# Mathematical "Axioms"

## by Tim Kirchner and Sujan Kapadia

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 :)

### Axiom of Consistency

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.

### Axiom of Self-Evidence (Axiom of Mathematical Duh)

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:
One cannot find a better method of proof.
One cannot find a disproof.

### Theorem of Existence (Yes, this IS justified)

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

### Corrolary to the Theorem of Existence

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.

### Axiom of Life (Postulate #42)

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".

Last updated May 1, 1997
Mathematical Axioms/Tim Kirchner/8tkirchn@upper-merion.k12.pa.us