Against Second-Order Logic: Quine and Beyond

Is second-order logic logic? Famously Quine argued second-order logic wasn’t logic but his arguments have been the subject of influential criticisms. In the early sections of this paper, I develop a deeper perspective upon Quine’s philosophy of logic by exploring his positive conception of what logic is for and hence what logic is. Seen from this perspective, I argue that many of the criticisms of his case against second-order logic miss their mark. Then, in the later sections, I go beyond Quine to develop a novel case that quantification into polyadic predicate position, understood as requiring quantifiers to range over relations, isn’t intelligible.