?How Weak Axioms Can Prove A Non-Self-Referential Paradox

We introduce a weak non-arithmetical theory in a language of predicate logic and give proofs for various versions of Yablo’s paradox in this weak system. We prove (Always) Yablo’s paradox and its dual version, called Sometimes Yablo’s paradox, using our weak axiom system that is much weaker than arithmetical setting. Also, we discuss circularity of Yablo’s paradox in our weak system consisting of three axioms in which no diagonal lemma nor recursion theorem are used