Polarity as a Generative Primitive for Mathematical Structure

We investigate whether a single minimal primitive—polarity—is sufficient to generate standard mathematical structure. A polarity is a two-element set equipped withan involution. From this primitive, we specify generative rules that construct orderedpairs, relations, and functions without presupposing sets, logical connectives, or categorical structure. We prove that these constructions satisfy the usual axioms forordered pairs and functional relations and show how logical, set-theoretic, topological,and thermodynamic polarities arise as instances of the same scheme.