This post falls in the category: what a non-expert wonders about when teaching X. (I expect to post many things of this sort, as I work through "History of Ancient Greek Philosophy" this Fall. May I hope that others, on the same path, will find such posts of interest?)
For years I've repeated the common claim that Anaximander, especially in his teaching about the earth, was relying upon something like the Principle of Sufficient Reason. Here are those familiar texts about the earth (texts and translations from Kahn):
The earth is aloft, not dominated by anything; it remains in place because of the similar distance from all points (Hippolytus).
th\n de\ gh=n ei)=nai mete/wron u(po\ mhdeno\j kratoume/nhn, me/nousan de\ dia\ th\n o(moi/an pa/ntwn a)po/stasin.
There are some who say that the earth remains in place because of similarity, as did Anaximander among the ancients; for a thing established in the middle, with a similar relationship to the extremes, has not reason to move up rather than down or laterally; but since it cannot proceed in opposite directions at the same time, it will necessarily remain where it is. (Aristotle, De Caelo, 295b11-16.)
ei)si\ de/ tinej oi(\ dia\ th\n o(moio/thta/ fasin au)th\n me/nein, w(/sper tw=n a)rxai/wn A).: ma=llon me\n ga\r ou)qe\n a)/nw h)\ ka/tw h)/ ei)j ta\ pla/gia fe/resqai prosh/kei to\ e)pi\ tou= me/sou i(drume/non kai\ o(moi/wj pro\j ta\ e)/sxata e)/xon: a(/ma d’ a)du/naton ei)j ta)nanti/a poiei=sqai th\n ki/nhsin: w(/st’ e)c a)na/gkhj me/nein.
And here are typical things that people say about this:
"...this explanation is the earliest certain instance of an appeal to the principle of Sufficient Reason" (Hussey, 26).But did Anaximander in fact accept this principle? I think not:
"For the history of ideas, Anaximander's theory of the earth's position is of an entirely different order of importance. Even if we knew nothing else concerning its author, this alone would guarantee him a place among the creators of a rational science of the natural world. ... More important for us is Anaximander's own use of this geometric idea [sc. of a circle] , as a general expression for the principle of symmetry or indifference. It is indeed the same notion which was glorified in modern times by Leibniz as his Principle of Sufficient Reason, according to which everything which is true or real implies a reason why it is so and not otherwise" (Kahn, 77).
1. His famous fragment specifically supposes that Sufficient Reason is false. Extremes dominate at different times and places (e.g. hot in summer, cold in winter) for no apparent reason; the only 'reasonability' of the scheme is that these extremes get equalized over time.
2. An appeal to equipollence of forces or conditions is not an appeal to Sufficient Reason. Suppose I embed a glass marble in a slab of heavy jelly. Someone asks why it doesn't move in the jelly. I reply that it is similarly affected by the jelly on all sides. No 'Principle of Sufficient Reason' there.
3. The correct way to describe Anaximander's innovation (and he does have an innovation) is something else. It involves (we may say) "re-characterizing the explanandum". E.g. Galileo postulated that a body in motion remains in motion: in doing so, he re-characterized the explanandum, from "Why does this continue moving'?" to "Why is this not slowing down?" Anaximander does this also with his theory of heavenly objects. E.g. we might want to ask: "Why is that planet shining brightly there?" But since (it seems) Anaximander takes a planet to be (roughly) a tube with a puncture, he thinks the question is properly posed, rather, as "Why is Venus not shining everywhere else?" (Answer: Because the tube with fire inside is punctured only there.") Similarly also with the earth. The correct question to ask is not: "Why isn't it moving?" but rather "Why shouldn't it remain at rest?" This sort of shift happens all the time in science; it is not a matter of an appeal to Sufficient Reason.