You stated that before Heraclitus 'Greeks thought reality was essentially chaotic and impossible to understand.' Thales is a counter-example who is earlier than Heraclitus. See the IEP http://www.iep.utm.edu/g/greekphi.htm or Edward Hussey's excellent book.
Speculating on a causal principle implies that there is causality in the universe. Consequently, order and the possiblity of some degree of understanding are also implied, although the translation from speculation to empirical confirmation is not.
I see. Well, sounds like you know more about the pre-Socratics than I. I was under the impression that it wasn't until Heraclitus that people thought things in our mind, like math, would correspond with external reality.
