Logic and Topology

Abstract

Mathematicians may find it odd that philosophers energetically debate the merits of structuralist “interpretations” of mathematics. Like it or not, a structuralist orientation is an essential part of contemporary mathematical practice. It is no coincidence that axioms characterizing, say, complete lattices are rich in diverse and interesting models from apparently far-flung fiields. They were intended to stimulate an abundance of interpretations, any constriction of vision to a privileged model being shunned on principle. (Set theoretic axioms may be an exception, but we question whether they ought to be. See Pollard, ch. 9.)