If God doesn't exist then what are the foundations of logic?

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Same as they are if God does exist. The idea that God (if such there be) has control over truths of math and logic is one that a few philosophers have argued for (Descartes, for instance, if I'm not mistaken) but even staunch believers in omnipotence typically understand omnipotence in a way that doesn't call for the puzzling idea that God could change the laws of logic. Briefly, the view of many theists would that God can perform any logically possible task.

One reason for saying that is that logical "constraints" help us make sense of what omnipotence might mean.Why anyone would want more is hard to fathom. Suppose someone asked God to light up a set of pixels on an infintely high-resolution screen so that these pixels made a figure that was perfectly round and perfectly square. What would count? Is there actually a genuine task to be done here? If not, then it hardly seems to be a limitation on God's power (or anyone else's) that s/he can't complete the task.

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