God vs Set theory

[ydoaPs]

Someone I know only over the internet came up with the following argument:

 

Let A the set of all actions that God can do.

 

If S is any subset of A, let T(S) be the action "God simultaneously thinks about reasons for doing the actions contained in S". This is another action, thus an element of A, since God can do all logically possible action. Different S lead to different T(S).

 

Thus the set of all T(S) - where S ranges over all subsets of A - is a subset of A, thus at most of the same cardinality of A.

 

But the set of all subsets of A - aka the power set of A - has strictly larger cardinality than A itself *). Yet the mapping S -> T(S) would embed it 1-1 in A. Contradiction.

 

Conclusion: Omnipotence is an inconsistent concept.

 

 

*) by Cantor's Power Set Theorem.

 

Regards,

HRG.

 

It seems like a fairly decent argument against omnipotence. Thoughts? Rebuttals?

[lemur]

I think I'd have to be a god to decode this level of formalism into language I could comprehend and process.

[pioneer]

For one thing logic is 2-D or based on cause and effect. That 2-D proof may not fly in 3-D.

 

Let me give an analogy. Say 2-D thought occurs on a thought plane. Then 3-D thought would be on an 3-D ball. The movement of logic on the 2-D plane may add up logically, but if the process was done in 3-D, one can tweak that plane by compressing the ball, so it will appear illogical on that plane, but nevertheless by valid within the ball.

 

As a more practical example, say we have democrat and republican. Both contain truth, but since the truth is distributed over the two orientations, a logical tweak with the full data set could result in a conclusion neither would reach with only their half of the data.

 

Say the Democrats use the red data points containing all shades of red. The Republicans use the blue data points and all shades of blue. Each will reason on their logic planes using that data. The more 3-D approach uses all the data, both the red and blue. The conclusions will be different and may not follow logically from either logic plane. The conclusion may say purple, yet purple will not follow logically from either logic plane which only has red or blue. That math proof assumes god uses 2-D. All that logic proves is God is not 2-D. What appears out of place in 2-D, can still be in the the right place in space and time, if the logic is 3-D or 4-D, since the data set includes data that will only appear in the future.

 

Here is another example. Say you went back into time 100 years knowing what you know today. You could come to conclusions that would make you appear like a witch, since the data and even the precedent that you know to be true, has not been established yet to them. You might be right, but everyone would say you were wrong based on their logic and data. They would have to use faith to believe what is true, but the skeptical will have no faith and will demand proof in their own terms and limitations. Since there is a 100 year wall between you and them, you would need to go backwards to their level of understanding and try to start the tweak based on the next logical step in thinking from 100 years ago. But you don't have 100 years to ween them. So you jump 10 years ahead, to create an intuitive connection with some but without the proof du jour. You still look like an idiot, with the logic of the day saying this proves nothing. God's job is not easy when there is a wall between 4-D and 2-D.

 

Theoretically, God can step out of time, such that future data is part of the logic of the present. This data is not on the present data plane and may not be considered a logical extrapolation of the data, yet at another level it follows very logically. Only the future can see.

[Mr Skeptic]

How many gods does it take to think about thinking about [...] thinking about changing the lightbulb?