II. On the algebraical analogues of logical relations

Abstract

The object of this paper is to examine the “mathematical theory of logic,” thus laid down by Dr. George Boole in his ‘Laws of Thought’ p. 37:—“Let us conceive of an Algebra in which the symbols x, y, z , &c. admit indifferently of the values 0 and 1, and of these values alone. The laws, the axioms, and the processes of such an algebra will be identical in their whole extent with the laws, the axioms, and the processes of an Algebra of Logic. Difference of interpretation will alone divide them.” For this purpose, first the laws of such an algebra have been investigated independently of logic; and secondly the laws of primary and secondary logical propositions as laid down by Dr. Boole have been developed in an algebraical form, and compared with the former.