This chapter examines the debate between advocates of classical logic and advocates of intuitionistic logic. It examines the semantic and epistemic issues on which this debate is usually conducted. After introducing the idea that logic is a model of correct reasoning, the chapter explores the viability of a logic intermediate between classical and intuitionistic.

The Yablo Paradox The Yablo Paradox implies there is no way to coherently assign a truth value to any of the sentences in the countably infinite sequence of sentences, each of the form, “All of the subsequent sentences are false.” Specifically, the Yablo Paradox arises when we consider the following infinite sequence of sentences: The … Continue reading Yablo Paradox →.

The proper translation of "unless" into intuitionistic formalisms is examined. After a brief examination of intuitionistic writings on "unless", and on translation in general, and a close examination of Dummett's use of "unless" in Elements of Intuitionism (1975b), I argue that the correct intuitionistic translation of "A unless B" is no stronger than "-B -> A". In particular, "unless" is demonstrably weaker than disjunction. I conclude with some observations regarding how this shows that one's choice of logic is methodologically prior (...) to translation from informal natural language to formal systems. (shrink)

Volume 40, Issue 2, May 2019, Page 204-205.

_Essays on Paradoxes_By HorganTerenceOxford University Press, 2016, xii + 322 pp.