From chapter 15 of Anselm's Proslogion
Therefore, Lord, you are not only that than which a greater cannot be conceived; you are also something greater than can be conceived. It is possible to conceive that there is something of this kind. If you are not such a thing, it is possible to conceive that there is something greater than you—which cannot be.Why not? Which is to say (I’m not being simple-minded about Anselm, here; I’m speculating more broadly)—viewed simply from the point of view of divine authority over humanity, mightn’t it be that God, though (as it were) our ‘superior officer’, has Himself a superior to whom he defers? Such a hyperGod would no more impact upon the specific duties we owe to our God than the existence of a Field Marshall has on the direct relationship between a sergeant and a private. Indeed, might this Godgod not also have a superior God figure, and so on ad infinitum? Perhaps it is, to coin a phrase, Turtles all the way up?
More specifically related to Anselm’s celebrated, much discussed ‘proof’ wouldn’t such a conception be necessarily ‘greater’ than the notion Anselm himself develops here? To put it another way: the traditional (the as it were medieval) conception of infinity as 'the greatest thing' is trumped by Cantor's invention of an infinity of infinities, with dire consequences for Anselm's thinking.
Stephen Maitzen has some very interesting things to say about this passage in his article ‘Anselmian Atheism’ (published in Philosophy and Phenomenological Research 70: 1 (Jan., 2005), 225-239):
‘I develop an argument that confronts theology with a trilemma: atheism, utter mysticism, or radical anti-Anselmianism. The argument establishes a disjunction of claims that Anselmians in particular, but not only they, will find disturbing: (a) God does not exist, (b) no human being can have even the slightest conception of God, or (c) the Anselmian requirement of maximal greatness in God is wrong. My own view, for which 1 argue briefly, is that (b) is false on any correct reading of what conceiving of requires and that (c) is false on any correct reading of the concept of God. Thus, my own view is that the argument establishes atheism. In any case, one consequence of the argument is that Anselmian theology is possible for human beings only if it lacks a genuine object of study.’Here’s his argument:
In the following argument, the phrase "our cognitive equals" means "whatever beings have only the conceptual power had by actual human beings." The argument uses "actual" and "actually" as rigid designators whose reference does not vary across possible worlds: from the perspective of any world, actual human beings, for instance, are all and only those human beings (past,
present, and future) who inhabit our world, the actual world.
(1) In at least one possible world, there exists something too great to be at all conceivable by our cognitive equals. [Premise]
(2) In any possible world, whatever is at least as great as something too great to be at all conceivable by our cognitive equals is itself too great to be at all conceivable by our cognitive equals. [Premise]
(3) So: In any possible world, whatever is not too great to be at all conceivable by our cognitive equals is not as great as whatever is too great to be at all conceivable by our cognitive equals. [From (2)]
(4) So: If God actually exists but is not too great to be at all conceivable by our cognitive equals, then God actually exists and God's actual greatness is not as high as the greatness of at least one thing in at least one possible world. [From (1), (3)]
(5) If God actually exists, then God's actual greatness is at least as high as the greatness of anything in any possible world. [Premise]
I’m not sure about this myself; there seems to be some creakage in the logic here. Why should I swallow (1)? Maitzen has a suggestion: ‘Why accept premise (1)? In a word, humility. (1) asserts, not that there is something too great to be at all conceivable by anything with only human conceptual power, but only that there logically could have been such a thing.’ The Humble Philosopher: fair enough—although humility, as a Christian (rather than, say, a Nietzschean) virtue, might be thought complicit with the subject of enquiry. And saying ‘there is in a possible world’ doesn’t seem to me the same thing as saying ‘there could be’. My imagination, after all, does not constitute a possible world. What else?(6) So: It is not the case that God actually exists but is not too great to be at all conceivable by our cognitive equals. [From (4), (5)]
(7) So: If God actually exists, then God is too great to be at all conceivable by our cognitive equals. [From (6)]
Premise (2) looks obviously correct.Really? Doesn’t it depend upon a buried belief that absoluteness (infinity) is a multiple, diverse and differentiated matter?—a dedicated monotheist (let’s call her ‘Ann Selm’) might reply: there is only one ‘inconceivable greatest’ -- bringing other inconceivable greatnesses is a false step, analogous to talking about temperatures below absolute zero.
(2), in turn, implies (3), the plainly true claim that whatever fails to achieve a given level of greatness—the level fixed by the predicate "too great to be at all conceivable by our cognitive equals"—is not as great as whatever succeeds in achieving that level of greatness.’Fails’ and ‘succeeds’ are hardly neutral comparators. And isn’t neutrality required here? Humility, if nothing else, ought to dictate that.
He goes on to consider a number of ‘objections and replies’, of course; and there’s nothing dogmatic or clumsy about the article. Still.
Objection A. Premise (1) is false for a reason you have not yet considered. Actual human beings understand the description "greatest possible being." Thus, the conceptual power had by actual human beings at least partly comprehends the greatest possible being, and so even the greatest possible being does not fit the description "too great to be at all conceivable by our cognitive equals." Since it is impossible for anything to be greater than the greatest possible being, it is impossible that anything should fit the description in (1)This isn’t exactly my objection, but it’s allied to it; and Maitzen’s reply seems strained. It reminds me, rather, of the ‘a ham sandwich is better than eternal happiness’ argument, which (as you’ll know) goes like this:
Reply. The objector's reasoning breaks down where it might appear least vulnerable: the claim that it is impossible for anything to be greater than the greatest possible being. For suppose that the expression "greatest possible being" fails to refer; suppose that it picks out nothing at all. Now, I am greater than nothing: I have nonzero greatness (however little)—something that, we are supposing, is not true of the greatest possible being. In a clear sense, then, I am greater than the greatest possible being.
1. Nothing is better than eternal happiness.
2. A ham sandwich, clearly, is better than nothing …
3. Ergo a ham sandwich is better than eternal happiness’
On the other hand, and to bring this post back to its starting point, there's some interesting discussion of premise (5), objection and reply:
Objection C. Premise (5) is false. God's actual greatness need not be logically unsurpassable, provided that God is the creator of all contingent beings and possesses enough of the traditional divine perfections—in particular, omniscience, omnipotence, and perfect goodness. Such a God remains worthy of worship, even if he should turn out to be logically surpassable because, say, being timelessly eternal is a perfection that he lacks. God's actual greatness, therefore, need not be unsurpassable, provided it is actually unsurpassed and it exceeds a threshold minimally sufficient to ensure that God is worthy of worship.One, here, doesn’t interest me (I’m curious about God, not just about Anselm’s conception of God); Two requires a paper all itself (though I don’t agree); Three introduces a brand new concept—cool, but hard to justify—of co-exemplification. And Four doesn’t seem to me to pass the ‘do I orient my service life via my sergeant or some distant Field Marshall a thousand miles away?’ test I suggest at the start of this post.
Reply. This anti-Anselmian objection invites four replies. First, the objection threatens to change the subject: if my argument is construed as concluding the non-existence of the Anselmian God, it is no rebuttal of that argument to reject the Anselmian description of God. But, second, the Anselmian description can be defended by noting that the objection suffers from the following instability. The more reason we have to regard, e.g., timeless eternality as a perfection, the more reason we have for insisting that anything properly called "God" must possess it and that, therefore, any scenario in which God lacks it is incoherent. On the other hand, the more confident we are that such a scenario is coherent—the more reason we have for allowing that God could lack, e.g., timeless eternality—the less reason we have for regarding that property as a perfection, in which case God's lacking the property would not imply that God is surpassable. The Anselmian description famously avoids this instability by insisting that the concept of God is the concept of an unsurpassable being. Third, there is the intuition, championed most notably by Morris, that "the divine perfections are all necessarily co-exemplified" and thus any scenario in which God has some but not all of the perfections is impossible. Fourth, there is Morris's argument that the Anselmian God exists in every possible world and thus excels any less-than-Anselmian God in any world in which the latter exists. In any world, then, in which the objector's God exists, there exists an even greater being, and our intuitions tell us that at most one of those beings—the greater one—deserves to be regarded as the one true God of monotheism.