 The last sentence of the fragment seems to say that individual things in the world “give signs” of the many forms of number. Our first experience of a musical scale comes through simple sense perception, but, when the phenomena are studied further, they “give signs of” or “point to” the whole-number ratios that govern the musical intervals. Once we grasp these ratios, we can claim to understand or know the scale. McKirahan (2012) argues that in Fr. 6a Philolaus formally demonstrates that ratios are numbers and that the many forms of numbers in Fr. 5 are the different types of ratios. Huffman (1993: 174) argues that Philolaus’ use of the term number includes ratios from the start and that the many forms of numbers are just the even and odd natural numbers (1993: 191; cf. 2012). Mourelatos has shown that Fragment 5 is also important in the history of the development of the concept of the universal. Philolaus distinguishes between numbers as individual species and their genera, even and odd, i.e. between subordinate and superordinate universals, as well as between numbers and things, i.e. between types and tokens, e.g. four and four pebbles. Moreover, the reference in Fragment 5 to things “giving signs” of numbers is “the first recorded attempt in the history of metaphysics at coining a term for [the relation between a particular and a universal]”(Mourelatos 2006, 66). 