From an essay by Rabbi Nosson Weisz
Human beings can only make sense of the world they see around them by filtering the information presented by their senses through the intellectual lenses provided by their cultures. Living through events doesn’t guarantee that we see them in the proper perspective.
The idol worshipper lives in a physical world that exists separately from the beings that he worships. His Gods cannot tamper with the fundamental rules of reality. Plato sincerely felt that even God could not make the sides of a square equal to its diagonal. He did not feel that he was imposing a limitation on God’s power when he made this statement. His God was a part of the same reality as his own and therefore was also subject to the rules and limitations imposed by logic.
When a person’s cultural background teaches him that there cannot be miracles that violate natural law, he can actually experience the splitting of the sea and not see it for what it is. He will think that there must be some natural explanation. For him the miracle can never happen even when it happens. This principle is behind the spiritual rule we have developed in this essay; for such people the miracle of splitting the waters cannot happen by definition. Anyone who cannot see a miracle even when he experiences it never experiences it. He can easily drown in the sea that has been miraculously parted.
“Plato sincerely felt that even God could not make the sides of a square equal to its diagonal.”
It appears that the Rambam agrees with Plato on this matter:
“That which is impossible has a permanent and constant property, which is not the result of some agent, and can not in any way change, and consequently we do not ascribe to G-d the power of doing what is impossible. No thinking man denies the truth of this maxim; none ignore it, but such as have no idea of Logic…. Likewise it is impossible that G-d should produce a being like Himself… to produce a square whose diagonal is equal to one of its sides….
We have shown that according to each of these theories there are things that are impossible, whose existence cannot be admitted, and whose creation is excluded from the power of G-d, and the assumption that G-d does not change their nature does not imply weakness in G-d, or a limit to his power.”
Moreh Nevuchim 3:15
(Taken from a blog post on this topic by R’ Micha Berger, at http://www.aishdas.org/asp/2005/07/hashem-and-logic.shtml)