1. God = that than which nothing
greater can be thought (d) [nominal definition of ‘God’]
2. d is in the understanding
(i.e., d can be thought) [self-evident, unless the nominal definition of ‘God’ is
contradictory, which would be tough to swallow]
3. d is not in reality
[assumption]
4. If something is in the
understanding and not in reality, then something greater than it can be thought
(namely, something that is in reality) [self-evident, based on the meaning of
“greater”]
5. Something greater than d can
be thought, i.e., something greater than that than which nothing greater can be
thought can be though [1, 2, 3, 4, by UI, MP, CON, ID]
But 5
is contradictory, so one of the premises from which it
followed has to be false. But it cannot be either of the self-evident premises,
so it has to be the assumption, namely, 3. So, its denial, namely, that is d is
in reality is true; therefore, by 1, God is in reality, God really exists.
“Versions of this
argument have been defended and criticized by a succession of philosophers from
Anselm’s time through the present day (see ontological arguments). Our concern
here is with Anselm’s own version, the criticism he encountered, and his
response to that criticism. A monk named Gaunilo
wrote a "Reply on Behalf of the Fool," contending that Anselm’s
argument gave the Psalmist’s fool no good reason at all to believe that that
than which nothing greater can be thought exists in reality. Gaunilo’s most famous objection is an argument intended to
be exactly parallel to Anselm’s that generates an obviously absurd conclusion. Gaunilo proposes that instead of "that than which
nothing greater can be thought" we consider "that island than which
no greater can be thought." We understand what that
expression means, so (following Anselm’s reasoning) the greatest conceivable
island exists in our understanding. But (again following Anselm’s reasoning)
that island must exist in reality as well; for if it did not, we could imagine
a greater island--namely, one that existed in reality--and the greatest
conceivable island would not be the greatest conceivable island after all.
Surely, though, it is absurd to suppose that the greatest conceivable island
actually exists in reality. Gaunilo concludes that
Anselm’s reasoning is fallacious.
In order to defend
himself against Gaunilo’s criticism, Anselm would
have to show why Gaunilo’s argument about the island
is not in fact analogous to his own argument about that than which nothing
greater can be thought. Surprisingly, he never does this. His long-winded and
indeed somewhat intemperate "Reply to Gaunilo"
asserts more than once that the island example fails, but he never
explains why it fails. The usual reply given on Anselm’s behalf (and
indeed often attributed to Anselm himself) is that the notion of a greatest
conceivable island is incoherent; however great an island might be, one could
always conceive of a greater. This is a lame response, since it is open
to Gaunilo to say exactly the same thing about the
greatest conceivable being; it is therefore no wonder that Anselm did
not say anything of the sort. (For a reading of the argument that
endorses a response of this sort, see Klima 2000.)”
Thomas
Williams: Saint Anselm, http://plato.stanford.edu/entries/anselm/#2
“I find the author’s dismissive remark on the rebuttal of Gaunilo’s objection, calling it “lame”, rather unjustified. For the justification the author offers for this remark is simply that Gaunilo might say the same concerning the greatest (most perfect) being thinkable that Anselm would say concerning the greatest (most perfect) island thinkable, namely, that its concept is inconsistent. But this justification is patently invalid, which can be shown in the following way. The concept of the greatest island thinkable is inconsistent iff for any given island a greater is thinkable (just as the concept of the largest prime number is inconsistent, because for any given prime there is a larger, as was shown by Euclid). But since the concept of island implies limited perfection (i.e., whatever is an island has to be of some limited perfection, since it is a body, etc.), it is clear that for any given island, which can have only some limited perfection, a greater is thinkable, i.e., one that has more perfection; ergo, etc. However, the notion of being does not entail that whatever is a being has to be of some limited perfection, for otherwise the notion of a being of unlimited perfection would have to be explicitly inconsistent. But then, if the notion of a being of unlimited perfection is not clearly inconsistent (as one would hope, unless one holds that all believers in God are at least as irrational as believers in round squares), then the same type of reasoning that applied to the greatest island thinkable is obviously not applicable to the greatest being thinkable; so, the dismissive remark is rather unjustified, q.e.d.” (My critique of Williams’ argument.)