(I have talked about this to some of you, but I thought it would be a good idea to get it out in writing).
The following is Alexander Pruss’ (2006) reconstruction of Peter van Inwagen’s (1983) argument against the Principle of Sufficient Reason (PSR). (Roughly the principle of sufficient reason says that anything that is the case has a sufficient explanation for why it is the case. Pruss and others have restricted the principle to exclude necessary truths, so that only contingent truths are the kinds of things that need a sufficient explanation).
(1) If the PSR holds, then every true contingent proposition has an explanation.
(2) No necessary proposition explains a contingent proposition.
(3) No contingent proposition explains itself.
(4) If a proposition explains a conjunction, then it explains every conjunct.
(5) A proposition q explains a proposition p only if q is true.
(6) There is a Big Conjunctive Contingent Fact (BCCF) that is the conjunction of all true contingent propositions, perhaps with logical redundancies removed, and the BCCF is contingent.
(7) Assume PSR for reductio.
(8) So, the BCCF has an explanation, q. (1, 6, 7)
(9) So, the proposition q is not necessary. (2, 6, 8)
(10) So, q is a contingent true proposition. (5, 8, 9)
(11) So, q is a conjunct in the BCCF (6, 10)
(12) So, q is self explanatory. (4, 8, 11)
(13) But q is not self explanatiory. (3, 10)
(14) Therefore, PSR is false (7, 12, 13)
Pruss argues that we have good reason to reject (2) and (3). Spinoza denied (6), since he thought that there were no contingent facts at all (and therefore no conjunction of them). The rest of the premises seem plausible.
My objection is as follows: (1)-(14) is formally invalid.
It is hard to point out whether the fallacious inference is (9) or (10). Here is why:
(1) claims that every contingently true proposition has an explanation. The inference to (10) (and plausibly to (9) as well) assumes that the explanation of a contingently true proposition must itself be a proposition. In order to amend this, and make the argument valid, we should rewrite (1) as follows:
(1*) If the PSR holds, then every true contingent proposition has an explanation that is itself a proposition.
With (1*), the argument above is valid. But it is not clear to me that we should accept (1*). Consider the following account of explanation of conjunctive facts:
(A) The explanation of a conjunctive fact is the plurality of its conjuncts.
(A) contradicts (1*), since a plurality of conjuncts is not itself a proposition. But I take (A) to be fairly plausible. If we are looking for the explanation of a proposition of the form p & q, and we give an explanation of p, and an explanation of q, it does not look like there is anything left to explain.