Imagine there is an allmighty god. Inspired by the question of "what would make you as a rational person believe, that book X was written by God Y", I thought of this:

That book must present to me pi, as a fraction of 2 integers (in the decimal-system), which is, as far as I know, impossible.

I certainly know that different persons will have different opinions on this, depending on what they define as "God", but the question is, as I think, quite interesting.

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    Why do you think that's interesting? Could God make 1 + 1 = 3? That makes the same sense as your question, since pi is in fact irrational. Sep 7 '13 at 22:13
  • "Imagine there is an allmighty god". I might as well imagine that pi is rational; the result will be the same - a contradiction. Sep 7 '13 at 22:13
  • Oh that's interesting. I can imagine there's an almighty god far more easily than I can imagine that pi is rational. Sep 7 '13 at 22:17
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    Is there any chance you might be able to share a little more about what you might have been reading or studying that has made this an interesting question or concern for you? What hypotheses have you formed? What has your research turned up so far?
    – Joseph Weissman
    Sep 8 '13 at 14:13
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    I suppose one way we might rephrase this question to make it mathematically tractible would be "to what extent does the proof of the irrationality of pi rely on properly transfinite mathematics, and to what extent is the stability of this theorem dependent on hypotheses or axioms in higher set theory". God might have something to do with this, in that he represents something like "truth in some particular very very high set theory".
    – Paul Ross
    Sep 8 '13 at 18:02

Imagine there is an allmighty god

If an almighty god is some entity which can cause any proposition to be the case, then if such a god existed it would be possible for it to express pi as the ratio of two integers. I would take that to be a pretty strong argument against such an entity existing, but I imagine there have been views to the contrary historically.

If an almighty god is some entity which can cause any possible proposition to be the case, then since it is not possible to express pi as the ratio of two integers such an entity would not be able to do so.

So yes, the answer relies on what you think an almighty god is. But not in an especially novel or interesting way, in my opinion.


If there is a God, it is conceivable that God created the universe and all of its physical laws. Most people are able to comprehend this bit quite easily.

What is harder to conceive, is the possibility that if there is a God, not only did he create the physical universe and all of its laws, but also that he could have created the abstract universe of logical reasoning and mathematics. If this is so, then it is conceivable that outside of our universe, in the realm where God dwells, that he could easily create a new universe that is not bounded by a current laws of logic and reasoning that was created by God.

God could thus express Pi however he wanted, by altering the laws of logic in a particular universe, or creating a new universe with new laws of logic, and expressing Pi in whatever form he wishes.

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    I think this misses the mark entirely. In some other particular universe with new laws of logic etc., there is no mapping from our reality to that one. IF the logic of this universe doesn't apply to that universe THEN er... um... hmmm... Sep 8 '13 at 19:32
  • I agree the person who asked the question was not thinking along the lines of me. However I am providing this answer as an alternative to dbmag9's, who considers the argument to be one against the existence of God. I'm saying it is possible that God created our laws of logic, and is thus not bounded by them.
    – Kenshin
    Sep 9 '13 at 1:45
  • The difficulty with this approach is that if there is a being that is not bound by logic, then it is not possible to reason about this being. You might say "God is almighty" and I might say "Well, IF that is so THEN..." and you might as well say "sorry, no such logic applies, you just have to trust me". Sep 9 '13 at 1:52
  • Yes that difficulty could apply, but there is still no contradiction with say the christian God, who does say you should believe in him through faith/trust. But I agree if there is a God, you wouldn't be able to apply our wordly/universal reason to understand or deduce it.
    – Kenshin
    Sep 9 '13 at 3:32

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