdisciplinary concerns which are encompassed by the philosophy of science have this much in common: (I) they arise from reflection upon the fundamental concepts, the formal structures, and the methodology of the sciences; (2) they touch upon the characteristically philosophical questions of ontology and epistemology in a unique way, bringing to traditional conceptions the analytic apparatus of modern logic, and the new content and conceptual models of active scientific investigations. These sources are reflected in the present volume, which consists of the major portion of the papers presented to the Boston Colloquium for the Philosophy of Science in the academic year 1961-1962. There is no central theme nor any dominant approach in this colloquium. Initiated in 1960 as an inter-university interdisciplinary faculty group, the Colloqnium is intended to foster creative and regular exchange of research and opinion, to provide a forum for professional discussion in the philosophy of science, and to stimulate the development of academic programs in philosophy of science in the colleges and universities of metropolitan Boston. The base of the Colloquium is our philosophic and scientific community, as broad and heterodox as the academic, cultural and techno logical complex in and about this city. The Colloquium has been supported in its first full year, as an inter-institutional cooperative association, by a generous grant to Boston University from the U. S. National Science Foundation. We are most grateful for this help.
Exactly four hundred years after the birth of René Descartes (1596-1650), the present volume now makes available, for the first time in a bilingual, philosophical edition prepared especially for English-speaking readers, his Regulae ad directionem ingenii / Rules for the Direction of the Natural Intelligence (1619-1628), the Cartesian treatise on method. This unique edition contains an improved version of the original Latin text, a new English translation intended to be as literal as possible and as liberal as necessary, an interpretive essay contextualizing the text historically, philologically, and philosophically, a com-prehensive index of Latin terms, a key glossary of English equivalents, and an extensive bibliography covering all aspects of Descartes' methodology. Stephen Gaukroger has shown, in his authoritative Descartes: An Intellectual Biography (1995), that one cannot understand Descartes without understanding the early Descartes. But one also cannot understand the early Descartes without understanding the Regulae / Rules. Nor can one understand the Regulae / Rules without understanding a philosophical edition thereof. Therein lies the justification for this project. The edition is intended, not only for students and teachers of philosophy as well as of related disciplines such as literary and cultural criticism, but also for anyone interested in seriously reflecting on the nature, expression, and exercise of human intelligence: What is it? How does it manifest itself? How does it function? How can one make the most of what one has of it? Is it equally distributed in all human beings? What is natural about it, and what, not? In the Regulae / Rules Descartes tries to provide, from a distinctively early modern perspective, answers both to these and to many other questions about what he refers to as ingenium.
The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
©2020 GoogleSite Terms of ServicePrivacyDevelopersArtistsAbout Google|Location: United StatesLanguage: English (United States)
By purchasing this item, you are transacting with Google Payments and agreeing to the Google Payments Terms of Service and Privacy Notice.