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As long as "our system" is defined as 3D spaced then it would be perfectly coherent mathematically as a lot of Cosmological theories contain different dimensions. Trying to conceptualize these different dimensions with our human experience though... LOL not going to happen.
Right, and I think the fact that we can't conceptualize something, is different than saying that conceptualizing it is impossible because it's nonsensical. Which is why I think that God's existence in space-time, however unfathomable, is not quite the same as the objection to a paradox.