(p1) 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. (Axiom S5 of Modal Logic)
(p2) It is possible that it is necessary that some sort of supernatural being exists.
(C) Therefore, it is necessary that this being exists.
(p1) Modal logic deals in possible worlds; something is necessary if it obtains in every possible world, and something is contingent if it could be either true or false. For example, there is no possible world where 2+2 is not equal to 4 – that statement is necessarily true. On the other hand, if I say to someone, “my Toyota Camry is black,” it is logically possible that my Camry could have been a different color. Or even that I do not own a Camry at all (which happens to be the case!).
So let’s cash this out in terms of a possible worlds landscape. Imagine some enormous excel spreadsheet where each square is a possible world, and in each square there are the necessary facts about that world as well as the contingent facts about that world. The premise begins with it being possible that a necessary being exists; from this we can say that one of these possible worlds has in its necessary facts the existence of a supernatural being. But necessary facts cannot be otherwise – they are true in every possible world; therefore, because we know that at least one possible world has this necessary fact, we know that all possible worlds, including our actual world, has this necessary fact. So if it is in fact possible that a necessary being exists then that being exists. Hopefully that makes it feel intuitive – if not, read it a few more times :P.
(p2) is where the battle begins since, as this is a valid argument, the truth of both premises guarantees the truth of the conclusion and most people are okay with (p1). So now what has to be argued for is that it is indeed possible that a being of this sort exists. Before we get going it might help to glance through an earlier post of mine in which I talk about necessary and contingent propositions (this will help if the previous section is at all confusing) as well as the Principle of Sufficient Reason (PSR). The PSR, at least to me, is quite intuitive (whether this means I should accept it is a story for another day) – for every contingent fact there is an explanation for that fact; if something could have been either X or Y there is a reason that it is X.
Now the PSR that I just put out is a strong version and is the recipient of much criticism. Gale and Pruss, however, decide to use a weak version of the PSR (when arguing a case it is advised to use the most conservative premises that are sufficient for your conclusion). So rather than saying that there is an explanation for every contingent fact, they say that it is possible that there is an explanation for any particular contingent fact. This is a lot less controversial – we are saying that if something could have been either X or Y, and it is X, it is possible that there is an explanation for that fact. Most everyone should be more comfortable with this version, though it should be noted that the weak PSR does entail the strong PSR.
They move forward with this PSR and proceed to characterize possible worlds. Possible worlds, as we saw above, all have the same necessary facts. This means that the difference between any possible world is their contingent facts, and we can call the totality of their contingent facts the Big Conjunctive Contingent Fact (BCCF). What this means is that it is possible that there is an explanation for the BCCF – so what would the nature of this explanation be? This is the crucial step.
We can first of all say that the explanation cannot be contingent – if it were contingent then it could be itself part of the BCCF, and as such it would not be able to explain the BCCF. So we know that this explanation is necessary. In addition to this we can know that the explanation cannot be scientific – a scientific explanation would necessarily talk about contingent facts, and therefore would not be the necessary explanation we need. From here it is reasoned that the explanation has to be intentional, that is, because we do not have access, in principle, to a scientific explanation we are left with the intentional action of some agent (I need to learn more about this move). Think of it this way: George walks over to the water cooler and has a drink of water. We could explain this action scientifically by talking about the various physical actions and laws involved in his journey, but the other way we would explain it is by talking about George as an agent; George was thirsty and desired to quench his thirst so he went an got a drink of water. Since we do not have the scientific option in this case we are left with the agent based explanation. And there you have it – the explanation would be the intentional act of a necessary being and, remembering the PSR, it is possible that there is such an explanation (that a necessary supernatural being of some sort exists). Combined with (p1) we conclude that this necessary being does in fact exist.
I am currently in the process of learning about its criticisms, and I will eventually write up that post as a foll0w-up, but I think this has more immediate appeal than other cosmological arguments (I feel somewhat similarly about Aquinas, once you understand the metaphysics (enough!)).
Also, putting all the atheism tags on this post sort of betrays me as a minor troll.