Bertrand Russell’s Philosophical Logic and its Logical Forms

Abstract

From 1901 to 1919, Russell persistently maintained that there were two kinds of logic and distinguished between one and the other as mathematical logic and philosophical logic. In this paper, we discuss the concept of philosophical logic, as used by Russell. This was only a tentative program that Russell did not clarify in detail; therefore, our task will be to make it explicit. We shall show that there are three (-and-a-half) kinds of Russellian philosophical logic: (i) “pure logic”; (ii) philosophical logic investigating the logical forms of propositions; (iii) philosophical logic exploring the logical forms of facts: in epistemology and in the external world. In particular, Russell’s program or philosophical logic of the facts of the external world remained less than sketchily outlined. Keywords: Russell, mathematical logic, philosophical logic, Wittgenstein