Logic and omnipotence
Posted by Martin Orr on Wednesday, 20 September 2006 at 16:51
This is something I have considered before from a mathematical logic perspective, but never really from a theological one. In consideration of the existence of pain in a world created by a loving God, it is often asserted that this is an inevitable consequence of free will (or at least of having multiple agents of free will). However why should it be inevitable? If we assert the omnipotence of God, then we must accept that God is capable of creating a world in which there are multiple agents of free will and no pain.
However that's not really the question I am interested in. This is: Is God bound by our conceptions of logic? In mathematical logic, we make a few basic rules called axioms such as:
If (A and B) is true, then A is true.
Facts are then accepted as true if they can be deduced using these axioms. By starting with different axioms, it is possible to create different systems of logic; for example, some people reject the law of the excluded middle which says:
Either A is true or (not A) is true.
Nevertheless, in trying to proof facts about what makes these logical systems different from each other, we are forced to fall back on our intuitive rules and especially on modus ponens:
If A is true and (If A then B) is true, then B is true.
When I claimed above that believing "Multiple agents of free will implies pain" is a restriction on divine omnipotence, I was creating such a restriction myself by assuming that God was bound by something at least vaguely resembling the logic we are used to.
Does the above: prove that omnipotence is possible; prove that omnipotence is a paradox; contain unsound reasoning; or avoid properly answering the question?
-- Martin