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I remember reading a brief note in Scientific American years ago about a mathematician/physicist who had published a paper that formally stated that no entity could both participate in a given system and simultaneously know all information about that system. His conclusions were not particularly ground breaking for the physics/math community since he did little more than apply Godel's Theorem to physical systems but he did generalize his results for any conceivable entity in any conceivable system irrespective of number of dimensions etc.

After I realized that the article formally proved the impossibility of omniscience, I wanted to be able to refer to it. Sadly, I did not think to clip this little article from the magazine when I read it and I have never since been able to find anything on the subject.

Does anyone know of such a formalism or paper drawing this conclusion?

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This has a pretty large problem, however: We don’t know if Goedel’s theorem actually applies to nature, i.e. if nature follows the rules put into place by man-made logic. And since we cannot gather experimental proof whether logical rules apply or not, we don’t know. –  Claudius Oct 11 '12 at 18:01
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More on Godel's Incompleteness Theorem: physics.stackexchange.com/q/14939/2451 –  Qmechanic Oct 11 '12 at 18:23
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I don't know the article, but if you know the argument for Godel's theorem, it's simple enough to reconstruct the argument that surely appears there. If you have an omniscient entity you can talk to and query in finite time, you can write the following program:

  1. Print's it's code into a variable R.
  2. Asks the omniscient entity whether the code "R" will print "hello" or "not hello"
  3. does the opposite.

If you make the omniscient entity a computer program, this proves Turing's theorem. If you make the omniscient entity an axiomatic system, this proves Godel's theorem. If you make the omniscient entity a divine being, this proves that either you can't get answers from the divine in finite time, or else you can't formulate step 2, "code R queries the divine entity" in any reasonable way.

The anti-omniscience sentiment can be captured in the religion of Maimonism, whose fundamental tenet is the following:

  • Fundamental tenet of Maimonism: God is omniscient, but unfortunately for Maimonism, God doesn't agree with it's fundamental tenet.

There's a problem for God now, in that God can't have a consistent opinion about the fundamental tenet of Maimonism. This is the same argument, except making a gloss without the detailed construction.

The argument against omniscience is weak, because it only proves no omniscience in finite time. God is generally understood to be an asymptotic entity, only partly revealed, in most religious faiths. The omniscience is a property of the limit of infinite time, not of any finite time state. No religion that I know claims that its revealed truths are the complete word of God, rather, the revelation is gradual, as new trials reveal new acts of faith and so on.

This isn't physics, and there is a near duplicate of this on philosophy, but philosophy is disfunctional, and has little chance of improving.

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I'm not sure if your logic is flawless. A omniscient entity could lie to the program and still know the exact outcome. –  A.O.Tell Oct 11 '12 at 19:15
    
I'm confused as to why the entity couldn't tell if its code writes "hello" or "not hello" and I'm also confused why "does the opposite" is relevant, or who would be doing it. –  AlanSE Nov 2 '12 at 16:23
    
@AlanSE: Because the code simulates the entity, finds the predicition regarding itself, and then does the opposite. This is the template for proving Godel's theorem, as discussed here: physics.stackexchange.com/questions/14939/… . –  Ron Maimon Nov 2 '12 at 16:46
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