"[M]athematical apriorism... has not gone completely unquestioned. J. S. Mill attempted to argue that mathematics is an empirical science, thereby making himself the subject of Frege's biting criticism. More recently, W. V. Quine, , and Imre Lakatos have... challenged the... thesis. However, none of these have offered a systematic account of our mathematical knowledge. ...[T]he alternative...—mathematical empiricism—has never been given a detailed articulation. I shall try... I have gained much from insights of Quine and Putnam... [and] learned from Mill... My quarrel with earlier empiricists is, for the most part, that they have been incomplete rather than mistaken."