My purpose here is purely historical. It is not an attempt to resolve the question as to whether Russell did or did not countenance nonclassical logics, and if so, which nonclassical logics, and still less to demonstrate whether he himself contributed, in any manner, to the development of nonclassical logic. Rather, I want merely to explore and insofar as possible document, whether, and to what extent, if any, Russell interacted with the various, either the various candidates or their, ideas that (...) Dejnožka and others have proposed as potentially influential in Russell’s intellectual reactions to nonclassical logic or to the philosophical concepts that might contribute to his reactions to nonclassical logics. (shrink)

The transition from the traditional to the representational theory of measurement around the turn of the century was accompanied by little sustained criticism of the former. The most forceful critique was Bertrand Russell''s 1897 Mind paper, On the relations of number and quantity. The traditional theory has it that real numbers unfold from the concept of continuous quantity. Russell''s critique identified two serious problems for this theory: (1) can magnitudes of a continuous quantity be defined without infinite regress; and (2) (...) can additive relations between such magnitudes exist if magnitudes are not divisible? The present paper shows how the traditional theory answers these questions and compares the traditional and representational theories as contributions to our understanding of the logic of application. (shrink)