Tuesday, April 14, 2009

A New Modal Cosmological Argument

I've been thinking a lot lately of the recent modal versions of the cosmological argument. Peter van Inwagen has developed an intriguing objection to the principle of sufficient reason (PSR). What he states is that, "If X is the set of all contingent states of affairs, then X cannot be explained by something necessary. For, what is necessary will necessarily entail its explicandum, which means that X is actually necessary. This is a contradiction; therefore, the PSR is false."

Pruss and others have responded to van Inwagen's argument, but I'd like to assume for the sake of argument that he is correct. Can a sound modal cosmological argument (MCA) still be developed? Specifically, I'm referring to a possible MCA other than the already existing ones (i.e. the W-PSR, R-PSR, etc.). Here's my attempt to do so:

1. It is possible that a necessary being explains the contingent universe.
2. If something is possibly necessary, then it exists in all possible worlds.
3. Whatever exists in all possible worlds exists in the real world.
4. Therefore, a necessary being exists in the real world.

This argument avoids van Inwagen's objection, since we're no longer talking about states of affairs, but simply concrete "things" (re: "beings") in general. For example, then, there is a difference between what a thing is and what it does. It is possible that Jones is sitting under a tree, and it is also possible that Jones is not sitting under a tree. Regardless of which is true, Jones is still Jones. Applied specifically to the argument, therefore, a necessary being could exist without entailing some particular state of affairs. As Craig summarizes (emphasis in original):

"[The PSR] merely requires any existing thing to have an explanation of its existence, either in the necessity of its own nature or in some external cause. This premise is compatible with there being brute facts or states of affairs about the world. What it precludes is that there could exist things - substances exemplifying properties - which just exist inexplicably." [1]

Hence, I don't believe there is any contradiction in the notion of a necessary being. The other possible objection for the skeptic is to deny the S5 axiom on which (2) is dependent. The S5 axiom basically states that, "if p is possibly necessary, then p is necessary," or, "◊□p --> □p."

However, this axiom is fairly easy to defend. Its contrapositive is this: "~□p --> ~◊□p." In other words, if something is not necessary, then it's not possibly necessary. Davis puts it this way: "if p is not necessarily true, then it is not possible that p be necessarily true." [2]

Given the equivalence of "~□p --> ~◊□p" with "◊□p --> □p," and the obvious truth of the former, it follows logically and inescapably that the latter is also true. As a result, there is seemingly no tenable objection to the S5 axiom.

Now, since (3) follows from (2), and the real world is contained in the class of all possible worlds, it follows that (4) is correct and that a necessary being exists.

Works Cited

[1] William Lane Craig, "The Cosmological Argument," in The Rationality of Theism, edited by Paul Copan and Paul K. Moser, Routledge Press, 2003, p. 115.

[2] Stephen T. Davis, "The Ontological Argument," ibid., p. 107.

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