Existence and Logical Form

Abstract

“Whatever may be the true nature of things and of the conceptions which we have of them. . . . , in the operations of reasoning they are dealt with as a number of separate entities or units,” the English mathematician A.B. Kempe noted in 1885 in his ‘Memoir on the Theory of Mathematical Form,’ a neglected work much admired by Peirce, Royce, Whitehead, and Woodger, among others.¹ “These units come under consideration under a variety of garbs — as material objects,” Kempe continues,

intervals or periods of time, processes of thought, points, lines, statements, relationships, arrangements, algebraical expressions, operators, operations, etc., etc. — occupy various positions, and are otherwise variously circumstanced. . . . . The units which we have to consider exhibit endless variety; thus we may have a material object dealt with as one unit, a quality it possesses as another, a statement about it as a third, and a position it occupies in space as a fourth. The task of specifying the units which are considered in an investigation may in some cases be one of considerable difficulty, and mistakes are likely to occur unless the operation is conducted with great care.