27 Jun
2026
27 Jun
'26
10:18 a.m.
Dear all, I would like to include the following distinction in a manuscript: There are two styles of reasoning in mathematics: 1. *analytic*: structures built from a “point-set” substrate; 2. *synthetic*: axioms imposed directly on the available types. At present, the only source I have found stating this distinction in this form is the nLab page on synthetic mathematics ( https://ncatlab.org/nlab/show/synthetic+mathematics ). Could anyone point me to a published reference where this terminology or this formulation of the analytic vs. synthetic approaches is explicitly discussed? Many thanks in advance. Best regards, JMRC