Peano, Frege, and Russell’s Logical Influences

Abstract This chapter addresses the historical influences on Russell’s views in logic and his particular style of symbolic logic. Some credit Gottlob Frege as the main source of Russell’s advocacy of symbolic logic in philosophy and endorsement of logicism, the theory that mathematics reduces to logic. In fact, Russell came to these positions independently, having first discovered modern symbolic logic in the writings of the Italian mathematician Giuseppe Peano and his school. Russell adopted his own notation by modifying theirs and, through it, first became convinced of logicism. He discovered the (mostly earlier) works of Gottlob Frege only later, but Frege’s ideas thereafter became more influential, especially as Russell toiled at solving logical paradoxes and puzzles about meaning hampering his earlier work. Russell’s mature views about philosophical and mathematical logic, propositional functions, classes, logical types, and the theory of meaning can be seen in many ways as a reaction to the flaws in Frege’s.