In Part IX of Hume's Dialogues Concerning Natural Religion, we can extract a series of criticisms of the cosmological argument. First, Hume's character Cleanthes argues that an apriori argument for the existence of anything is impossible. This objection is not directly relevant to aposteriori versions of the cosmological argument, which is the only kind we have studied. Nonetheless, Hume's argument can be transformed into an argument that necessary existence is impossible.
Nominalists hold that there is no such thing as natures or essences. There is no such thing as humanity, only individual humans and the name or concept of "human". Since things have no real natures, there is nothing in things that can make certain conditions possible or impossible. Instead, possibility and impossibility are simply by-products of our use of language and concepts. An impossible condition is one that would correspond to an inconsistent or incoherent mental picture.
In contrast, realists like Plato, Aristotle or Aquinas, hold that there are real natures in things. Our use of words like "human" is grounded by the shared nature of humanity. Our concepts are linked causally to these real natures. Conceivability and possibility are not the same thing: some things that are conceivable are not really possible, and some things are possible of which we have no positive conception.
Hume was well aware of this alternative, Realist tradition. He attempts, therefore, to force a dilemma upon the theist. If the theist rejects Hume's identification of possibility with conceivability, then, Hume argues, the theist has no basis for arguing that the physical world is only contingent. The theist argues that, since we can conceive of the non-existence of physical things, this means that their non-existence is really possible. This is exactly the sort of connection between possibility and conceivability that Hume used in Cleanthes' original argument.
However, Hume's dilemma is a false one. In effect, Hume asks the theist to choose either option 1, in which possibility is identified with conceivability, or option 2, in which possibility and conceivability are independent. There is a third alternative. The theist could insist that possibility cannot be simply identified with conceivability, but still claim that conceivability and inconceivability are reliable but fallible guides to possibility and impossibility. The fact that we can conceive the non-existence of matter gives us good (but rebuttable) grounds for believing that that the non-existence of matter is possible.
What, then, happens to Cleanthes' original argument? Can't Hume argue that the conceivability of God's non-existence gives us good grounds for believing that God's non-existence is possible? To be consistent, the theist must admit that it does. In the end, the theist is forced to reconsider the other premises of Cleanthes' argument. If the theist challenges the second premise, then the theist must argue that there is some special feature of our conception of God that makes his non-existence inconceivable. This commits the theist to the key premise of the so-called ontological argument. If the non-existence of God is really inconceivable, then we don't need the cosmological argument to establish God's existence.
A defender of the cosmological argument should instead challenge the first premise: that we can conceive of God's existence. As we have seen, defenders of this tradition, like alFarabi and Aquinas do in fact emphasize the incomprehensibility of God.
As we have seen, the theist must accept that there is a connection of some kind between conceivability and possibility. Similarly, it seems that there is some such connection between inconceivability and impossibility. We are confident that, since a four-sided triangle is inconceivable, it is also impossible. Thus, the theist faces a problem if she admits that God's existence is inconceivable. This would seem to provide us with a reason for thinking that God's existence is impossible. In Part IX, Cleanthes presses this objection, urging that the words "necessary existence" have no meaning, or at least, none that is consistent.
However, we need to examine the ideas of incomprehensibility and inconceivability more fully. There are several ways in which an idea or proposition can be inconceivable: (1) it may involve a logical inconsistency, or be in some other way repugnant to reason, (2) it may involve one or more terms that are devoid of meaning, or (3) it may fall under neither of these two categories, and yet be in some sense incomprehensible. An incomprehensible proposition would be one that is logically consistent, and composed only of meaningful elements. Its incomprehensibility would consist in one or more of the following features.
The Humean has at least one more plausible response. Hume might argue that, since we cannot know that God's existence is possible, we certainly cannot know that God exists in actuality. Here is a plausible argument:
If God's existence is incomprehensible, then, unless we know that God's existence is actual, then we cannot know that it is even possible.
There are two ways to learn that something is possible. One way is to form a clear conception of the possibility. The second way is to discover that the thing is an actual fact. For example, I know that it is possible for bumblebees to fly because I have observed them actually flying. I can know that bumblebees actually fly without first having proved to myself, independently, that it is really possible for them to fly (which is, I understand, a tricky problem in aerodynamics).
There are two additional lines of argument against Hume's critique in Part IX of the Dialogues that I would like to consider. First, we need to consider more carefully the relationship between possibility and conceivability. When we conceive of a positive, particular situation, our conception provides good grounds for thinking that the situation is possible. For example, I can conceive of an octagonal medallion composed entirely of platinum. I have never seen or heard of such a medallion, but my clear conception of the idea provides good (although not infallible) grounds for believing it to be impossible.
Our ability to conceive of negative or infinite situations is much more problematic, and apparent successes in such conceptions provide much weaker reason to believe in the possibility of the corresponding situation. For instance, it seems to me that I can imagine a 3-D object with a front surface but no back surface. However, this apparent "conception" provides little reason to think that such a thing is possible. Similarly, in Hume's Treatise (Book I, Part III, Section III), Hume claims that he can imagine a contingent fact occurring without a cause. Such a purely negative "conception" (conceiving of an A without conceiving of a related B) provides little or no grounds for believing in the real possibility of the corresponding situation (an A really existing without a related B). Consequently, when Hume argues that we can conceive of God's non-existence, this conception seems to have little evidentiary value.
The second line of argument involves pointing out that the theist does not have to rely on any conceivability/possibility connection, if the theist focusses (as I do) on all contingent facts, and not only on facts of contingent existence. We know that physical facts are contingent, not just because we can imagine them being other than we are, but by the fact that we observe them actually changing. The reality of change provides a direct proof of the contingency of physical facts -- we do not have to rely on conceivability. Thus, we have good grounds for believing that the First Cause is non-physical.