A Geometry of Logic

This paper1 will sketch a theory of partial identity or partial congruence for the elements of a Boolean algebra, and will establish the equivalence of this theory with the theory of metric Boolean algebras and with that of unnormalized measures. (It is not suggested that this latter equivalence is not well known.) The merit of the theory, and of others like it, is that it allows us, with no departure from classical two-valued logic, to contemplate how scientific hypotheses may approximate to each other, as well as to the truth. The theory also suffers from some disadvantages, which will be noted.