Authored by: Mitchell LeBlanc.

Richard M. Gale, an agnostic philosopher of religion has formulated an argument which combines the three main types of arguments for God. In this article I will introduce his argument.

The Argument

(1) If it is possible that it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe), then it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

(2) It is possible that it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

(3) It is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

Axiom S5

Premise (1) is an instantiation of the Axiom S5 of the S5 modal logic. It states both:

(A) If possibly p, then necessarily possibly p

(B) If possibly necessarily p, then necessarily p

To understand these axioms, it is first important to understand six different types of modal status. Modal logic is our logic of possibility (among other things), it allows us to discern which propositions are true, false, necessary, possible,   contingent or impossible. Possible worlds are a tool which we use to assist in understanding these three types of modal status. A possible world can be thought of as a set of compossible propositions or in a simpler manner, a way in which reality might have been. Now, it is not important to discuss whether or not possible worlds are real in the sense of actually existing things. While this is the view of the modal realists, we can simply think of possible worlds as abstracta, propositions or even conceptions.

Propositions under modal logic are classified into the six aforementioned classifications (the term ‘obtains’ means ‘achieves trueness’):

A proposition is true if it obtains in the actual world (for example: Obama is the first black president of the United States)

A proposition is false if it fails to obtain in the actual world (for example: Obama is the first white president of the United States)

A proposition is necessary (or necessarily true) if it obtains in all possible worlds (for example: All bachelors are unmarried)

A proposition is possible if it obtains in at least one possible world (for example: There are no human beings)

A proposition is contingent if it obtains in some possible worlds and fails to obtain in others

A proposition is impossible (or necessarily false) if it fails to obtain in all possible worlds (for example: 2+2=5)

So what the Axiom S5 reveals to us is the following:

(A*) If there is some proposition that is possible, then it is necessarily possible

(B*) If there is some proposition that is possibly necessary, then it is necessary

To understand further: (A*) states that if some proposition is possible, that is, it obtains in at least one possible world then it must obtain in at least one possible world. This follows from the definition of possible, such that if a proposition p is possible, it is true in every possible world that p is possible.

Additionally, (B*) shows us that if there is some possible world where the proposition p is necessary, then it follows that p is necessary (and obtains in all possible worlds). That is, consider there is some possible world w1 in which the proposition ‘Banana’s are yellow’ is necessarily true. So, in w1 the proposition ‘Banana’s are yellow’ is true necessarily – the proposition will obtain in all possible worlds. Since in w1 the proposition is necessarily true, it must be true in all possible worlds (otherwise it wouldn’t be necessarily true). Again, we see that this is true by definition.

Now that we understand the Axiom S5, let us re-examine the argument.

The Argument (again)

(1) If it is possible that it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe), then it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

(2) It is possible that it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

(3) It is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

As we can see, premise (1) is merely a form of the conditional found in (B) and so if (2) is true (3) follows and the argument is sound.

Conclusion

A defense of (2) will cause this article to become far too technical for its intended purposes. I will simply direct anyone interested in a defense of (2) to Gale’s paper entitled “A New Argument for the Existence of God: One that Works, Well, Sort Of.”

If the argument is sound it establishes a necessary being that is creator of the universe. Of course, there are no established attributes beyond this so that being is not necessarily any particular religious version of God. In fact, it seems that the conclusion is wholly consistent with the creator of the universe being malevolent. Further argumentation is certainly required to establish further attributes of the proposed necessary being.