Chapter

Synthesis and the Principle of Addition

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/9780199583652.003.0010
Synthesis and the Principle of Addition

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This chapter studies the mathematical concept of a group, early ancestors of the concept found in the works of Descartes and Leibniz. Here, it is shown exactly how the four conditions expressed by a group underwrite all of mathematics, in particular the operations of arithmetic.

Keywords: semigroup; Monoid; group; Boolean Algebra; ring; field; mathematical structure

Chapter.  6479 words.  Illustrated.

Subjects: History of Western Philosophy

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