The Principle of Sufficient Reason

As previously discussed¹¹⁷, Anaximander argued that the earth’s stability was to be explained not by any one material supporting factor, but rather the absence of a reason to move. This explanation is usually analyzed as utilizing the same reasoning that much later would be explicated in one of Leibniz’ two “great principles”, The Principle of Sufficient Reason¹¹⁸.

117 See 3.2.3 Position and shape of the earth in this essay.

118 ”the Principle of Sufficient Reason, in virtue of which we believe that no fact can be real or existent, and no statement true, unless it has a sufficient reason why it should be thus and not otherwise” (Leibniz, Monadology,

§32). This means that nothing can be so without a reason why it is so; that nothing occurs by blind chance.

Barnes (1979:23-28) formalizes Anaximander’s use of this principle in explaining the earth’s rest thus:

A straight line drawn from the centre of the earth to the border of the finite cosmos is a cosmic spoke. A spoke s1 is similar to a spoke s2 if every point, p1, n units from the earth along s1 is qualitatively indistinguishable from the corresponding point p2, n units from the earth along s2. While Hippolytus’ text suggest that all cosmic spokes are similar, Aristotle’s text suggests only that spoke directly opposed (‘opposed’ in this context means that two spokes form an angle 180° in all planes at the centre of the earth) to each other must be similar. Anaximander does not need any premise which includes more than

(1) For any cosmic spoke si, there is a distinct spoke sj such that sj is similar to si.

Now the claim of Anaximander is that the earth does not move either along spoke sj nor along spoke si, because it has no more reason to go in one direction than the other. But if we now suppose that the earth is moving, Barnes suggests, e.g. along spoke s1, then

(2) The earth is moving along spoke s1

The motion described in (2) must then for Anaximander have a reason and thus be subject for explanation. Anaximander is then implicitly relying on some such principle as

(3) If a is F, then for some φ, a is F because a is φ From (2) and (3) Anaximander may validly infer

(4) For some φ, the earth moves along s1 because s1 is φ If the explanatory feature of s1 is G, then we would have

(5) The earth moves along s1 because s1 is G, And then

(6) s1 is G Then, by (1) and (6)

(7) Some sj distinct from s1 is G Suppose, then

(8) s2 is G

At this point, Barnes (1979:25) writes, Anaximander needs another principle, namely that explanations are ‘universalizable’. A fitting formula here would then be

(9) If a is F because a is G, then if anything is G it is F

Between them, (3) and (9) amount to something like the Principle of Sufficient Reason: (3) asserts that happenings need some explanation, (9) indicates how that explanation must be a sufficient condition for what it explains. From (5) and (8) and (9) follows

(10) The earth is moving along s2

Since nothing can move in two directions at once, (2) and (10) are incompatible. Therefore (2) is false and the earth must stay where it is.

This argument reveals an awareness of certain central features of our notion of explanation, Barnes (ibid.) writes. Of course, the argument is not sound; premise (1) is based on Anaximander’s astronomy of ‘similarity’ and is easily falsified. Philosophically, though, the Principle of Sufficient Reason can be attacked both by questioning premise (3) and premise (9). Premise (9) can be countered by claiming that certain features should simply have an effect on some occasions and not on others. Premise (3) can be countered by chance effects. Another objection is employed by Aristotle in De caelo 295b30-33. He creates an analogy to the Principle by saying that if a hair is pulled on in both ends, when each pull is of exactly the same strength, according to the Principle the hair will not break no matter how hard the pull is. A similar objection to this Principle is what is the paradox known as

‘Buridans ass’, recreating the picture with an ass and two identical portions of hay.

Subsequently the ass would starve to death for it inability to choose between the portions. It should prove the Principle wrong, then, that a real ass would not starve to death in a similar situation. The animal would simply choose one of the portions, either for no explainable reason, which would make (3) false, or the choice is explained by the chosen portion having a feature that the other portion also has, thus making (9) false.

Barnes concludes that objections to (3) and (9) are not conclusive against

Anaximander, “for these are presuppositions of any scientific astronomy; if (3) or (9) collapse then the goal of astronomy itself is unattainable, and we cannot find universal laws

explanatory of the celestial phenomena” (1979:26). Even though we cannot a priori prove (3) or (9), we should not abandon them, Barnes says, because to abandon them is to abandon the ideals of science.

It seems, then, as if Anaximander through implications invented the generalization of

sufficient cause. But is this ingenious type of reasoning really Anaximander’s? It is Aristotle that presents this claim and the reasoning behind it. That context, then, might suggest that the reasoning is Aristotle’s own. However, Aristotle, as we have seen above (De caelo II.13, 295b30-33), argues against Anaximander and the use of this principle as such; earth must be where it is because that is earth’s ‘natural place’, Aristotle says. This at least indicates that the reasoning is indeed Anaximander’s own.

There is one more invaluable piece of information from Aristotle in this context; right before he presents his objection, he says:

“There are some who name it ‘indifference’ as the cause of its [the earth] remaining at rest, e.g. among the early philosophers Anaximander. These urge that that which is situated at the centre and is

equably related to the extremes has no impulse to move in one direction (…) This argument is ingenious, but not true: for according to it, whatever is placed at the centre must remain there, even fire; the property is not particular to earth.” (Aristotle De caelo II.13, 295b10-20, my emphasis)

What Aristotle here asserts is that according to Anaximander anything situated at the centre of the extremes will not move, and adds even that this property is not one particular to earth.

This must be viewed as a clear indication of generality of explanation, and, hence, the generality of sufficient cause.

Hankinson (1998:15) reminds us that Anaximander presumably did not formulate the Principle of Sufficient Reason with any such generality that Leibniz did. However the use of something very closely resembling the Principle means that there is a reason or cause for everything that occurs and that these reasons must in principle be explicable. Further, Hankinson claims, Anaximander’s disqualification of the problem with the earth’s stability means that explanations must be general. Furthermore, explanations should at least aspire to completeness, if there is a genuine class of things of a certain type, then their individual type-ness must be susceptible of a unified explanation (ibid.). Thus explanations would be, ideally, both necessary and sufficient for what they explain. Thus it promises a fully intelligible world. Hankinson writes (ibid.): “But ultimately its truth must be an empirical matter: there is nothing logically impossible about causal indeterminacy, and in an indeterministic world the Principle of Sufficient Reason fails to hold, at least in full generality. But even so, to the extent to which they are explicable, the workings of the universe must conform to the Principle of Sufficient Reason”.

From this I hold that Anaximander indeed postulated that in the deterministic mechanistic world of strict physical causes, causation is universal.