(Revised in light of Dr. Rizz's excellent comments)
It's commonly thought that a naturalist can't accept the Principle of
Sufficient Reason (PSR), on the grounds that (i) she thereby commits herself to the existence of a metaphysically necessary being, and that
(ii) this is incompatible with any plausible version of naturalism. I
have my doubts about (ii), but here I want to focus on (i). For it seems
to me that (i) is false. To be a tad more precise: there is a plausible
version of PSR, the acceptance of which doesn't thereby require one to admit a
metaphysically necessary being into one's ontology. William Lane Craig has recently defended a version of PSR as a component of his favored formulation of the Leibnizian cosmological argument. I will therefore use his treatment of PSR as a foil.
In several places, William Lane Craig has endorsed the following restricted version of PSR:
Every existing thing has an explanation for its existence, either in
terms of the necessity of its own nature or in terms of an external cause.
it seems to me that there is an ambiguity in Craig's notion of a thing having an explanation "in terms of the necessity of its own nature". As Craig
defines the notion in Reasonable Faith (p. 107 of the 3rd
edition) such a being is one that exists of its own nature, and thus has
no external cause. But this definition allows for at least two
epistemically possible sorts of beings that could play such a role:
metaphysically necessary beings and factually necessary beings. Metaphysically necessary beings are such that their inner natures cause them to exist in all possible worlds. By contrast, the necessity of factually necessary beings is world-indexed. Thus, a being must meet at least two conditions if they are factually necessary at a given possible world. First, their inner natures render them uncaused, beginningless, and existentially independent. And second, while there are possible worlds at which they fail to exist, they are de facto indestructible in the possible world at issue -- i.e., nothing else exists in that possible world that has what it takes to knock them out of existence.
It's important to note that both metaphysically necessary beings and factually necessary beings stand in contrast to beings whose existence is explained
in terms of an external cause. Furthermore, both sorts of beings stand in
contrast to brute facts -- i.e., beings whose existence have no explanation at all. Because of this, we should distinguish two versions of Craig's PSR to account for the distinct glosses:
The Metaphysical Necessity Version of PSR (PSRmn):
Every existing thing has an explanation of its existence, either in
terms of the metaphysical necessity of its own nature or in terms
of an external cause.
The Factual Necessity Version of PSR (PSRfn):
Every existing thing has an explanation of its existence, either in
terms of the factual necessity of its own nature or in terms of an
Given these distinctions, it seems to me that
one could accept a version of PSR -- viz., PSRfn -- even if one did not
accept the existence of metaphysically necessary beings. For it's
epistemically possible that all contingent dependent beings are
ultimately composed of factually necessary beings (i.e., contingent
independent beings). So, for example, perhaps matter-energy is a
factually necessary being. According to such a scenario, the contingent
dependent beings (e.g., rocks, trees, planets, you and I, etc.) come
into being when two or more factually necessary/contingent independent
beings are combined, and the contingent dependent beings cease to exist
when they decompose into their elements. However, the elements of which
contingent dependent beings are composed (i.e., the factually necessary
beings) can't pass away, for there is nothing around in the actual world that has what it takes to knock these uncaused, beginningless, existentially independent beings out of existence.
On this picture, then, we have an explanation for all contingent
dependent beings in terms of contingent independent beings. Furthermore,
we have an explanation of contingent independent beings in terms of the factual necessity of their own nature
-- i.e., in terms of their eternality, existential independence, and de
facto indestructibility. Is PSR violated in this scenario? It depends:
PSRmn is, but PSRfn is not. It therefore seems to me that a
naturalist can accept a version of PSR without thereby committing herself to
the existence of a metaphysically necessary being.
The point I argued for above, if at all on track, is significant in itself. However, I think there is promise for the naturalist to go further than this and to argue that PSRfn is to be preferred to PSRmn on theoretical grounds. Here's a sketch of how this might be argued. First, PSRfn appears to at least match PSRmn in terms of explanatory scope, as both versions provide an explanatory terminus for the existence of contingent dependent beings. Second, PSRfn is more theoretically conservative and qualitatively parsimonious than PSRmn with respect to the ontology
Finally, beyond its theoretical virtues as an explanatory principle with respect to actual phenomena, PSRfn arguably does a better job of explaining our modal
intuitions with respect to merely possible phenomena. So, for example, we seem to have little or no trouble imagining or conceiving of worlds in which God does not exist. We also have no trouble imagining or conceiving of contingent independent beings (i.e., factually necessary beings). So if conceivability is at least prima facie evidence of metaphysical possibility, then the existence of contingent independent beings, and the non-existence of God, are both prima facie metaphysically possible. But if either is possible, PSRmn is false. Neither possibility poses a problem for PSRfn, however.
In this way, then, one might plausibly argue that PSRfn has more going for it than PSRmn. But if it does, then PSR is not only consistent with naturalism; it's more at home in a naturalistic universe than in a theistic one.
 One might reply that PSRmn has wider explanatory scope, as it can also explain the existence of contingent independent
beings (i.e., factually necessary beings), if any such beings exist.
However, this is mistaken, as the latter sorts of beings are beginningless, uncaused, and existentially independent essentially.
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