0. Introduction
Contingent beings might be defined as things which do not contain within themselves. The complete reason of their existence, which is to say that they are things which might not exist. In contrast, a necessary being would be one which contains with itself the reason of its existence. Something which must exist and cannot not-exist, i.e. a being whose non-existence is impossible. Which is to say, a metaphysically necessary being is one who exists with the strongest kind of necessity, in every possible world, one whose nonexistence is impossible, whose essence entails existence (or in Thomistic language, one whose essence just is existence). God has traditionally been defined as a necessary being. Contingency arguments seek to prove the existence of at least one necessary being from the fact that there are contingent beings. Since the time of Aristotle, this has been a popular method of arguing for the existence of God. I will summarize a few arguments against the existence of a necessary being.
1. Hume and Conceivability
Hume presented an argument against the existence of a necessary being from the conceivability and inconceivability theses. Hume explained these theses in the following manner:
“Tis an established maxim in metaphysics, that whatever the mind clearly conceives includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible. We can form the idea of a golden mountain, and thence conclude that such a mountain may actually exist. We can form no idea of a mountain without a valley, and therefore regard it as impossible.” — David Hume, A Treatise of Human Nature (London: Oxford University Press, 1965, ed. L.A. Selby-Bigge), p. 32
The theses are commonly used in metaphysics even to this day and thereby remain “established” by their use. Much of our work in metaphysics would seem quite hopeless if conceivability is not a guide to metaphysical possibility and impossibility. The conceivability thesis states that if some state of affairs S is clearly conceivable, then it is not “absolutely impossible,” which is to say that it is metaphysically possible. We may clearly conceive of a gold mountain. The inconceivability thesis states that if some state of affairs S is inconceivable, then it is metaphysically impossible. As Hume states, we cannot conceive of a mountain without a valley, either in a mental picture or conceptually, because mountains by their very definition have valleys otherwise they would not be mountains. For a modern discussion of these theses see Paul Tidman’s Conceivability as a test for possibility (American Philosophical Quarterly 31. no. 4, 1994), p. 297-309.
Hume, in his Dialogues Concerning Natural Religion makes an argument against the existence of God from these theses which he considered a conclusive refutation of traditional monotheism. The argument might be summarized this way:
1. Anything we can conceive of as existing we can conceive of as not existing. (Premise)
2. We can conceive of God existing. (Premise)
3. Hence, we can conceive of God not existing. (From 1, 2)
4. Whatever we can conceive of not existing, does not necessarily exist. (Premise)
C. Therefore, God does not necessarily exist. (From 3, 4)
I think that Hume, quite correctly, regards arguments of this sort as clear refutations of the concept of a metaphysically necessary being:
“I shall begin with observing, that there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable [in this way], unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable. I propose this argument as entirely decisive, and am willing to rest the whole controversy upon it… The words, therefore, necessary existence, have no meaning; or, which is the same thing, none that is consistent.” (Ibid, Part 9 Section 5, 6.)
This kind of objection is not new, and has been levied by plenty of metaphysicians, I would not know who the first is. I recall Bertrand Russell said something like, ‘for Leibniz, every proposition seems to be analytical.’
2. Inwagen, the PSR and God
I have altered and edited Inwagen's argument against the Principle of Sufficient Reason (PSR) into an argument purporting to show an incompatibility between existence of a necessary being such as God and the PSR.
1. No necessary proposition explains a contingent proposition. (Premise)
2. If the PSR is true, then all true contingent propositions have an explanation. (Premise)
3. If a proposition explains a conjunction it explains every conjunct. (Premise)
4. Some proposition x only explains a proposition y if x is true. (Premise)
5. Suppose the PSR is true and God exists. (Assumed for reductio ad absurdum)
6. There is a Big Conjunctive Contingent Fact (BCCF), that is the conjunction of all true contingent propositions. (Premise)
7. The BCCF has an explanation. (From 2 and 6)
8. If God exists, then God exists necessarily and explains the BCCF. (Premise)
9. God exists necessarily and explains the BCCF. (From 5 and 8)
10. If God exists necessarily and explains the BCCF, then the BCCF is necessary. (Premise)
11. The BCCF is necessary. (From 1, 9 and 10)
12. The explanation of the BCCF is contingent. (From 1 and 7)
13. If the explanation of the BCCF is contingent, then the BCCF is contingent. (Premise)
14. The BCCF is contingent. (From 12 and 13)
15. Thus, the explanation of the BCCF is necessary and contingent (From 9 and 12) and the BCCF is necessary and contingent (From 11 and 14)—and that is contradictory.
C. Hence, it is false that God exists and that the PSR is also true.
To illustrate P1, if some proposition x is necessary, then it is the case in every possible world, and if x explains some proposition y in some possible world, then it explains y in every possible world, hence x and y would both be necessary.
The BCCF is contingent by definition, as it is the conjunction of all contingent facts. It is the Big Conjunctive Contingent Fact. Typically, the move by the modern theologian here is to weaken the PSR, and deny premise 2, and along with it a host of contingency arguments. The other move is to embrace a sort of necessitarianism. For these and other possible solutions see Alexander R. Pruss’ The Principle of Sufficient Reason: A Reassessment published in 2006 by Cambridge University Press, 2006.
3. Swinburne’s Argument
Richard Swinburne is an Eastern Orthodox theologian who does not believe that God is metaphysically necessary. While he would say that God exists, he does not believe that God exists in every possible world. He presents an argument for this conclusion in his article What Kind of Necessary Being Could God Be? published in 2012 by the European Journal for Philosophy of Religion 4 (2):1:18. The basic idea is this, a necessary being is one whose nonexistence is impossible. Therefore the proposition God exists, would be an analytical proposition which is to say that it must be true and could not possibly be false. Conversely, the proposition God does not exist, would be necessarily false. We can only analyze the meanings of these propositions by studying the sentences that express them. But there is no contradiction in the sentence “God does not exist” or any equivalent sentence. Which is to say there could not possibly be a necessary being of that sort. There might exist a God with a weaker kind of necessity, but there could not be a God, which is metaphysically necessary in the traditional sense of that term.