simple and being x must be the same attribute. But then any simple being will be
identical to x. So there can be at most one simple being. So if being a G entails being
simple, there can be at most one G—and if attribute-identities are necessary, at most one
possible G. Thus, there is at least a good argument from premises Anselm clearly
accepted to back his belief that at most one possible being is a G.
ii. As the doctrine of divine simplicity is controversial, perhaps a better answer lies with
what Anselm means by “greatness.” It's axiomatic in Western theism that whatever
precisely worship is, at most one thing deserves it, and this thing coexists with no rivals
for worship (see, e.g., Isaiah 40:25, 44:6–7, 46:5, 9). Anselm argues that any G must as
such exist necessarily and necessarily be a G. If he's right, and it's also the case that
maximal greatness in a possible world W excludes having a rival in W, then in no
possible world does a G coexist with another G, and there is at most one possible G.
I now turn to Anselm's reasoning.
The Reasoning
On one reading, Anselm's premises are
- Someone thinks of a possible object which is a G, and
- If any possible G is thought of but not actual, it could have been greater than it actually
is.
The reductio runs this way. By definition, if a possible object g is a G, no possible object
in any possible state is greater than g actually is: g is in a state than which there is no
greater. Let g be the G someone thinks of. Then, as a G, g is in a state than which there is
no greater. Per (2), if g is not actual, g could have been greater than g actually is. So if g
is not actual, g is not in a state than which there is no greater. So if g is not actual, g both
is and is not in such a state. So g is actual. So a G exists.
The argument is valid. So let us ask if its premises are true.
end p.83
Ontological Commitments?
(1) is not innocent. It asserts a relation between a thinker and a possible object that is
actually a G, and so brings an object into our ontology. Anselm needs it to do so if (1) is
to give him a G to which to apply (2). But then if he is not blatantly to beg the question of
God's existence, Anselm must also assume that this possible object is there, and is a G,
even if it does not exist. And odds are that Anselm did believe in nonexistent objects.^5
But this puts an unflattering gloss on his argument. For then it seems to amount to: grant
that something actually is in a state with no greater. This thing either does or doesn't
exist. But how could something that didn't so much as exist be as great as all that? And of
course, if that's what the argument amounts to, it's hard to see why one should grant that
something actually is in such a state. The step from this admission to the conclusion
seems vanishingly small.