A Refined Geometry of Logic

Abstract

In order to measure the degree of dissimilarity between elements of a Boolean algebra, the author’s (1984) proposed to use pseudometrics satisfying generalizations of the usual axioms for identity. The proposal is extended, as far as is feasible, from Boolean algebras (algebras of propositions) to Brouwerian algebras (algebras of deductive theories). The relation between Boolean and Brouwerian geometries of logic turns out to resemble in a curious way the relation between Euclidean and non-Euclidean geometries of physical space. The paper ends with a brief consideration of the problem of the metrization of the algebra of theories.

Keywords

• Boolean algebra
• Brouwerian algebra
• metric
• measure
• partial identity