# The Conceptual Roots of Mathematics

## Abstract

*The Roots of Mathematics* argues for a chastened Logicism.
Although mathematical arguments are *a priori*, they are not all deductive,
and we can justify Peano's Fifth Postulate and the Axiom of Choice
if we construe them as principle of argument between two rational seekers after truth.
Our mathematical concepts are grounded in logic,
although often developed by extrapolation to something essentially new.
The logic of transitive relations exhibits Set Theory and Mereology as two paradigms of orderings,
with topology as a natural development.
A *Which?* guide to geometry recommends Euclid's as the Best Buy.
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