  \(\dq{\vee}\) and \(\dq{\ddagger}\) will count as logical constants, because their sense-constitutive rules are purely inferential, while \(\dq{\dagger}\) will not, because its rules are not. (In the same way we can distinguish \(\dq{\exists}\) from \(\dq{W}\).) Note that appropriately rewritten versions of \(\refp{or-intro}\) will hold for \(\dq{\ddagger}\) and \(\dq{\dagger}\); the difference is that one can grasp \(\dq{\ddagger}\) and \(\dq{\dagger}\) (but not \(\dq{\vee}\)) without finding these rules primitively compelling (Peacocke 1987, 156; cp. Sainsbury 2001, 370–1).