Friday, September 30, 2011

Leibniz and the necessity of optimality

Leibniz famously holds that:

  1. God creates the best logically possible world.
In order to resist logical fatalism, Leibniz denies that (1) is a logically necessary truth.

But this causes a problem for him that I am not sure he recognizes. Either (1) does or does not logically follow from God's perfection. If it does follow, then (1) will be logically necessary, since Leibniz thinks it is logically necessary that there be a perfect God because of the ontological argument.

But if (1) does not logically follow from God's perfection, then how do we know that (1) is in fact true? Leibniz is not so blind to the evils of the world as to think we can conclude (1) from an optimistic appraisal of the world around us. His theodical work insists on our not knowing much about what the infinite universe is like, and our thus being unable to form a justified judgment that the universe is non-best. If we could see that the universe is best, he wouldn't have to go to that trouble.

Leibniz does have a backup plan. In one piece, he notes that even if (1) were true, it wouldn't logically follow that it is logically necessary that this world is best. For Leibniz, a proposition is logically necessary provided it has a finite proof, whereas contingently true propositions have only an infinite proof. Thus, Leibniz insists—and very plausibly so—that even if our world is best, that fact cannot be finitely proved. So Leibniz could simply affirm that (1) is necessary, but that fatalism does not follow. He doesn't want to do that, though.

To make it harder for Leibniz to resist the logical necessity of (1), consider the following little argument:

  1. Logically necessarily, a being that fails to create the best possible world is imperfect (in power, knowledge or morality).
  2. Logically necessarily, there is a perfect being, and God is that perfect being. (By the ontological argument.)
  3. So, logically necessarily, God creates the best possible world.
Leibniz defends the idea that a perfect being couldn't create less than the best, so he seems committed to (2). And he is definitely committed to (3).

I think, though, there is a neat way out for Leibniz. I do not know if he ever takes this way out—it would be interesting to search the texts carefully to see. The neat way out is to deny (2). Instead, recall Leibniz's controversial but insistent claim that if a perfect being were faced with a choice between two equally good worlds, that perfect being would not create anything. More generally, it is plausible that Leibniz would say:

  1. Logically necessarily, if x is a perfect being and there is no best possible world, x creates nothing.
Moreover, on Leibnizian grounds, the following is very plausible:
  1. Logically necessarily, if there is a perfect being and a best possible world, the perfect being creates the best possible world.

Putting (5) and (6) together, we get a way to both deny the necessity of (1) and a way to know that (1) is true. First, there is no finite proof that there is a best world. Any proof would require comparisons between infinitely many worlds and would, plausibly, be an infinite proof. So it is not logically necessary that there is a best world or that God creates the best on Leibniz's finite-proof understanding of necessity. Second, because we can know with certainty that God created something (argument: necessarily, anything other than God is created by God; I exist and am not God because I lack many perfections; hence, something is created by God), by (5) we conclude that there is a best possible world, and by (6) that God created it.

I do not know if this line of thought is in Leibniz's texts, but I think every step in the story is one that he should endorse given his other views.

1 comment:

Mike Almeida said...

Alex, this is an interesting argument. Let me advance a worry for the claim that there is no finite proof for the existence of a best world. The value of possible worlds depends on God's creative activity, since every contingent being that exists in a world and every contingent state of affairs that obtains there depends on God's creative activity. So (and I concede that this gets tricky) it might be true that the space of metaphysical possibility includes no ties in highest value among worlds, given the nature of God. To put it another way, metaphysical space includes worlds tied in highest value only if it is possible for God to create a broad profile of contingent beings/states of affairs across possible worlds that ensure he could not actualize any possible world. Maybe such a profile is inconsistent with God's existence. I leave aside questions of whether some world must be actual.