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 :)
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
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".