Pure Logic and Higher-Order Metaphysics

Abstract

Abstract Quine famously defended two theses that have fallen rather dramatically out of fashion: first, that properties, relations, and propositions are “creatures of darkness” that ultimately have no place in respectable philosophical circles and, second, that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. Thanks both to formal developments in possible world semantics and concomitant philosophical developments in metaphysics, Quine’s first thesis has come as close to refutation as a philosophical thesis can. However, current trends notwithstanding, in this paper I argue that there are still good reasons to think that the battle for Quine’s second thesis is not yet lost. Specifically, in §1 I will argue that our most basic logical and semantical intuitions suggest that the correct framework for logic is first-order, type-free, and hyperintensional: properties, relations, and propositions exist alongside other things in a single domain of quantification; and propositions, in particular, have very fine-grained identity conditions. In §2 I will flesh out the formal foundations of a logic exhibiting these characteristics and, in §3, I will apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account I have defended here.