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Different types of logic are different paths that lead to the answer. And the truth is at the crossroads, waiting for the traveler. Can you go one way to the truth and not go the other if all roads lead to it?
It depends on the meaning of the word “logic”. If you mean logic as a mathematical discipline, then yes, there are different” types ” of logic, but the same premises in them produce the same result.
But there is also “logic” as a way to get a conclusion in the thinking of a single person. Everyone has their own logic, and what one person somehow proves, another can somehow refute.
For example: a person can believe that 2×2=5, and the way he proves this statement will be his personal logic. Within the framework of the other person's logic, this statement can be refuted.