Still Wondering about Contradictions

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As I understand it, a logical contradiction is the conjunction of a statement S and its denial not S. It is a proposition that implies two opposing conclusions S and not S. In a truth table, (P and not P) is always false.
P true implies (P and not P) false.
P false implies (P and not P) false.
If it is indeed a logical contradiction then would you say that it is true…
{P and not P) is always false and never true in a truth table.
If it is indeed a logical contradiction then would you say that it is true that it exists?
I don’t see existence questions coming into the picture as I pointed out above with the mathematical example which is logically true, even though the elements involved in the example do not exist in the real material world.
 
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I think it materially exists. That’s opinion though. Wasn’t there a man who described objects in motion as being in a place and not being in a place simultaneously?

I think we experience contradictions whether we understand them or not. I also don’t like how the system you’re using automatically assigns the value false to {p and not p} I don’t think it’s accurate.
 
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