As you know Gale_ Pruss improved The cosmological argument using WPSR instead of Strong PSR. They in their 1999 article said if it be possibly that there be a God who freely created the world using S5 modal system there be such God. http://alexanderpruss.com/papers/NewCosmo.html they proved this possibly using the notion of possible worlds and BCCF of the actual world And the W_principle of sufficient Reason. My question is if By S5 any possibly necessary being is necessary Why we do not simply say there is possible to existence of a necessary God so he is actual ? Why we need at all to use WPSR and BCCF of the actual world?

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    – J D
    Commented Mar 11, 2020 at 15:57

1 Answer 1


Welcome! There's nothing wrong with what you are saying, but they are two different arguments with a different set of premises. Gale and Pruss present a cosmological argument for the existence of God, and your suggestion is more of an ontological argument.

Consider the following:

  1. Possibly necessarily X exists. (Assumption)
  2. If possibly necessarily X exists, then necessarily X exists. (S5, substituting in premise 1)
  3. Therefore, necessarily X exists.

If we substitute "an omnipotent, omniscient, omnibenevolent being" for X, then we have the skeleton of an ontological argument for God's existence. But what if I reject (or am uncertain about) the premise that "possibly necessarily an omnipotent, omniscient, omnibenevolent being exists"? You could try to convince me (by way of some other arguments) that I should believe in the possibility of the necessity of such a being (see Godel's or Plantinga's ontological argument). That's one approach. But Gale and Pruss present a cosmological argument that doesn't depend on that premise as an assumption (even though it may perhaps be a consequence of their other assumptions).

A skeleton cosmological argument goes something like this:

  1. Every fact has an explanation. (PSR)
  2. The conjunction of all contingent facts is a fact.
  3. Therefore, the conjunction of contingent facts has an explanation.
  4. If the conjunction of all contingent facts has an explanation, then that explanation involves a necessary being.
  5. Therefore, there is a necessary being.

Then, cosmological arguments typically continue on to flesh out some of the attributes of this necessary being.

Nowhere in this argument did we need to explicitly assume S5 or that a necessary being is possible. The novelty of the argument from the WPSR is that it weakens premise 1. Gale and Pruss show that we only need to assume that it's possible that every fact has an explanation (even though the fact may be a brute fact, in our world). Then, they show how the WPSR entails PSR in the first 7 steps of their argument. Again, they did not assume S5 or that possibly God exists in their derivation of PSR from WPSR.

  • thank to your answer.
    – MHghasemi
    Commented Mar 11, 2020 at 0:05
  • thank to your answer. In fact I read the Stanford plato cosmological argument about Gale Pruss WPSR whera claims S5 is one of their premises! You can see it and tell me your idea. In fact the author of plato have had such a gread odd mistake? they said:
    – MHghasemi
    Commented Mar 11, 2020 at 0:44
  • They phrase the argument in terms of contingent and necessary propositions. A contingent proposition is one that is both possibly true and possibly false (i.e., true in some worlds and false in others); a necessarily true proposition is true in every possible world. In its simplest form, the argument is (1) if it is possible that it is necessary that a supernatural being of some sort exists, then it is necessary that a supernatural being of that sort exists. Since (2) it is possible that it is necessary that a supernatural being of some sort exists, (3) it is necessary that this being.
    – MHghasemi
    Commented Mar 11, 2020 at 0:50
  • If one grants modal Axiom S5 (if it is possible that it is necessary that pp, then it is necessary that pp), the critical premise in the argument is the second, and Gale and Pruss proceed to defend it using their weak PSR.
    – MHghasemi
    Commented Mar 11, 2020 at 0:50
  • @MHghasemi Yes, the SEP article does seem to say that... I believe the author of the Stanford Encyclopedia article is simplifying the argument by presenting a different form using S5. In Gale and Pruss's paper, they do not (as far as I can see) make this assumption. However, my answer can be rewritten removing the parts about S5: the ontological argument still makes the assumption that it's possible that a necessary being exists, which the cosmological argument does not. S5 does not by itself show that there is a necessary being (every being in every possible world might still be contingent) Commented Mar 11, 2020 at 1:03

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