  We show that numerous distinctive concepts of constructive mathematics arise
automatically from an "antithesis" translation of affine logic into
intuitionistic logic via a Chu/Dialectica construction. This includes apartness
relations, complemented subsets, anti-subgroups and anti-ideals, strict and
non-strict order pairs, cut-valued metrics, and apartness spaces. We also
explain the constructive bifurcation of some classical concepts using the
choice between multiplicative and additive affine connectives. Affine logic and
the antithesis construction thus systematically "constructivize" classical
definitions, handling the resulting bookkeeping automatically.
