When we reason per impossibile we posit some impossible thing. However, we never reason from the impossibility. The reason we posit the impossibility is that it's useful for abstracting from particular details....
In this sense we can see reasoning per impossibile as a form of idealization -- indeed, idealization taken to an extreme. We are not committing ourselves to the impossible idealization's being the way things are; rather, we are idealizing in order simply to clarify some particular point or other about the non-idealized (and therefore possible) case.
I still think this is right. If we say, "If, per impossibile, I existed by nature, I would always exist," we are not interested in what follows from the impossibility; we're interested in what follows from existing by nature. However, much more can be said about this, in particular with regard to counterfactuals in general. It's obvious, in fact, that reasoning per impossibile is reasoning that uses a certain type of counterfactual. The basic idea behind such reasoning is, "Were this impossible thing possible, such-and-such would be the case." Given this, however, we should be able to handle the puzzling nature of reasoning per impossibile directly, by recognizing a peculiar feature of certain counterfactuals.
As I've pointed out before a lot of counterfactual statements are really disguised factual statements. Brian Ellis puts this type of position very nicely in the case of causal conditionals:
The truths relating to causal conditionals are the underlying ones on which their assertability depends. That I am thirsty, for example, is a fact about me. It is also a fact that I like beer, and that there is nothing in the world that I would like better at the moment. Consequently, I would say, "If there were a beer in front of me I should drink it." It simply does not matter whether it is really possible for there to be a beer in front of me. And if this makes it vacuous, then it does not matter whether it is vacuous. By asserting the conditional, I tell you graphically what my desires are at the present time, and what you could do to satisfy them. It is better than saying "I am thirsty," because you might then offer me water, which is not what I want most. It is better than saying "I am thirsty, and I like beer," because this is compatible with my not wanting a beer at the moment.
[Brian Ellis, Scientific Essentialism. Cambridge UP (New York: 2001) 282.]
A mistake we often make is to assume that factual statements are always easier to deal with than counterfactual ones, as if they were more straightforward. But given how pervasive counterfactual thinking is, it seems plausible to say that this is not always the case. Sometimes it's easier to think through a matter counterfactually than to think it through factually, because thinking counterfactually allows you to highlight features directly that could only be highlighted factually in very complicated ways. This fits with some thoughts in cognitive research on the ways counterfactuals works; but in any case it seems a safe supposition to make until and unless we find clear evidence to the contrary.
It's clear that per impossibile counterfactuals would have to be this kind of counterfactual, because the counterfactual situation used is itself impossible. Take reasoning based on the following fictional epitaph from George MacDonald's David Elginbrod:
Here lies Martin Elginbrod.
Have mercy on my soul, Lord God,
as I would do, were I Lord God,
and you were Martin Elginbrod.
Now, however you slice the counterfactual situation -- that Martin Elginbrod and God were in each other's place -- it is impossible, particularly in the Scottish Christian context the epitaph assumes. It is not logically possible, it is not metaphysically possible, it is not physically possible, it is not epistemically possible. And yet we can make sense of it immediately, and take Martin's point without any trouble. We don't have to think through the impossible situation in order to see where Martin is going with this. The reason is that it's clearly not about a situation in which Martin and God are switched; it's about the actual situation, in which Martin is dead and needs mercy, and God can give it. If we were to try to be put "If Martin were God he'd be merciful to God, were God Martin" entirely into factual statements, we would have some difficulty because getting it right would be a bit complicated -- we'd have to go through facts about Martin's sense of mercy, how it works, etc., and we'd still fall short of the perlocutionary force of the statement, the petition for mercy. The per impossibile inference cuts through that to reach the point at once. And this, far from being unusual, is fairly typical of counterfactual reasoning generally.