Central to Plantinga's formulation of the FWD is the notion of "weak actualization". In the Profiles volume, Plantinga defines this as follows:
- God weakly actualizes S iff there is an S* such that God strongly actualizes S* and S* → S, where → is "counterfactual implication".
Theorem 1. If (1), and → is centered, then if God strongly actualizes any actual state of affairs, God weakly actualizes every actual state of affairs.
(Proof: Let S* be any actual state of affairs that God strongly actualizes. Let S be any actual state of affairs. Then, by centering S*→S, and so by (1), God weakly actualizes S.)
Theorem 1 is clearly problematic, as we can see by substituting "Al" for "God". Since Al strongly actualizes some state of affairs (say, the writing of The Nature of Necessity), it follows that he weakly actualizes the Battle of Waterloo.
In light of Theorem 1, we could simplify the concept of "weakly actualizes": God weakly actualizes S iff S is actual and there is an S* such that God strongly actualizes. But if that is what "weakly actualizes" comes down to, it is not a very interesting concept. It is a pretty trivial concept, and I think it does not seem to support the proof that Plantinga gives of Lewis's Lemma.
The crucial assumption in the above is that → is centered. Here are some reasons to think so. First, the Lewis/Stalnaker conditional is centered. But I've heard Plantinga be friendly to the idea that → fits into the Lewis/Stalnaker framework for an appropriate closeness relation. Second, one's reason for believing in conditionals of free will might be that one believes conditional excluded middle (p→q or p→~q for all p and q), but every conditional satisfying conditional excluded middle and modus ponens is centered (proof: suppose p and q; then p→q or p→~q by conditional excluded middle; if p→~q, then by modus ponens ~q, since p, but that contradicts q; so, p→q).
Moreover, even if centering does not hold in general, we get implausible conclusions. Consider, for instance, back-tracking conditionals, like: "Were Al not to have written The Nature of Necessity, the Battle of Waterloo would (still) have taken place." If that back-tracking conditional holds, surely so does: "Were Al to have written The Nature of Necessity, the Battle of Waterloo would have taken place", albeit it is awkward. (This awkwardness may simply be due to the awkwardness of "p→q", for the counterfactual conditional →, when p holds. However, Plantinga cannot complain about this awkwardness, because (1) defines weak actualization precisely in terms of a conditional whose antecedent is true.) But then if we extend weak actualization to Al, we get the conclusion that because Al strongly actualized The Nature of Necessity, he weakly actualized the Battle of Waterloo.