Traditional cosmological arguments typically include a premise about what things have causes or explanations. Modal cosmological arguments rely instead on a premise about what things could have causes or explanations. The aim of Pruss and Rasmussen's fifth chapter is to uncover the weakest/safest/most modest principle about possible causes that can be used to construct a valid modal cosmological argument. They arrive at the following (I retain their numbering):
As Pruss and Rasmussen note, the "normally" in The W Principle makes the inference to (14) defeasible. Otherwise, the argument is clearly valid. Further, (15) follows from S5 together with the non-circularity condition just described. The remaining premises, however, are open to question.
As usual, the authors motivate each premise, then consider a series of objections. It seems to me, however, that they do not consider the most important objection. The property C they have identified is a modal property, and this makes it unlike the examples that motivate The W Principle. Hence, it seems to me, an opponent could either say that The W Principle should not apply to modal properties (rejecting 8), or that modal properties are not basic properties or determinates of basic properties (rejecting 12). The authors offer no defense of (12) beyond the observation that existing contingently is "a determinate of the basic property of existence" (p. 102). This seems like cheating: arguably everything is a determinate of existence (possessing any property is a way of existing). In a footnote, the authors say that if you don't think existence is a property, you might think the property contingent existence is itself basic. Maybe. But actually this doesn't seem like a very plausible line for Pruss himself to take, since he endorses a powers theory of modality, so on his view an object exists contingently if, at some earlier time, there was a substance that had the power to initiate a causal chain whereby that object would not end up existing (or some such). That's an extrinsic property, and extrinsic properties are typically not thought to be basic. The same is going to be true if you construct modal properties out of possible worlds: contingency won't be a basic property of the object, since the predicate 'contingent' will apply in virtue of the object's non-existence in some other possible worlds, not in virtue of how the object is in the actual world.
In other words, my suggestion is that the opponent could either endorse a causal principle restricted to intrinsic categorical properties (or maybe intrinsic categorical properties plus primitive powers/dispositions, but not modal properties more broadly), or else hold that all basic properties are intrinsic categorical properties (plus primitive powers/dispositions). Perhaps there is some more complicated replacement for C that will still make the argument work if the opponent makes this move, but I don't know what it would be.
While the authors do not consider this among the objections in this chapter, it is closely related to the first weakness of the argument that they identify in their concluding assessment (p. 108): that the property C might be thought to be somehow special in a way that makes it not causable. The underlying issue here is that even if just any open formula specifies a property, it must not be the case that just any open formula specifies a basic property, else The W Principle wouldn't be any weaker than the principle employed in the previous chapter. So the issue of what properties are basic needs considerably more attention if we are to have any confidence that C is a basic property or a determinate of a basic property.
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