I am not entirely convinced of the arguments below. But they are fun.
Say that p is explanatorily prior to q provided that p contributes to some explanation of q. I shall assume that explanatory priority only holds between true propositions. Let us suppose that:
- No contingent proposition is explanatorily prior to itself.
Now, let us posit two plausible formal principles for explanatory priority:
- If p is prior to q, and r is prior to s, then p&q is prior to q&s.
- If p and q are conjunctions, and differ only in the order of the conjuncts, and p is prior to r, then q is prior to r.
Now suppose that a backwards infinite regress of contingently true propositions is possible:
- ... p−3 prior to p−2, p−1 prior to p0.
- ..., p−3 prior to p−2, p−1 prior to p0, p0 prior to p1, p1 prior to p2, p2 prior to p3, ....
- If A and B are two sets of propositions, with a one-to-one correspondence c between the members of A and those of B, such that c(a) is prior to a for every member a of A, and if p is the conjunction of all the members of A, and q is the conjunction of all the members of B, then q is prior to p.
The weakness of this argument is that (6) seems less plausible than the finite version (2).
An argument against (2) (and hence also against (6)) is that (2) implies that p can be prior to q even though p and q have a conjunct in common. (Suppose p is prior to q and q is prior to r; then p&q is prior to q&r.) And that might be implausible.