 Second, a doctrinal criterion is applicable. Anyone who espouses the philosophy assigned to the Pythagoreans by Aristotle can be regarded as a Pythagorean, although Aristotle presents that philosophy under an interpretation that must be taken into account. It is important that the use of such a doctrinal criterion be limited to quite specific doctrines such as limiters and unlimiteds as first principles and the cosmology that includes the counter-earth and central fire. Particularly to be avoided is the assumption that any early mathematician or any early figure who assigns mathematical ideas a role in the cosmos is a Pythagorean. Mathematicians such as Theodorus of Cyrene (who is included in Iamblichus’ catalogue) and Hippocrates of Chios (who is not) are not treated as Pythagoreans in the early sources such as Plato, Aristotle and Eudemus, and there is accordingly no good reason to call them Pythagoreans. Similarly, the sculptor, Polyclitus of Argos, stated that “the good comes to be … through many numbers,” (Fr. 2 DK), but no ancient source calls him a Pythagorean (Huffman 2002). As Burkert has emphasized, mathematics is a Greek and not just a specifically Pythagorean passion (1972a, 427).