## Infinities and the Concept of Omnipotence

Posted by Michael Dickens on November 27, 2008

(This is an essay I wrote for school as a response for the first two chapters of *Mystery of the Aleph* by Georg Cantor. I ended up writing about omnipotence. I thought this was worth posting.)

Mystery of the Aleph: chapters aleph null and one

In the first chapter of The Mystery of the Aleph, it is described how Georg Cantor was working on the “continuum hypothesis” for the later years of his life. This hypothesis consisted of a single equation: 2^aleph null = aleph one. This problem, combined with a possible genetic disease, drove Cantor to insanity, and he was institutionalized many times.

The second chapter discusses Pythagoreans, and the first notions of infinity. The Pythagoreans discovered irrational numbers through the Pythagorean Theorem, and kept it a well-guarded secret. They practically went insane because of irrational numbers.

Later on, infinity was further explored and understood. The last sentence mentions that infinity was brought up in the medieval ages, in the form of religion. It is not elaborated, but it seems like this is referencing the supposed omnipotence of God. He is all-knowing and all-powerful, hence infinity.

This led me to think of a joke question: can God make a rock so big that he himself cannot lift it? I began to ponder the true meaning of this. What this really is is infinity minus infinity. The rock weighs X, and God’s strength is Y. So if X – Y is greater than one, He cannot lift it. And if X – Y is zero or less, he can lift it. So that raises the question, what is infinity minus infinity? A little bit of research turned up two possible answers: either it’s zero or it’s undefined. So that means either God can lift it, or we don’t know. But is that really true? If your strength is Y and an object weighs X and X = Y, wouldn’t that mean that you can lift it, but it takes an infinite amount of time? This is truly a difficult question that there is to straight answer to. Here’s the straight answer: it is not logically possible, much less physically so, to be all powerful.

## Phynnboi said

“…can God make a rock so big that he himself cannot lift it?”

What if God splits into two versions of himself, one unable to lift the rock and the other able to do so, and the two versions are able to coalesce at will? More generally, what if God is non-deterministic and can therefore be in multiple states at once through some mechanism?

## mtgap said

Well yes. You can always say that God does not follow the rules of logic as we know them.

But I think that’s still flawed. The definition of all-powerful follows the rules of logic. So to be all-powerful as defined by logic, you must follow the rules of logic. (Does my logic work?)