Friday, August 6, 2010

God and Abstract Objects

Brian Leftow has defended a version of the cosmological argument which posits that if God possibly causes abstract objects to exist, and abstract objects exist necessarily, then God must exist necessarily. One reason Leftow puts the argument this way (presumably) is to avoid the problem of compromising God's unique aseity. If God is not the only self-existent entity, then that is apparently a difficulty.

I wouldn't go that far. In fact, even if the Platonists are correct in saying that abstract objects have necessary existence, God's unique aseity may be salvaged by pointing out that only God stands in a causal relationship to other entities. Abstract objects, if they exist at all, are causally inert, so their aseity is of one type, whereas God's aseity is of another type. Nevertheless, the idea of anything other than God existing a se does leave the Christian, myself included, with an uneasy feeling.

The problem I see with Leftow's argument is that it doesn't seem to be possible to cause abstract objects, for the reason given above. If abstract objects literally cannot cause anything, why think they can be caused themselves? St. Augustine, having been trained in the neo-Plantonic tradition, solved this difficulty by postulating that abstract objects exist as concepts in the mind of God. This means that even though abstract objects exist a se, and are not caused to exist, they are still dependent on God's mental activity (theological conceptualism). I think we may incorporate Leftow's modal argument with this conceptualist model of abstract objects:

1. Abstract objects are possibly necessary. (Premise)
2. Whatever is possibly necessary is necessary. (Premise, S5)
3. Abstract objects possibly exist necessarily as mental concepts. (Premise)
4. Therefore, abstract objects are necessary concepts of a mind. (From 1, 2, and 3)
5. Abstract objects cannot be concepts only in contingent minds. (Premise)
6. Therefore, abstract objects are concepts of a necessary mind. (From 4 and 5)

Briefly, in support of (5), abstract objects (if they exist necessarily) cannot be concepts of just any mind. For, there are possible worlds in which contingent minds (such as you and I) do not exist, and so abstract objects must be concepts of a necessary mind in those possible worlds. Given (2), it follows that a necessary mind also exists necessarily.

Of course, there are also positive reasons (other than S5) to conclude that abstract objects must be mental concepts. One of these reasons is the causal objection against Plantonism.

1 comment:

  1. "Abstract objects, if they exist at all, are causally inert, so their aseity is of one type, whereas God's aseity is of another type."

    Yes, so I think the deeper issue is whether they are, so to speak, modally neutral (i.e. simple as God is simple). It may not be up to God to cause WHAT a subtraction relation is, nor is it up to said relation to cause how many instances of itself are actualized, but it may be up to Him to cause THAT such a relation exists, and, of course, how such a relation is instantiated in the actual world. By "modally neutral" I mean something that is "necessary": it is neutral with respect to causal modality, ante et post. Hence, I have to wonder if abstract entities are necessary, or if they are subject to modal contingency. Could it be the case that, say, "twoness" never existed? That there was never such a thing as twoness? Imagine if God had created a world entirely made of a single spiritual power. There would not BE any(other)thing in that cosmos by which "twoness" could have any meaning.

    The rejoinder is probably that, at least in God's mind, the possibility of a world with twoness in its grounds the modal neautrality of twoness, and, thus, all other abstract entities. But this only begs the question in favor of your argument in this post. My point, I think, is to buttress what Leftow's intuition might be, and which you address explicitly, namely, that, while abstract entities in our world do seem modally neutral, yet, at a higher level of abstraction, we can recognize their contingency with respect to at least some 'possible worlds,' and thus the only way to ground them in their own notional identity (channeling Hegel, am I?) is by seeing them in God's Mind or nowehere at all.

    I also think a more Scotistic account of modality would shed light on how even abstract concepts depend on the absolute will of God. James Ross, e.g., argues against "modal talk" per se since the actual creation is what grounds modality, and not vice versa. See his last book, _World and Thought_.

    And so it came to pass that I am once more drawn to direct your attention to my post about "uncomprehended logic" and naturalism.