How do we know the logic we use to logically infer is correct? What makes it correct? Why is "If X exists, then Y exists. X exists. Therefore Y exists." true?
Logic like mathematics is based on an axiomatic system, it is a formal system. Therefore, it is producing immanently tautologous propositions out of itself by its axioms. I am not sure if there has been a Kolmogoroff of all systems of logic exemplifying the axioms, though.