HoPwaG: Pythagoras

Recall: Xenophanes as concerned with distinction between mere belief and knowledge. Mathematics, at least apparently, a clear example of latter. Some ancients [who?] think of number as a foundational cosmological principle (a la the pre-Socratics with their various candidates), but apparently the Pythagoreans themselves don't (at least not literally).

Pythagoreans:

• posit a 'counter-Earth', because of mismatch between number of visible celestial bodies and the "mathematically projected" number, 10;
• influence extends to neo-Platonists (e.g. Iamblichus);
• some [or was it the neo-Platonists?] endorse idea that soul as not separate from body, rather it's a kind of harmony (evidenced by states of the soul "resonating" [producing emotion] with music); i.e. the "attunement" of the body that keeps it in "good playing order";
• but Pythagoras himself apparently endorses transmigration of souls (entailing dualism, and influencing Plato);
• similarity between the positing of the immaterial, enduring soul and number: both abstract, avoiding the variability of physical objects.