Descartes wrote many puzzling things about what is impossible, many of them connecting issues about what is impossible with issues about God’s power. For example,
I do not think we should ever say of anything that it cannot be brought about by God. For since every basis of truth and goodness depends on his omnipotence, I would not venture to say that God cannot make an uphill without a downhill, or that one and two should not be three. But I merely say that he has given me such a mind that I cannot conceive of an uphill without a downhill, or a sum of one and two which is not three, and that such things involve a contradiction in my conception. (Descartes, letter to Arnauld, CSMK: 358–9.)
On the basis of such dark sayings, it is tempting—and many have been tempted—to attribute to Descartes one or both of the following pair of theses:
(Voluntarism) Insofar as anything is impossible, that is because God has decreed that it be so.
(Libertinism) There is nothing that is impossible for God.
Amongst the problems facing this pair is that they seem to entail that nothing is impossible. Suppose that God has decreed that it is impossible that one and two not equal three. Still, nothing is impossible for God, so God could have decreed that one and two not equal three. So, it is possible that God decree that one and two not equal three. And, since such a decree would suffice to make possible that one and two not equal three, it is therefore possible that one and two not equal three. Not only does that seem to undermine God’s power to make it impossible that one and two not equal three; in addition, it seems to deliver a contradiction: it is both impossible (due to God’s actual decree) and possible (due to God’s possible decree) that one and two not make three. And of course the difficulties ramify. Doesn’t the question whether these are genuine entailments depend—since A entails B only if it is impossible that A is true and B is not true—on God’s decree? And doesn’t the question whether the outcome contradiction is problematic—that is, an impossibility—also depend on God’s decree?
Numerous attempts have been made to soften Descartes’ fall. Some restrict the range of impossibilities that he aims to treats, allowing that some genuine impossibilities are left standing in the face of God’s power over other merely seeming impossibilities. Others exploit the distinction between something being merely impossible and it being impossible that it not be impossible, and so forth, in order to block the slide from its being possible for God to make it possible that one and two not make three to its being possible that one and two not make three. I wish briefly to consider a nuanced version of the latter type of manoeuvre due to Jonathan Bennett.
Bennett’s account takes off from Descartes’ appeal, in the above quotation, to a connection between what we cannot conceive and what is impossible. His proposal has two main components:
(Conceptualism about impossibility) Insofar as anything is impossible, that is because it is inconceivable by us.
(Conceptual voluntarism) Insofar as anything is inconceivable by us, that is because God has decreed that it be so.
On this view, the reason that it is impossible that one and two not make three is that it is inconceivable by us that one and two not make three. That is, we are unable clearly to conceive of a circumstance in which one and two makes, e.g., four, or a cake. (Notice, but don’t dwell on, the appearance that the core notion of inconceivability is itself bound up with impossibility, the impossibility of our clearly conceiving something.) And the reason that it is inconceivable by us that one and two not make three is that God has decreed it.
Bennett’s proposal is deep and interesting, and seems to fit well much of what Descartes wrote. However, as Bennett notes, issues remain. Consider again the following, quoted above:
I would not venture to say that God cannot make…that one and two should not be three.
Why not? Assume the following:
(A1) If it is impossible that A, then everything is such that it cannot make that A.
(A2) If everything is such that it cannot make that A, then God is such that He cannot make that A.
(A3) It is impossible that one and two should not be three.
On the face of it, we have grounds for (A1)–(A3). (A3) seems obviously correct, and also follows from (Conceptualism about possibility), given that we cannot conceive of one and two not being three. (A1) seems to expose a necessary connection between the notions of ability—what things can and cannot do—and impossibility. And (A1) seems to entail (A2) and, moreover, it seems inconceivable to us that (A1) is true while (A2) is not true. But if we accept (A1)–(A3), we seem forced to accept that God is such that He cannot make that one and two not be three. And that leaves Descartes refusal to venture that claim looking coy: at best, a response to constraints on what one shouldn’t say that are distinct from a simple concern to speak only truth.
Now Bennett seeks to respond to a version of this difficulty. His response amounts to the following. Descartes accepts (Conceptual voluntarism). It follows that God’s decrees—that is, the specific decrees that God has made, including that it is impossible that one and two not make three—form part of “what has to be the case for the modal concepts [i.e. the concept of impossibility, GL] to be usable at all.” (Bennett, 2001: 70.) It follows that, when we try to consider, or conceive of, what would be the case had God’s decrees differed, we find that our modal concepts are inapplicable. In response to the difficulty sketched above, I think that the idea would have to be that our modal concepts have no traction on questions about their own bases, including God’s decrees. We can’t say, or judge, that it is impossible for God’s decrees to have been other than they were, or that it is possible for them to have been other than they were. Thus, we should venture no claims, or judgments, in this area.
As I said, the proposal is deep and interesting, and demands further reflection. One putative difficulty with which further reflection should engage is a concern about (Conceptual voluntarism)—that is, the claim that insofar as anything is inconceivable by us, that is because God has decreed that it be so. The concern is that it might seem natural to think that we understand the “because” here only insofar as we understand the co-variation of God’s decrees with the space of what is inconceivable, and that seems to depend in turn on our understanding the possibility that God’s decrees might have been other than they were. The outcome of Bennett’s discussion, however, seems to be that that is something we can’t understand: we have no conception of possibility such that we can conceive of God’s decrees as varying.
Well, there appear to be at least four potential ways out. (1) We might seek to deny that our understanding of the “because” depends on our understanding the co-variation of God’s decrees and what is conceivable. (2) We might deny that our understanding that depends in turn on our having a positive conception of God’s decrees being other than they were. (3) We might distinguish our optimal judgments about what is impossible from what is really impossible, thus rejecting (Conceptualism about impossibility): God’s decrees fix the space of what is conceivable by us, and so determine the extent to which we have access to the space of possibility, but (as far as we can tell) are impotent to affect the independent space of genuine possibility. (4) We might accept that God’s decrees might have been other than they were, and so accept that the space of what is conceivable might have been different, while denying that that would make a difference to the space of possibility. That is, we might tie our conception of what is possible, and so what is possible, to what is fixed by God’s actual decrees and, so, accept the argument sketched above to the conclusion that God could not have decreed otherwise, while allowing that we could have had a concept in some ways akin to our concept of impossibility—impossibility*—but which allowed that it is not impossible* that one and two not make three.
J. Bennett (2001) Learning from Six Philosophers, vol.2. Oxford: Clarendon Press.
J. Cottingham. R. Stoothoff, D. Murdoch, and A. Kenny (eds.) (1991) The Philosophical Writings of Descartes, vol. 3. Cambridge: Cambridge University Press. [CSMK]