We use logic to analyze concepts that refer to truth. The question is: Can we prove the truth using logic? Sad as the answer may be. We can't prove the truth through logic, for the simple principle that if logic determines that a proposition is false, then between this duality we can create another proposition p1 related to p, forming the duality p1 and within this duality we can form another logical bridge p1x1 and so on, so it's impossible to determine all the relevant proofs about a given proposition.
While it is clear that it is not possible to determine all the implications in all cases, and in all possible analyses, it is possible with infinite physical property to determine the main points of what the truth is, even if it is not total and can be broken down into other particles related to the initial particle, or any of the particles that are created have the possibility of denying the truth.
In other words, if we define a proposition p to be true, and its negation ¬p ompletes our view of it. Logic is used because there is no other comprehensive way of getting closer to the truth.
We use logic but in the knowledge that there are limitations on it, and every time logic violates existence, then we are in a paradox in which we will return to the universal axiom.