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Matter MattersMetaphysics and Methodology in the Early Modern Period$
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Kurt Smith

Print publication date: 2010

Print ISBN-13: 9780199583652

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199583652.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 June 2021

How Analysis and Synthesis are Related

How Analysis and Synthesis are Related

(p.203) 12 How Analysis and Synthesis are Related
Matter Matters

Kurt Smith (Contributor Webpage)

Oxford University Press

This chapter shows how the combinatorial nature of bodies expresses the permutation group concept, the latter expressing the conditions underwriting a genuine mathematical system. The chapter explains how synthesis, or a synthetic system, is isomorphic to a permutation group. What is more, it is shown how analysis, or the system of concepts resulting from analysis, is isomorphic to a synthetic system. This, it is argued, establishes a sense in which analysis and synthesis are ‘flip sides’ of the same conceptual coin. Since an analytic‐synthetic system is a group, and a group is a genuine mathematical system, it is seen the important role that Descartes's enumeration played in establishing a ‘mathematized’ physics.

Keywords:   Latin squares, magic squares, Pascal's triangle, combinatorial tables, permutation group

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