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Friday, July 25, 2008

A note on God and unsurpassable worlds

Let us say that a possible world is unsurpassable if there is no possible world which is better than it. (This allows for the epistemic possibility that there may be more than one unsurpassable world, as opposed to the term “best” which is commonly understood to presuppose uniqueness.) Now, suppose for the sake of argument that (roughly) the God of traditional theism—an incorporeal, omniscient, omnipotent, omnibenevolent (etc.) being—exists. The question I want to examine is this: If God is infinitely good, not just in the sense of being omnibenevolent but also in the sense that God is of infinite value, is every possible world in which God exists an unsurpassable world? The answer depends on what we take into account in assessing the value of possible worlds. I see at least two ways of carrying out such an evaluation.

On the first way, we ignore any weight that might be assigned to the goodness of individuals and simply regard one possible world as being better than another if and only if the set of all good things which exist in the latter is a proper subset of the set of all good things which exist in the former. In this sense a possible world which contains God and one sentient being is—assuming all sentient beings possess at least some value--better than a world which contains God alone (not counting necessarily existent abstracta), and this is so quite irrespectively of the fact that God is infinitely good. It seems to me that there is no unsurpassable world in this sense, for given any possible world w_x there is always another world w_y such that the set of all good things which exist in w_x is a proper subset of the set of all good things which exist in w_y. On this view possible worlds can only be ranked according to their goodness, one cannot say how much better one world is than another.

According to the second way one should take into account not only the number of instances of goodness but also, so to speak, their intensity. For when we say that God is infinitely good we do not (or should not) mean that God has aleph-null (or some other transfinite cardinal) units of goodness, but rather that God’s goodness is “infinitely intense” or “unsurpassably intense”. We might characterize this by saying that in our moral considerations God’s goodness ought to be given an infinite and/or unsurpassable weight. Given that God’s goodness is infinitely or unsurpassably intense in all possible worlds where God exists, it appears that taking the “intensity” of something's goodness into account in determining the value of possible worlds yields the result that all possible worlds where God exists are unsurpassable.

So it seems that if God exists either none of the worlds which God can actualize are unsurpassable or that all of them are, and in neither case is there a unique "best" world that God can actualize. The interesting question is then, if that’s so, does it follow that God must choose a world to actualize at random?

7 comments:

Mike Almeida said...

Randomizing doesn't help. Take a typical probablity distribution over the worlds, 1/2 w2 + 1/3 w3 + 1/4 w4 +. . .+ 1/n wn. It is easy to see that if these worlds increase in value so that each wn has n units of value, then the sum will be infinitely valuable. But no matter what world comes up on the randomizer, shift the worlds from right to left and a better world would have been actualized. It's the same problem over again.
The problem is generally taken to be that God could actualize no world since they're all surpassable, and yet must actualize some world, since there must exist a world containing some contingent states of affairs and all necessarily existing things.

John Falicki said...

Jason -- I'm happy to see you're importing a concept like INTENSITY into Philosophy! We need things like this; after the overwhelming triumph of Physics in the 20th Century, humans have become too obsessed with EXTENSIVE properties to the *life*-denying neglect of INTENSIVE properties. We apply the root notion of Total Ordering to everything now, seeking to make everything *measurable*, to our detriment. Of course a quantity like Intensity of light is measurable, but the *intensities* of our everyday lives are not, and are left to be played out in movies or music, etc. I think notions like Intensity and the whole world(s) of INTENSIVE qualities need to be brought out into intense examination and dialogue.

Quirinius_Quine said...

Hi Mike,

I think that's a problem only if we suppose that God, as an omnibenevolent being, cannot actualize a surpassable world. If there are any unsurpassable worlds that God could actualize instead that would indeed pose a problem, but if all the worlds which God can actualize are surpassable I don't see what the problem is. If we do not in general hold agents responsible for failing to do something which is impossible for them to do, why should we in this case? If there are no unsurpassable worlds, not being able to actualize one is no more of an imperfection than not being able to create a square circle.

Anonymous said...

Hi Jason. Regarding your conclusion that God might end up actualizing a world at random, it seems to me that God might just subtract himself (or his value) from the different possible worlds in which he exists, in order to calculate which one is unsurpassable.

-carlos

Quirinius_Quine said...

Hi Carlos,

That's a really good objection. I don't think God's subtracting God's value would have have any affect on the first way of evaluating worlds, for then we aren't taking the intensity of something's value into account, and it's still true that for any possible world there's another which contains even more good things. On the second way, though, I think God's subtracting God's value might have an effect. It would no longer automatically follow that every world was unsurpassable. Although, now that I think about it, we might nevertheless have a situation similar to the one we have on the first way of evaluating worlds. For even if only God's value is unsurpassably intense, it might still be true that for every possible world there is another possible world whose total value is greater due to the fact that it contains something whose value, while only surpassably intense, is still more intense than anything contained in the world of lesser total value. Once again, we would get the result there is no unsurpassable world. The question is, then, do we have any reason to think that, excluding God, there is an upper limit on how intense something's value can be?

Anonymous said...

A response regarding the first way: Perhaps goodness of worlds does not just depend on the added value of the things contained in that world. For example let's say that world 1 has 1,000 good things in it, and world 2 has 1,002 good things in it. It might seem that world 2 surpasses world 1 in value. But perhaps the relations of the things in a world are also valuable. And perhaps the value of relations is in an inverse relation to the value of the number of worlds, namely the fewer relations a world has, the more valuable they are. So if one were to graph these value measurements of objects and relations, it might look this way: let's say that on the y-axis value is measured, and on the x-axis quantity is measured. There would be two lines on the graph. The number of objects-to-value line would slope upward, and the number of relations-to-value line would slope downward. Value would be maximized at the intercession of these two lines, and God would create a world with the number of objects and relations at the point of such intercession.

Carlos

Anonymous said...

...at the point of such intersection.