Yablo's Paradox in Second-Order Languages: Consistency and Unsatisfiability

Picollo, Lavinia (12. October 2012): Yablo's Paradox in Second-Order Languages: Consistency and Unsatisfiability. In: Studia Logica, Vol. 101, No. 3: pp. 601-617

Abstract

Stephen Yablo introduces a new informal paradox, constituted by an infinite list of semi-formalized sentences. It has been shown that, formalized in a first-order language, Yablo's piece of reasoning is invalid, for it is impossible to derive falsum from the sequence, due mainly to the Compactness Theorem. This result casts doubts on the paradoxical character of the list of sentences. After identifying two usual senses in which an expression or set of expressions is said to be paradoxical, since second-order languages are not compact, I study the paradoxicality of Yablo's list within these languages. While non-paradoxical in the first sense, the second-order version of the list is a paradox in our second sense. I conclude that this suffices for regarding Yablo's original list as paradoxical and his informal argument as valid.

• Item Type: Journal article
• Keywords: Paradoxicality, Consistency, Ω-Inconsistency, Second-order languages, Unsatisfiability, Finiteness
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic
• Subjects: 100 Philosophy and Psychology > 160 Logic
• ISSN: 1572-8730
• Language: English