Abstract
Both Russell and Frege reject the Kantian view of logic and mathematics, and in particular, they reject the claim that the subject-predicate division is essential to the nature of judgement. This led them to attempt to develop a symbolic logic capable of showing that mathematics is reducible to logic, thereby showing that mathematics has the same necessary status as logic. In constructing their symbolic system, they develop a notion of logical truth as one true for all objects whatsoever. Central to their logical calculi is a notion of logical consequence: Frege introducing the “conditional stroke” and Russell introducing the notion of “material implication.” The object of this paper is to trace the evolution of the notion of consequence in their work, and observe its relationship to the notion of logical truth. This development illustrates how Frege influenced Russell’s development of his realist model of propositions.
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