A Logical Development of Arithmetic as Based on the Theories of Guiseppe Peano and Gottlob Frege
Rudell, Lucinda Robbins, 1947-1990
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The search for a foundation from which all of mathematics can be developed through prescribed motions is a pursuit that in the past has always failed. Even while concepts today considered elementary were causing arguments among the mathematicians of a century ago those same men were looking for ways to develop the more complex mathematical notions from the simpler ones. Mathematicians finally settled the pursuit down to a question of finding a set of axioms and primitive ideas from which elementary arithmetic could be generated by specified procedures; then, the rest of classical mathematics seems to fall rather reasonably from this beginning. (C. G. Hempel, p. 154.) (With the exception perhaps of geometry, which seems to have its own axioms and systems of development. But even geometry can be brought together into the scheme of math via set theory.) This paper is an inquiry into the idea of axiomatizing arithmetic using Peano as its base and Frege's philosophy as its substance.If you are not a current K College student, faculty, or staff member, email email@example.com to request access to this SIP.