FOM: ontological arguments in mathematics

[Neil Tennant]

Many thanks to Jeff Ketland for his statement of rational atheism.
FOM-ers acquainted with Anselm's Ontological Argument for the
Existence of God might be interested in the following structurally
analogous argument for the Non-Existence of the number Zero.
Those who prefer to do so may make it a little more sophisticated, by
using The Empty Set in place of Zero.

This argument was first presented to a mystified audience of about 300
God-fearing and gum-chewing Philosophy 101 students at The Ohio State
University in January 1996.

Enjoy.

Neil Tennant

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An `Ontological' Argument for the Non-Existence of Zero 
(courtesy of Saint Anselm)

We believe [zero] to be something than which nothing of greater
nullity can be conceived. So we understand the expression ``something
than which nothing of greater nullity can be conceived''.

Thus something than which nothing of greater nullity can be conceived
exists in the understanding. Call such a thing E. So E is a thing
than which nothing of greater nullity can be conceived, and which
exists in the understanding.

Now suppose (for reductio) that E does exist in reality.

We can conceive of something than which nothing of greater nullity can
be conceived existing only in the understanding but not in
reality. Call such a thing F.

Because F does not exist in reality but E (by supposition) does, F is
of greater nullity than E.

We have conceived of F; and F is of greater nullity than E.

But E is supposed to be that than which nothing of greater nullity can
be conceived!---a contradiction.

Thus our supposition that E does exist in reality must be wrong.

Hence E does not exist in reality.