Please note that these axioms have not been accepted by any higher-power authority that I know of, and hence should not be used to prove anything. However, I simply fail to understand what makes my logic faulty :)

Let us
associate with *n* a statement *Sn* for
all *n* in the set of natural numbers. We may assume consistency of
*Sn* provided the following conditions are
satisfied:

There exists a *k* such that *Sk* is true (*k* is a natural number)*Sk+1* has a truth value that seems consistent with
*Sk* and any known premises *Px*.

Suppose that for all *n* in the set of
natural numbers there is associated a statement *Sn*, which is true for *Sk*.
One may assume *Sn* to be true for all *n* provided the following
conditions are satisfied:

The assignment is not graded.

One cannot
find a better method of proof.

One cannot find a
disproof.

Let
*S* be a statement, then *S* exists on the basis that it has
already been formulated.

If a person, *Pn*, cannot understand a given
statement *Sx*, then *Pn* would not be able to formulate *Sx*, and therefore we cannot prove the existence of
*Sx*. But *Sx* does,
in fact, exist on the basis that it has been given. By this
contradiction, such a person, *Pn*, cannot
exist.

Suppose we have a
statement *Sx* which is equal to some given
fact for all *x*. By the axiom of existence, *Sx* does exist, and it does so for all *x* by the
axiom of consistency.

Now, we have an infinite number of statements
*Sx*. However, the brain of a person *Pn* can only comprehend a finite number of facts, where
*n* is not equal to *"God"*. Therefore, for all *n* there
exists an *x* such that *Pn* cannot
understand *Sx*. By the Corrolary to the
Theorem of Existence, there exists no *n* not equal to *"God"*
for which *Pn* exists. Therefore, people must
not exist.

Yet amazingly, the existence of *Pn* where *n*=*"God"* remains to be justified,
since we have not officially formulated *P"God"*.

Mathematical Axioms/Tim Kirchner/8tkirchn@upper-merion.k12.pa.us

All code on this page is free. Please copy it at will.