The mathematical context behind Frege ’ s analysis of function and object ∗

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. Presentations of Dirichlet’s proof over the next century show a very gradual transition to a modern perspective, whereby certain functions that appear in the proof assume the status of ordinary mathematical objects. In prior work [3, 4] we studied this transition in detail, and explored the methodological and philosophical ramifications. Here we use these considerations to illuminate the treatment of functions and objects in Frege’s work on the foundations of logic, and we argue that his philosophical and logical decisions were influenced by many of the same factors that shaped the mathematical developments.