Anselm's Real Argument
While Anselm probably did not intend (6)–(10), he did develop the first modal argument
from perfection, in a slightly later work, the Reply to Gaunilo:
Whatever can be thought and does not exist, if it existed, would be ablenot to exist. (But)
something than which no greater can be thoughtif it existed, would not be ablenot to
exist—for which reason if it can be thought, it cannot not exist. (Charlesworth 1965, 60)
Anselm's reasoning is this:
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- If it can be thought that a G exists and no G exists, any G would exist contingently if
it did exist. - It is not possible that a G exist contingently. So
- It is not the case that it can be thought that a G exists and no G exists.
So - If it can be thought that a G exists, some G exists.
- It can be thought that a G exists.
- Some G exists.
There are strong a priori arguments for (12). We can recast (11) as - If it is possible that a G exists and no G exists, any G would exist contingently if it
did exist.
and alter the rest of the argument accordingly. The advantage of doing so is that (17)
comes out true within the Brouwer system of modal logic, a weaker system S5 includes.
The Brouwer system is weaker than S5 because it makes a weaker claim about possible
worlds: rather than assert that every world is possible relative to every other, it asserts
that relative possibility is symmetric: that if A is possible relative to B, B is possible
relative to A. To see that (17) is true in Brouwer, suppose that these boxes represent all
the possible worlds there are: