 The system is the result of a combination of a priori principles and reliance on observation. Philolaus is the first to incorporate all five planets commonly known in antiquity into an astronomical scheme in the correct order, which indicates that he was aware of the most up-to-date astronomical data (Eudemus as cited in Simplicius, in De Caelo 471.4; Huffman 1993, 260; Zhmud 2012: 336–7 thinks that Eudemus is referring to an earlier Pythagorean system). On the other hand, there are a number of features that appear to be explained by appeal to a priori principles of order. Thus, moving the earth from the center of the universe did not serve to explain astronomical data better. There is no explicit reason given for moving the earth; Aristotle reports that some others (Platonists?; see Kingsley 1995, 175–80) thought it should be moved because fire was thought to be a “better” element than earth and hence to belong at the center of the cosmos, which is a position of honor (Arist., De Caelo 293b2). We are explicitly told that the Pythagoreans accepted one of the premises of this argument, that the center is the most important part of the cosmos (Arist., De Caelo 293b2–3), and it is likely that the whole argument should be assigned to Philolaus (Huffman 2007, 76–80). This is consistent with the evidence of Frs. 7 and 17, which clearly indicate that the cosmogony began in the center. Philolaus may have assigned fire the position of honor, because of the analogy with human birth, since he argued that the human embryo develops from the hot (see 5.3 below). The case of the counter-earth is more complicated. Aristotle suggests that it was introduced for a priori reasons: to raise the number of heavenly bodies around the central fire from nine to ten, which the Pythagoreans regarded as the perfect number (Arist., Metaph. 986a8–12; on the other hand Zhmud 2012:407 argues that the number ten had no particular significance for the Pythagoreans). Some scholars have objected that, if we count the central fire, the introduction of the counter earth makes eleven bodies in Philolaus’ system (Burch 1954, 284; Kingsley 1995, 174); the ancient evidence consistently talks in terms of bodies arranged or moving around the central fire, however, and obviously the central fire cannot be counted as one of these (Aetius 2.7.7; Arist., Fr. 203 and Metaph. 986a10), so that Aristotle’s explanation retains considerable plausibility (Burch 1954 suggests that the counter-earth was introduced as a counter-weight to the earth, so that the center of gravity of the cosmos would coincide with the spatial center, but there is no evidence that Philolaus had the concept of a center of gravity). On the other hand, Aristotle also comments that the counter-earth was introduced to explain lunar eclipses (De Caelo 293b18–25). Graham has recently made a convincing case that the counter-earth could in fact account for eclipses of the moon at dawn and dusk, which otherwise would be inexplicable on Philolaus’ model (Graham 2015, see also Graham 2014: 57–60). Graham speculates that the term for counter-earth in Greek (antichthon), may refer to the counter-earth’s “taking the place” (anti) of the earth in accounting for these lunar eclipses, which cannot be explained by the interposition of the earth (Graham 2015: 229). Thus, one of the main features of Philolaus’ system that had been thought to show its non-scientific character, may, in fact, be motivated by an attempt to make the system better explain the phenomena. The doxography also assigns the counter earth to the Pythagorean Hicetas (DK 50A2; cf. Mansfeld 2010a: 90–93). The fixed stars do not literally move in Philolaus’ system but they, like the planets, sun and moon, have an apparent diurnal movement caused by the motion of the earth. Even Philolaus’ basic assumption that the cosmos is spherical (Frs. 7 and 17) may be based on Parmenides’ a priori arguments that reality is similar to a sphere in perfection (Fr. 8.42–44).There is no explicit statement about the shape of the earth in Philolaus’ system and some have supposed it to be flat (Burch 1954: 272–273). Analogy with the cosmos suggests that it was spherical as well and several of Aristotle’s descriptions of the Philolaic system show that it was (Dicks 1970: 72–73). Philolaus appears to have believed that there was also fire at the periphery of the cosmic sphere and that the sun was a glass-like body which transmitted the light and heat of this fire to the earth, an account of the sun which shows connections to Empedocles; Philolaus also posited a great year of 59 years in which the lunar and solar cycles were reconciled (Huffman 1993, 266–70 and 276–279). Philolaus’ great year may be connected to the doctrine of the periodic return of all things, which Dicaearchus assigns to the Pythagoreans (Porphyry, Life of Pythagoras 19), which may be in turn a generalization of reincarnation (Riedweg 2005, 63). 