Chapter

How Analysis and Synthesis are Related

Kurt Smith

in Matter Matters

Published in print April 2010 | ISBN: 9780199583652
Published online September 2010 | e-ISBN: 9780191723155 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199583652.003.0013
How Analysis and Synthesis are Related

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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

Chapter.  7245 words.  Illustrated.

Subjects: History of Western Philosophy

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