If God is all-powerful and can do anything and everything, can he build a wall high enough so that he could not jump over it?
No. The God of the Bible is incapable of numerous things. Essentially, all of these things are summed up in 2 Timothy 2:13 which states that God "cannot deny Himself".
The God of scripture is a logical God, which is the only reason why the laws of logic, such as the law of non-contradiction, can be trusted to be universal and invariant. For worldviews that do not believe in a logical God who "cannot deny Himself", such as atheism for example, there is absolutely no basis for believing that the laws of logic are invariant and universal.
In other words, in atheism, there is no legitimate reason to believe that tomorrow the law of non-contradiction will be valid. Perhaps tomorrow, something could be alive and not alive at the same time and in the same way. The atheist has no legitimate reason to deny this possibility, because he has never been to tomorrow, and he has no authority upon which to rest his unfounded and naive belief that the law of non-contradiction will not suddenly become invalid.
Additionally, within atheism there is no reason to believe that, in other solar systems, the law of non-contradiction holds true. After all, we have never been to other solar systems, and, in atheism, there is no "word of God" telling us that the law of non-contradiction is universally valid. Therefore, in atheism, we would have no basis upon which to claim that this law is universally valid.
In short, in worldviews that deny the existence of a logically non-contradictory God, there is no basis to believe in the universality or the invariance of the laws of logic.
And, if there is no basis to believe in the laws of logic, there is no basis for knowledge itself. One cannot really know anything at all if it is even remotely possible that the laws of logic are not universal or invariant. You believe that 2 + 2 = 4? Well, if the laws of logic cannot be trusted as universal and invariant, that simple mathematical equation could be both true and false at the same time and in the exact same way! Or it could be true today and false tomorrow! Or it could be true today, but not have been true during the time of Christ! If we accept that we cannot know anything at all (which we would be forced to accept if we reject the idea of a logical God), not only must we reject all possibility of knowledge, but we must also recognize that science too becomes impossible.
In order for us to accept the claims of science, we must either do so on total and absolute blind and even superstitious faith, or else on the basis of the existence of a logical God.
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