03 September 2005

Did Anaximander Accept "Sufficient Reason"?

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).

"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).
But did Anaximander in fact accept this principle? I think not:

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.


Scott Carson said...

You can add Barnes (The Presocratic Philosophers) to your list of folks who attribute the PSR to Anaximander.

I'm not so sure we should be so quick to dismiss the possibility of PSR being at play in Anaximander. It seems to me that what you're demanding of him is something stronger than the PSR. If we were to pursue a mechanistic explanation of every observable feature of the universe to its ultimate cause, we would find in each case that the PSR is violated, simply because you've got to start somewhere. So I don't think, for example, that because he posits a dynamic tension for which he offers no justification that we are really justified in assuming that he is, as you say, explicitly assuming that PSR is false--that tension is itself an explanation for other phenomena, which it, in turn, explains. It is the "sufficient reason." To ask why this starting point is as it is would be the sort of question that Aristotle attributed to folks who don't understand what sorts of things can be inquired into.

What you're calling "re-characterization of the explanandum" is not, I would say, the dodge that you make it out to be, but rather an attempt to make a more successful explanation than one that is already in place. There still has got to be some reason for postulating a different explanation, whether the difference lies in new empirical data or a new theoretical perspective.

Michael Pakaluk said...


Is it possible to adhere to PSR, but only sometimes? Suppose Anaximander thought that some things happen for no reason. Then he argues: "The earth is at rest because there is no reason why it should move." Someone could retort: "That's not an explanation. Lots of things happen for no reason, as you admit."

It seems to me that Leibniz agrees that commitment to PSR has to be thoroughgoing, which is why he thinks any commitment to PSR implies a commitment, likewise, to the existence of a God who is a necessary being. (That's the way one escapes the universe's being a brute fact.)

Mustn't PSR explain ex ante rather than ex post? If Anaximander is asked, "Why is it very hot now, in the summer?", he cannot say, "Because it is going to be very cold later, in the winter."

I didn't mean 're-characterization of the explanandum' to be a dodge. No, I meant that this is the nature of theoretical advances in science. (It's comparable to Aristotle's point about how we start by wondering how the diagnonal could be incommensurable but end by wondering how it couldn't be.) My point was simply that that sort of advance is not a matter of commitment to PSR.


Scott Carson said...

I'm not sure this will explain (if you will excuse my use of the term here--I can't decide if it counts as a pun or not) our difference, but perhaps what is at issue is merely the Leibnizian PSR as opposed to a proto-PSR being ascribed to Anaximander. My own understanding was always that nobody was seriously attributing to Anaximander a conscious statement of a full-blown PSR on the order of Leibniz's, but rather he gives an argument in which the validity of a certain kind of inference depends on the assumption that you can't get from A to B unless there is some sort of compulsion, a kind of normativity in reasoning, which writers such as Barnes have interpreted as having the force of a kind of PSR-like axiom.

I think Leibniz is right: if you apply the full-blown PSR in a consistent way, then nothing will have any explanation unless you posit a God. But of course even then it will fail, since you will have no explanation as to why there is a God rather than not. If we posit a necessary being things are only a little less murky, since we have as yet no explanation as to why God is (not 'must be in order for things to be as they are') a necessary being rather than not.

So the PSR, if it is to be useful in any context outside of a Leibnizian one, must make allowances for first principles, it seems to me, and I'm not convinced (at least not yet) that this would have to count as Anaximander believing in PSR "only sometimes." If Aristotle could believe, in the Posterior Analytics, that knowledge is possible with neither infinite nor circular explanatory chains, then perhaps there is a certain congeniality for the role of first principles in the Greek Weltanschauun? Anaximander, of course, is a lot earlier than Aristotle, but we're talking here about the beginnings of something that develops more fully later on, whether we call it the use of first principles or a foreshadowing of the PSR.

Or do you think the commitment to PSR has to go "all the way down", as it were, on pain of going nowhere?

Michael Pakaluk said...


Sorry for taking so long to reply.

I'm aiming to shift the burden of proof. Suppose we put aside all the talk in the commentaries about Anaximander's accepting PSR and look at the texts afresh. What are the arguments for claiming that he does? Is there some weaker view that just as plausibly accounts for the texts?

(Sure, I understand wanting to make the presocratics more interesting by magnifying their discoveries.)

Suppose someone were to argue (against Thales) : "The sun is not water, because the sun is hot; heat excludes cold; and water is cool." It would be much too puffed up to say that he's invoking the Principle of Non-Contradiction. He simply has the idea that contraries exclude each other. Similarly, if Anaximander thinks (say) that something will not move in the absence of a force, then it seems puffed up to call this an appeal to PSR.

Again: suppose we say that what Anaximander does is draw attention to a consequence of the earth's being at the center of the cosmos: no need, then, that it should fall, and then no need that it should be supported to stay at rest. That doesn't look like PSR.


Anonymous said...

By the way, add McKirihan to the list:

"This too is to be understood as a criticism of Thales, who had the earth resting on water. What, then, did the water rest on? As long as one thing needs to be supported by another, there is no end. Anaximander cuts off this infinite regress at the start with the first known application of the Principle of Sufficient Reason...In the present case, Anaximander reasons that the earth is at rest since its 'equal relations to the extremes' implies that there is no sufficient reason for it to move in one direction rather than any other." 

Posted by Michael Pakaluk

May Sim said...

To the extent that Anaximander intended his apeiron to be the first principle of everything, he is giving a reason for everything. And if doing so satisfies the PSR then we can say that the PSR is at work in Anaximander's thinking. Nevertheless, this does not mean that Anaximander's reason is always sufficient to explain the things we want him to explain. Michael and Scott--you seem to be arguing about the quality of Anaximander's reason instead of whether he is attempting to provide a reason.

Michael Pakaluk said...


But Anaximander's identifying something as a first principle (in his case, the apeiron) wouldn't set him apart from other presocratics and give him the distinction (as commentators say) of being the first to formulate PSR.


Scott Carson said...

True, postulating a first principle may not set him apart, but--again, unless I misunderstand what folks are trying to do in attributing PSR to him--the idea is that he appears to think that certain sorts of inferences are warranted, in part, precisely because of the notion of a "burden of proof". I take it that our evidence for the other Milesians isn't sufficient to attribute anything like that to them. The key passage is the one you cited--the earth remains at rest because what is situated in the middle has no more reason to move one way rather than another. This is already an interpretation, right, from Aristotle, so of course we have to be careful in doing this kind of thing.

I think I agree with May, though--our disagreement is seeming to me to be over the quality of Anaximander's explanation. An assertion that the earth "has no need" to move up or to fall down seems very much to me to mean that, if there were a need (that is, some reason why it should move up or down--a reason sufficient to bring about a different state of affairs than what we actually observe) well, then, by golly it would move. I'm not sure I see why that isn't just a roundabout, sloppy application of PSR.

In his own apologia for making such attributions, Barnes notes that if it is anachronistic to read the Presocratics this way, then "all attempts to understand the Presocratics are doomed to failure." I might have said rather "doomed to merely antiquarian interest." If Anaximander is not making use of something like PSR, then what he says has no philosophical interest, because it is just one more banal metaphor about why things look the way they do among many other such metaphors floating around at the time.

(Don't get me wrong--I have nothing against antiquarianism per se. I'm a trained classicist, after all! But I think there needs to be something different about what Anaximander is doing if we are to distinguish him from the Usual Suspects like Homer and Hesiod.)

Anonymous said...

It seems to me that KRS have it right when they say that Anaximander's achievement is that "he completely broke away from the popular idea that the earth must be supported by something concrete, that it must have 'roots'" (170). Yet then they are unjustified to add, as they do, that "his theory of equilibrium was a brilliant leap into the realms of the mathematical and the a priori "--for which they cite Kahn.

And then in the immediately following sentence KRS add, quite sensibly in my view, that this 'leap' is "one which he would not have been tempted to take, it might be suggested, if vortex-action had been applied in his cosmogony and was at hand, as it were, to explain the stability of the earth". That seems right. But one might just as well say that equipollence of forces was already at hand for him--commonsensically so--and that that is what made the leap unnecessary.

As for Barnes, he poses a false alternative. KRS point out, amusedly, that Barnes is rather free with 'logical' principles and 'logical' necessity. Of Xenophanes, for instance, KRS remark that "Xenophanes thus appears to accept the well-established Greek criterion of seemliness"; and then in a foonote they chide: "J. Barnes...interestingly maintains that 'seemliness' is logical: 'it is not logically possible...that divinities locomote.'"

Should we say that if we don't read Xenophanes in this strange way, as wielding 'logical' principles, then he can be only of antiquarian interest'?  

Posted by Michael Pakaluk

Scott Carson said...

Well, I would say that you're taking your turn at offering false dichotomies. Whether or not one is sympathetic to Barnes' love affair with logic, I don't think we have to be afraid to use the logical machinery of contemporary philosophical methodology when approaching the ancients. Does this approach, in and of itself, save them from being of merely antiquarian interest? No, but it can make the philosophical interest of these writers plainer, in some cases. Does avoiding logical machinery reduce them to merely antiquarian interest? Not necessarily--it would depend on what you replace it with. Some approaches may very well leave the Presocratics looking like nothing more than bizarre examples of the mythographers that we're supposedly trying to distinguish them from. There are folks even now (and we all know who she is) who are arguing that the Presocratics were not, in fact, philosophers at all. If we don't want to agree with that judgment, we need to be able to show in what sense they are philosophers, and one way of doing that might be simply to illustrate ways in which they were "speaking our language". Granted, it won't work every time, but I don't see what the harm is.

Michael Pakaluk said...


I agree with you, that we should look for as much genuinely philosophical insight as we can find in the presocratics (and--I would add--as is actually there).

But I think there's lots of insight already in Anaximander, without our needing to attribute PSR to him.

I remember a story about Wittgenstein, who wanted to illustrate what was wrong with the popular idea that people at the antipodes risk falling off the earth--and with that, to illustrate something about philosophical mistakes generally. He took a piece of paper, drew a circle, drew it so that a stick figure was on the circle 'head down', and then he rotated the paper, so that the same person was now 'head up'. That removed the worry.

Wittgenstein's exhibition, I take it, expressed a philosophical idea. But it wasn't that "Wittgenstein had made a particularly apt use of the Principle of Sufficient Reason."

But also: Shouldn't we reject the sharp distinction between philosophy and natural science, especially for the Milesians? (The distinction is only a couple of centuries old, after all.) For Barnes, there is a sharp distinction; the philosophical is the logical; and that is why he must be looking for 'logical' innovations in the presocratics.


Wes DeMarco said...

May told me about the PSR discussion; here’re two more cents. Part of the difficulty in all this is that even now there's a diversity of PSRs floating about, more or less restrictive.

Leibniz distinguished between contingent truths, based on the PSR, and necessary truths, which are all at base, identities or founded on identities. These two principles are supposed to be disjunct and exhaustive. However, it seems to me that basic principles of physics, such as symmetry principles, lie at the cusp of these two, fitting uncomfortably into either class.

The Anaximanderian point of contention is the forebear of such principles, is similarly at the cusp, and for that reason in one respect seems quite trivial and uninformative, while in another respect seems to imply something substantive (the world is where it is because there is no sufficient reason why it should be elsewhere).

Emmy Noether’s well-known theorems, phrased informally, are curiously reminiscent of old Anaximander: a stationary body in empty space would have no tendency to start turning, since it would 'find' all directions equally good. Its having no 'preference' for clockwise as opposed to anticlockwise rotation, etc., is its rotational symmetry. And that rotational symmetry is equivalent to spin conservation, a deep principle of our physics. Ditto for translational symmetry and linear momentum conservation, temporal translation symmetry and energy conservation, and so on for the others. Though Anaximander’s intuition is far more primitive, I do not think he would find this mode of thinking to be alien.

So I think there is a kinship in mode of thinking here. But, no, I don’t believe it’s exactly the PSR at work. (Nor, helpfully, a proto-PSR.) That, however, doesn’t imply that Anaximander’s thought must reduce to an identity, either.
Neither A's nor Noether's are comfortably PSRs. That is, perhaps, because when we encounter such principles we are passing from contingent truths to necessary ones. The idea that the 'right' set of symmetries would hold for any physical world is, of course, contentious.