The Principles of Mathematics

B, Russell

TPM is, arguably, the culmination in print of a long process of thought and concern, philosophically speaking, of Russell's intellectual preoccupations from his adolescence, youth and maturity with questions relating to the foundations of mathematics. Ever since Russell read Mill in his adolescence he had thought there was something suspect with the Millian view that mathematical knowledge is in some sense empirical & that mathematics is, so to speak, the most abstract of empirical sciences, but empirical nonetheless. Though he lacked the sophistication at the time to propose a different philosophy of mathematics, his concerns with these topics remained with him well into the completion of Principia Mathematica. Logic and Mathematics were, by that time, seen as separate subjects dealing with distinct subject-matters; it came to be, however, the intuition of Russell (an intuition shared, and indeed, anticipated by Frege) that mathematics was nothing more than the later stages of logic. He did not come into this view easily; after a long period of Hegelianism and Kantianism in philosophy, in which Russell sought to overcome the so called antinomies of the infinite and the infinitesimal, etc; Russell saw light coming, not from the works of philosophers, but from the work of mathematicians working to introduce rigour into mathematics.

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