 It is logical to begin with the very first thing that is put together in Philolaus’ cosmos. In Fragment 7 Philolaus asserts that “The first thing fitted together, the one in the center of the sphere, is called the hearth.” From other evidence we know that this hearth in the center of Philolaus’ cosmos was known as the central fire, around which all the heavenly bodies, including the earth, orbit. Since the central fire is explicitly said to have been “fitted together,” according to Fr. 1 it must have been fitted together out of a limiter and an unlimited, like everything else in the cosmos. It appears that the term “central fire” itself identifies the limiter and unlimited from which it is composed. It is composed of the unlimited fire, which is limited by its position in the center of the sphere. One interpretation then would be that unlimiteds are stuffs and limiters are shapes (Barnes 1982, 387 ff.). It is striking confirmation of this conjecture that many earlier Presocratics described their material principles as “unlimited.” Anaximander posited the unlimited as the source from which the basic material principles of the world, the opposites such as hot and cold, emerged, and his successor Anaximenes explicitly described his basic material principle air, as unlimited (DK 13 A1 and A6). Anaxagoras, in the generation before Philolaus, described all the things in the original mixture from which the world emerges as unlimited and this list would appear to include air, aither (Fr. 1), dry, wet, hot, cold, bright, dark (Fr. 4), dense and rare (Fr. 12). Thus, Philolaus’ unlimiteds probably included stuffs in the broad Presocratic sense, which treats opposites such as the hot and the cold as material substances. The next stage in Philolaus’ cosmogony after the construction of the central fire helps to identify yet more unlimiteds. In his lost work On the Pythagoreans Aristotle describes the universe as drawing in time, breath, and void from the unlimited (Arist., Fr. 201). This text certainly means that the universe was surrounded by an unlimited from which time, breath and void were drawn, but it probably also means that time, breath and void were regarded as unlimiteds. Breath can be equated with air as a typical Presocratic stuff, but time and the void show that we must expand Philolaus’ conception of unlimiteds beyond stuffs. Unlimiteds appear to be not just materials, which can appear in various shapes, but also continua, like time, which can be limited by various measures but which do not have a shape. Philolaus thus accepts the earlier Presocratic reliance on material principles but introduces two radical changes. First, he thinks it beyond human knowledge to identify any privileged set of unlimiteds, such as earth, air, fire and water, as ultimate elements. Second, he focuses not on the qualitative features of these stuffs (e.g. hot) but rather on their role as continua (Huffman 1993: 43–4; Graham 2014: 52).