Proving a Universal Negative: Aristotle's Principle of Non-contradiction and Transcendence vs. Omnipresence

"If a damsel that is a virgin be betrothed unto an husband, and a man find her in the city, and lie with her; Then ye shall bring them both out unto the gate of that city, and ye shall stone them with stones that they die; the damsel, because she cried not, being in the city." (If a woman does not cry out loud enough for someone to hear her while she is being raped, she is to be stoned to death.)

-Deuteronomy 22:23-24

This should hopefully be a short post. A long time ago, back before disco was popular, there was this dude named Aristotle. He figured out that you can't both be something and not be that same something at the same time, meaning the properties you have can't contradict themselves. For example, you can't be a married bachelor, because the term "bachelor" requires that you not be married. You cannot be both married and not married at the same time (I'm sure there are ways around this...don't bring them up ahaha). The point is, he realized that you can't have property A and also not have property A at the same time. This was titled "Aristotle's Principle of Non-contradiction" and he gets all kinds of credit for something that should be obvious. This does actually provide an important premise in disproofs of certain gods, however. For example, God is often referred to as "transcendent" and "omnipresent," however it can be shown that these two properties are mutually exclusive. That is, a being cannot satisfy both conditions, and therefore a god that is both transcendent and omnipresent cannot exist.

P1: If God exists, then he is transcendent (i.e., outside space and time).
P2: If God exists, then he is omnipresent.
P3: To be transcendent, a being cannot exist anywhere in space.
P4: To be omnipresent, a being must exist everywhere in space.

C1: Hence, it is impossible for a transcendent being to be omnipresent (from P3 and P4).
C2: Therefore, it is impossible for a transcendent omnipresent God to exist (from P1, P2, and C1).

This is a mostly trivial example, not very earth-shattering, but it is a good example to illustrate the Principle of Non-contradiction. A being cannot be simultaneously everywhere in space and nowhere in space and time/outside of space and time. Whether you are a theist or an atheist, this holds true. Whether you are a theist or an atheist, next time you hear someone say their god is both omnipresent and transcendental, call them on it!

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