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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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How Analysis and Synthesis are Related

How Analysis and Synthesis are Related

Chapter:
(p.203) 12 How Analysis and Synthesis are Related
Source:
Matter Matters
Author(s):

Kurt Smith (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199583652.003.0013

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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