The Role of Number in Philolaus' Philosophy

Abstract

Philolaus is a peripheral figure in the history of Greek mathematics. We know of no important advance in mathematics that is attributed to him, nor is there any evidence that he wrote a book exclusively or even primarily devoted to mathematical topics.' Indeed the tradition about Philolaus suggests that he wrote just one book and not a terribly long one at that.2 What is known of that book from fragments and testimonia suggests that it covered a wide range of topics despite a relatively small compass. There is evidence that after an account of the basic principles of the cosmos Philolaus went on to present his own astronomical system, his own views on the different psychological faculties of human beings, and a theory of the constitution of the human body and the origins of disease.3 Moreover, mathematical ideas were prominent. The whole number ratios that determine the concordant musical intervals are mentioned in Fragment 6 while other fragments are concemed with number (Fragments 4 and 5) and include a classification of number into two primary types (odd and even)