Smooth Infinitesimal Analysis

In previous chapters, notably in Chapters IV and V, we have used “synthetic arguments” at an informal level, trusting that the context would provide a meaning for the term “synthetic”, and would make the arguments themselves plausible. The aim of this final chapter is to make the notion of “synthetic reasoning” explicit, by setting up an axiomatic system which is adequate to formalize the arguments from earlier chapters, as well as some others which we will present below.