introduction

Bertrand Russell and Gottlob Frege are the two giants on whose shoulders analytic philosophy rests. Whilst G. E. Moore and Ludwig Wittgenstein also played a significant role in the emergence of analytic philosophy, it was Russell's and Frege's work on the foundations of mathematics and their development of new techniques of logical analysis that set the agenda, and without both Russell and Frege, Wittgenstein's own philosophy would simply not have evolved.

There are many similarities between Russell and Frege. Both were trained as mathematicians, and although they also studied philosophy, were both drawn seriously into philosophy through concern with the foundations of mathematics. Both wrote early works on geometry, but became increasingly interested in the nature of number. In the works that represent the highpoint of their intellectual achievements, both set out to demonstrate that arithmetic was reducible to logic, a project that required the development of logical theory itself. Both exerted a powerful influence on the young Ludwig Wittgenstein, whose Tractatus Logico-Philosophicus ushered in the second phase of analytic philosophy when the so-called ‘linguistic turn’ was taken. But despite these fundamental similarities in their mathematical background, achievements, and influence, their personal lives, characters, and careers were very different. Frege spent his entire working career (from 1874 to 1918) lecturing in mathematics at the University of Jena, remained a relative recluse, and grew increasingly embittered as he failed to receive the recognition he deserved.