An argument for the existence of some being---usually God---which relies on some ordering of
levels of being. Probably first developed by Anselm. Essentially,
his version of the argument proceeds as follows. "We" (that is, Anselm and those who agree with
him) claim that God is that entity such that no greater being can possibly
be conceived (in the usual translation, ``that than which no greater can be conceived''). Anyone, even the fool (Anselm here refers to Psalms 14:1; note that fool here does not denote an idiot,
but an immoral person), can understand the description ``entity such that no greater being can possibly be
conceived''. In other words, the fool can conceive of such a being. Now, according to Anselm, anything
that can be conceived of in the mind can be conceived of as existing in reality. It is better to exist in
reality than not to do so; thus, if the being conceived of by the fool does not exist in reality, then it is not
the entity such that no greater can be conceived---for one could conceive of that being
existing in reality. Since the assumption that the being conceived of by the fool does not exist leads to
a contradiction, Anselm concludes that the being then must exist.
In addition to being repeatedly attacked (by the likes of Thomas Aquinas and Immanuel Kant, who
were no atheists), various philosophers have tried to recast the argument to avoid the
objections of its detractors. This has led to so many different ontological arguments that
Alvin Plantinga has claimed that it is impossible to refute more than a handful at once. Plantinga
himself has contributed an interesting revision of Anselm's argument. Suppose the actual world is
a world (a fairly safe assumption). Further, suppose some entity B's being of unsurpassable greatness is
logically equivalent to (that is, entails and is entailed by) the statement that for any world
W, B exists in W and B has maximal excellence in W. Finally, suppose there exists a world Q and a
being B such that B exists in Q and has unsurpassable greatness. From this it follows fairly directly
that B exists in the actual world and has unsurpassable greatness. A problem I have with this argument
is that the third premise is equivalent to the conclusion (that is, granting
the conclusion and the first two premises, the third premise follows, so that with respect to the first two
premises, the third premise and the conclusion are equivalent); it thus seems question-begging to me.
In The Nature of Necessity, Plantinga claims that this argument is not question-begging, but I am not
convinced.
I have several problems with the ontological argument. In Anselm's version, there are
two premises I do not accept: first, that there are different levels of greatness (or in some
interpretations, amount of reality) among objects; and second, that there is some
limit to such greatness (or reality). On the greatness interpretation, Anselm's argument seems to require that things have greatness. One thing can be better than another. I don't
think this should be required. I might be able to accept situations or other
states of affairs as being better or worse than others, but things? On the reality interpretation,
I'm not sure what it is supposed to mean to say that something is more (or less) real than
something else.
At least Descartes picks something---perfection---which may reasonably be assumed
to have an intrinsic maximum. But still, I think it's really unclear what a perfection is supposed to
be. What little of a modal realist there still is in me wants perfections, if they are indeed
possible, to exist in some world or other, but I don't understand why they need be vested
in a single being, or how the perfections must reside in a being in the actual world.
Perhaps this is not a solution to the ontological argument; I hope at least that it will help continue
discussion of this argument or similar ones.