There are two interesting posts at "Desert Landscapes" on an argument for God's nonexistence and on conceivability/possibility in Hume & Descartes. I have some minor things to say about both.
-->First, as to the argument about God's existence. The argument is something like this. The 'canonical explanandum' is not a single event or fact, but a contrastive phenomenon, i.e., the purpose of an explanation is not to explain why q is there so much as to explain why q is there rather than not-q. We can then assume that some such explanations are causal. Now, the argument goes, appeal to God is explanatorily impotent, because there is no possible state of affairs he is unable to bring about; for any q and not-q, God could as easily cause one as the other. Thus, for any q or not-q, citing God as an explanation is just as good an explanation for q as for not-q. Thus "God caused q rather than not-q" is never a good explanation.
I'm inclined to think that this tactic irremediably fails. It is not in doubt that q happened rather than not-q (or vice versa): in explanation we already know that one of the options is/was actual, because it is its being actual that we are trying to explain. Since God, by the admission of the argument, is able to bring about any possible state of affairs, He is able to bring about q (or not-q). Therefore he is a possible cause adequate to explain the effect, and, indeed, adequate to explain why q happened (rather than not-q). The fact that he is omnipotent is just an issue about the full range of possible states of affairs his causal capability could cover; except in the sense that any causal explanation must appeal to a cause capable of producing the effect being explained, it is not actually relevant to the question of explanation itself; the actual thing that explains is exercise of causal power. And having cleared away that God's causal power is capable of being exercised to cause q (rather than not-q), we have ipso facto conceded that God's causal power is capable of being an explanation of q (rather than not-q).
Now, the author does consider this issue, somewhat, in recognizing that the argument as stated doesn't cover the question of whether God would cause q (rather than not-q). So he suggests a patch to the argument: it is not the appeal to God that does the explanatory work in a first-cause argument, but the appeal to God's reasons, which can't exist unless God exists. Thus, "What we are still missing is an explanatory context in which God might be introduced into our ontology in the first place." He then says that sometimes he thinks this is a decent reply, and sometimes a lame one.
I think it limps. First, while the issue of whether God would cause q (rather than not-q) is of some importance, it really is not the chief issue. The chief issue is the causal argument to which this would have to be a counter: that the existence of q (rather than not-q) requires the existence of a cause capable of making there to be q (rather than not-q), and that certain such cases will require a cause that can reasonably be called 'divine'. This is all any sort of causal argument for the existence of God requires, and the proposed counterargument affects neither of these. Second, the basic appeal in causal explanation is to the actual disposition of a cause; now, some sorts of states of affairs might, for all the arguments tell us, require appeal to the sort of actual disposition that would be what some would call 'divine reasons' or 'divine intentions'. In this case the introduction of God as the cause with divine intentions would be very reasonable; and the proposed patch doesn't seem actually to present anything that would prevent this sort of move - i.e., it doesn't actually present anything that would lead us to believe that there could be no appeal to divine intentions. The patch is intended to show this; but it seems, as far as I can see, to simply assume it. So I think this basic strategy is a complete dead-end.
(It's worth noting, incidentally, that the proposed argument could only show that we have no causal reason to think that God exists; if there is some other sort of argument that went through which was not based on causal explanation, the argument wouldn't touch it. --> Also, see the parable below for clarification of my point about omnipotence above.)
--> The other post has to do with Descartes and Hume on the link between conceivability and possibility. This is an interesting issue, and I'm not sure how to phrase Hume's actual view. It would be something like this:
1. There are two sorts of perceptions, ideas and impressions.
2. Ideas (a.k.a. thoughts) are copies (and rearrangments of copies, and copies of copies, etc.) of impressions.
3. When we think of something as possible, we are thinking of it as having a unified idea, i.e., one without confusion or contradiction. This is just what it means for us to say something is possible - it's where we get the whole notion of possibility in the first place.
I don't see anything quite like this in the author's suggestions; Hume's linkage of the two is that we can't say things are possible of which we cannot coherently think, and what we mean when we say we know something is possible is that we can coherently think of it (in a sense of thinking that goes with (1) and (2) above). (Imaginability and conceivability, by the way, are synonyms for Hume; 'imagination' is just his word for the standard and natural operations of the mind.)
Update: I realized that there was some obscurity in my response re the divine cause thing. Here is a parable to clarify.
Two philosophers are on an island currently inhabited only by themselves, and not known to be previously inhabited. They come across some curious markings neither of them had seen before.
A: What curious markings! What could be their explanation?
B: I think they were made by human beings.
A: That's not an explanation.
B: I don't understand. Of course it's an explanation!
A: To be a causal explanation of p, you must explain why p rather than not-p. But your supposed explanation does not explain that.
B: But it does: that a human being made these markings explains why these markings are here, rather than not here.
A: Ah, but a human being is capable of also not making the markings. For instance, you will agree that a human being can make a statue instead of making markings.
B: Yes, but...
A: So it follows that appeal to a human being doesn't explain why there are markings here rather than something else, because a human being could make things other than markings.
B: But a human being is an intelligent cause, and an intelligent cause is the sort of thing that can be disposed or oriented so as to make markings. The existence of such an intelligent cause would explain these markings.
A: But then what is really doing the explanatory work is the disposition or orientation, the reasons why the intelligent cause would make those markings.
B: But what would that change?
A: Ah, it makes all the difference. Because for there to be such reasons we would have to presuppose that there is an intelligent cause that could have them. So, you see, my friend, your attempt to explain these markings by appeal to a human being is secretly an appeal to reasons. But we can't do that without assuming that there was already a human being on this island capable of making these markings. But what we are still missing is an explanatory context in which we might make the appeal to a human being in the first place....
(This parable could, of course, be modified, e.g., scifi it by placing it on a newly discovered planet and make it about whether the markings are signs of alien intelligence. It shows, I think, that there is something wrong with the argument; for appeal to a human being could be a quite reasonable explanation, and can't be ruled out merely because human beings can cause all sorts of things. So there doesn't seem to be any way God, as cause, could be ruled out as cause merely because He can cause all sorts of things - which seems to be the move the argument makes. Perhaps I'm missing something.)