Spinoza and the logic of divine omnipotence

With my students I was going over one of Spinoza’s arguments concerning divine omnipotence — namely the argument that comes in the first Scholium to Proposition 17 in the Ethics.

For some background, Spinoza’s view is that God produces not just those things that he deems desirable (nor just the things that we deem desirable), but rather every possible thing — everything, as he puts it, that can be conceived by an infinite intellect (see Proposition 16 of Part 1 of the Ethics).

This is the basis of his religious vision of the world: we must accept all things as necessary and stop looking for meaning that isn’t there in a misguided notion of divine will. Nor can we find any meaning in the contingent development of history or path of evolution, since elsewhere in the universe it must be that all other possible paths have been followed.

One argument against this theory, which Spinoza considers, runs as follows. Suppose that God produces every possible thing. Then it is impossible for him to produce anything more. This appears “to be incompatible with God’s omnipotence [Dei omnipotentiae repugnare]”. And the latter was of course an indisputable premise in Spinoza’s historical context.

Spinoza doesn’t explain what he thinks is wrong with this argument. I suggested to my students that it was a kind of logical trick, and they all agreed. But is it a trick?

The crucial question is, of course, what should count as omnipotence. The argument seems to imply that God’s omnipotence entails that whatever he has done, he can always do more. The sense is that God’s power is unlimited.

It’s worth noting that this doesn’t seem like a compelling definition of omnipotence. For comparison, consider the view that God cannot think of any number greater than or equal to 5. There is a clear limit on God’s power. But his power is unlimited in one sense. However many numbers < 5 he has thought of, he can always think of more. If, for instance, he has thought of all the numbers < 5 up to 50 decimal places, he can go on to think of all the numbers up to 51 decimal places, and so on.

Still, if we have this definition of omnipotence in place, the argument does seem valid. Did anyone make it, or was Spinoza attacking a straw man? One related position was advanced by John Duns Scotus in the 13th century. Roughly, Scotus argued (against Avicenna, who held a very similar view to Spinoza’s) that it is a limitation on God’s omnipotence if he is compelled to produce everything possible, for then it is beyond his power to not produce any given thing.

This sort of thinking was Spinoza’s main target, I believe. But his implicit answer to it involves a number of other metaphysical assumptions. If it is always in God’s power to not produce any given thing, then we have no explanation of why there should be a world at all: God could just as well have not made the world. If we say that the world exists because it was God’s will that it should exist, we haven’t explained anything. Why was it God’s will? To this we have no answer. Scotus would be happy with this result — arguably it was precisely what he set out to prove. But Spinoza could not accept it; for him an unintelligible universe was intolerable.

The argument Spinoza actually presents hints at a deeper paradox. Suppose God is producing every possible giant. Since there is no limit to his power to make giants, it must be that for any giant God makes, he makes another taller giant. It also seems to follow that for any group of giants God makes, he makes a giant taller than any member of that group. But now take the group of all the giants God makes. Does God make a giant taller than any member of that group? If so, God would make a giant taller than all the giants he makes, which is contradictory. But if not, it seems that there is a limit to God’s power: having made a certain (infinite) group of giants, he cannot make any more.

One way to wriggle out of the paradox is to disallow quantification over the relevant infinite set. This is the path followed by certain solutions to related mathematical paradoxes, such as the Burali-Forti paradox. In the example above, we might say that there is no such thing as the group of all the giants God makes. God makes giants exceeding all number, and we cannot speak meaningfully of all of them. But that seems quite arbitrary — why can’t we speak of all the giants God makes?

In Spinoza’s case, one way to attack his conclusion that God produces every possible thing is to disallow quantification over the whole domain of possible things. There is, we might say, no such thing as the group of all things conceivable by an infinite intellect. Possibilities are endless, in the sense that however many one thinks of, one can always think of more. Then there cannot be such a thing as “everything conceivable by an infinite intellect”.

Yet Spinoza uses that phrase. Is it possible to speak of “everything conceivable by an infinite intellect” if there is no end to what the infinite intellect can conceive of? There could be, if you allow yourself to imagine that the infinite intellect can conceive of more things that it can conceive of. That seems obviously contradictory, but I wonder if Spinoza would have accepted it.

Descartes, from whose theory of omnipotence Spinoza borrowed, refers at times to God’s “superabundance of power [exuperantia potestatis]”. “Exuperantia” means “surpassing” — but in this case what does God’s power surpass? Every conceivable power? But then is God’s power itself conceivable? Many medieval philosophers would have said no, but Descartes needed to say yes or many of his arguments wouldn’t have worked. And in that case, it follows that God’s power surpasses itself.

One suggestive piece of evidence for this reading of Descartes’s “superabundance” is that he brings up the notion while proclaiming another paradox about God. Johannes Caterus, in his objections to Descartes’s Meditations, complains that Descartes takes the standard claim that God is “self-caused” much too literally. Self-causation, taken literally, is deeply paradoxical, since a self-caused thing must exist in order to bring itself into being but contrariwise must bring itself into being in order to exist.

Caterus suggests that when medieval theologians speak of God being “self-caused” they really mean only that he has no cause. But Descartes explicitly demurs from the medieval theologians on this point: he means “self-caused” in its literal and paradoxical sense, and he explains that God brings himself about by his superabundant power. Well, if we can say that God has a power that surpasses itself, why not say that God can bring himself into being?

If you can do one contradictory thing, you can do others. This is certainly true if the classic inference rule of “ex falso quodlibet” holds. But unfortunately it also follows from that rule that if you do one contradictory thing you can’t do others; it follows, in fact, that you can’t do anything at all, since anything follows from a contradiction (it also follows that you can do everything). Descartes clearly isn’t thinking in terms of EFQ. Nevertheless there is some intuitive plausibility in the view that if God can do one thing that seems logically impossible to us (cause himself), then he can do others. Our intuitions about what is possible do not limn the contours of God’s omnipotence. And so it might also be true that God’s power can exceed itself, absurd as that is to our intuitive logical understanding.

If Spinoza takes on Descartes’s theory of divine power, this is how he can hold that God brings about every possible thing. There is no end of possible things. But nor is there any end to divine power, and divine power produces all possible things. It follows that there is no end of actual things — not simply that there is an infinite collection of them, but rather that however many of them there are, there are more than that. The world itself becomes superabundant, in the paradoxical Cartesian sense. It might be, in the words of G.K. Chesterton, the best of all impossible worlds.