Analyzing (and synthesizing) analysis
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Equally surprisingly, Descartes’s paranoid belief was shared by several contemporary mathematicians, among them Isaac Barrow, John Wallis and Edmund Halley. (Huxley 1959, pp. 354-355.) In the light of our fuller knowledge of history it is easy to smile at Descartes. It has even been argued by Netz that analysis was in fact for ancient Greek geometers a method of presenting their results (see Netz 2000). But in a deeper sense Descartes perceived something interesting in the historical record. We are looking in vain in the writings of Greek mathematicians for a full explanation of what this famous method was. And I will argue for an answer to the question why this lacuna is there: Not because Greek geometers wanted to hide this method, but because they did not fully understand it. It is instructive to note the ambivalent attitude of the most rigorous mathematician of the period, Isaac Newton, to the method of analysis. He used it himself in his own mathematical work and in the expositions of that work. Yet when the mathematical push came to physical and cosmological shove, he formulated his Principia entirely in..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
L. Zhmud (1998). Plato as "Architect of Science". Phronesis 43 (3):211 - 244.
Emily R. Grosholz (1988). Geometry, Time and Force in the Diagrams of Descartes, Galileo, Torricelli and Newton. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:237 - 248.
R. Codinhoto, Lj Koskela, P. Tzortzopoulos & M. Kagioglou, How Analysis and Synthesis Have Been Understood in Design.
H. H. Benson (2012). The Problem is Not Mathematics, but Mathematicians: Plato and the Mathematicians Again. Philosophia Mathematica 20 (2):170-199.
Joop Niekus (2011). Brouwer's Incomplete Objects. History and Philosophy of Logic 31 (1):31-46.
Lj Koskela & M. Kagioglou, The Proto-Theory of Design: The Method of Analysis of the Ancient Geometers.
A. Raftopoulos (2003). Cartesian Analysis and Synthesis. Studies in History and Philosophy of Science Part A 34 (2):265-308.
Jaakko Hintikka (2011). Method of Analysis: A Paradigm of Mathematical Reasoning? History and Philosophy of Logic 33 (1):49 - 67.
Added to index2009-09-11
Total downloads24 ( #119,349 of 1,707,715 )
Recent downloads (6 months)0
How can I increase my downloads?