Russellʼs Theory of Propositions in Principles of Mathematics and British Idealism

Abstract

Russellʼs theory of propositions in “Principles of Mathematics” (POM) has long been considered a theory that was simply to be overcome by that of “On Denoting”.　We claim, however, that the theory has significant value in connection with the explanation of his development of thought as well as its relationship with various philosophical thought and is deserving of examination.
In order to make Russellʼs theory of propositions clear, we examine his dual use of the concept “terms” in POM, specifically ontological and propositional use. The former reflects his thought on “how things exist”, which is in sharp contrast with that of British Idealism. According to this school of thought, things exist owing to their relatedness to other things. The consequence of the well-known revolt of Russell and Moore against British Idealism was their entirely opposite, no-relational and atomistic ontology. On the other hand, Russell thought that propositions were not only collections of things, they were those things that were somehow united. For this problem of unity, which cannot be resolved within the framework of his atomistic ontology, the consideration of the second use of the concept “term” is needed. This shows his main feature of the theory of propositions; a same thing can “occur”differently and have a different role within propositions. He claimed that verbs and adjectives were important, because the occurrence of the former enables the synthesis of propositional elements, and the occurrence of latter can form a denoting phrase.
By examining the theory of propositions in POM and the problem originating therefrom, we can interpret Russellʼ s development of thought as the process of dealing with the problems in the theory, namely the problem of unity and denoting phrase occurrence. As regards former, given the fact that Frege and Wittgenstein have a different position concerning it, we gain a hint of understanding their difference by examining how they assure the synthesis of proposition with their own conception of logic. Considering the various implications that POM suggests, its historical significance should not be neglected.