 There is no evidence that Philolaus thought that numbers had a metaphysical status independent of the objects which they describe (for the contrary view, i.e. that Philolaus thought that the abstract was prior to the concrete, see Netz 2005: 87–88). Aristotle emphasizes that the Pythagoreans differed from Plato in not separating numbers from things (e.g. Metaph. 987b27–9), and Plato confirms this interpretation with his criticism of the Pythagoreans on the grounds that they looked for numbers in things rather than focusing on numbers in themselves (R. 531c). On the other hand, Aristotle’s assertion that the Pythagoreans thought that things were numbers or that they were made of numbers is also not supported by the fragments of Philolaus. When describing the components of things in the world, Philolaus always talks in terms of limiters and unlimiteds and never asserts that things are made or arise from numbers (cf. Fr. 1). In the surviving fragments, number is only explicitly introduced to solve epistemological problems. It is true, however, that Philolaus’ third metaphysical principle, “harmonia,” is a “fitting together” of limiters and unlimiteds in accordance with number. Number thus does play a metaphysical role in defining the essence of things, but there is no indication that it is the material out of which they are made. Aristotle’s assertion that the Pythagoreans thought that things were numbers is best understood as his own interpretation of what Philolaus’ system amounted to (Huffman 1993, 57–64; see Schibli 1996 for a defense of Aristotle’s assertion as historically accurate). Aristotle may well have thought that if numbers are what give us knowledge of things, then, in Aristotelian terms, they are the essence of things and hence that, in a sense, things are numbers. Philolaus appears to have thought that things were composed of unlimiteds such as material stuffs and structural features such as shapes; number describes the harmonia or fitting together that defines how the limiters and unlimited were combined and hence give us the “formula” of the thing in question. There is no evidence that he addressed the metaphysical status of the numbers themselves. 