Relevance of paradox in life?

Question: Relevance of paradox in life!?
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(One definition of a paradox is a statement or proposition seemingly self-contradictory or adsurd but in reality expressing a possible truth!.)
I would think that as a person works through solving an issue, logic plays a significant role in trying to determine whether something could be basically true or false, doable or impossible!.
A classic question comes to mind: is time travel possible!? While trying to determine the answer to this question, one can pose a situation that explores the plausibility of such travel: If I travel back into time and kill my grandfather, such action would prevent my birth, and as such, I would not exist!. If I never existed, could I have performed time travel!? This paradox would seem to disprove or validate that time travel is indeed not possible!. Yet, if the situation is taken a step further, one can still offer alternative or additional information that prevents one from definitely disproving the question!. For example, if upon killing one's grandfather or otherwise cause action to prevent one's own creation in the future, then perhaps this would skew time and create an alternative future universe!.!.!.
So now, this developement or discovery of a paradox now dictates one must consider alternative out-comes or information to prove, or at least continue to support, that time travel is still possible!. In other words, a paradox does not disprove a question, but it does prove that for the question to be true, the scope of the issue must change, or the out-come must be modified for the question to still be true!. In the time travel example, the isue now has to undergo a change in assumptions, out-come or new information developed to continue on the path of proving time travel is still possible!.
The relevance of paradox!? IMO, it serves to steer one to refine their information, sometimes refine the question, or otherwise modify their logical approach to a question!. It juices the power of pure logic, and oftentimes aids one in closing in on the possibility of something being true by eliminating certain avenues of lines of thought!. In shorter form, a paradox helps hone in on the true of false answer!.

Thanks for a great question!!

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