Sanggu Lee
Syracuse University
Philosophical orthodoxy has been that second-order quantification is unintelligible without reference to first-order quantification over properties, sets, or linguistic expressions. However, the idea of sui generis second-order quantification has received increasing support. Following the pioneering work of Prior (1971) and Boolos (1975), Rayo and Yablo (2011), Williamson (2003; 2013), Wright (2007), and Krämer (2014) think that second-order quantification is neither objectual nor substitutional. It is sui generis in the sense that it is irreducible to first-order quantification.
Cameron 2019 argues against Quine’s criterion of ontological commitment using sui
generis second-order quantification. The argument is stated in the following inconsistent triad: (Q) Quine’s criterion of ontological commitment is true, (R) reality is independent of us, i.e.,ontological realism is true, and (S) second-order quantification is sui generis. If Q, R, and S are incompatible, we must abandon one of them. Given that ontological realism is arguably uncontroversial and sui generis second-order quantification is assumed, Cameron argues, Quine’s criterion of ontological commitment has to go.
In this paper, I argue that Cameron’s argument fails. After presenting Cameron’s argument, I suggest two possible Quinean responses to the dilemma. After presenting Cameron’s dilemma (section 2), I offer two responses to the dilemma. One response is to deny a premise of Cameron’s argument for the dilemma (section 3). The other response is to introduce a new regimentation principle (section 4). The upshot is that the Quineans do not have to give up their criterion of ontological commitment while accepting sui generis second-order quantification.
Chair: Gabriel Levc
Time: September 8th, 15:20-15:50
Location: SR 1.006
SOPhiA 2026 