Fregean predication

My aim in this paper is to offer a novel justification for β-Equivalence. β-Equivalence is a standard principle of higher-order logic, but it is metaphysically controversial. My argument for β-Equivalence is based on a distinctively Fregean conception of predication. I argue that the Fregean conception motivates a non-standard notation for predicates, which can then be used to show that β-Equivalence is trivial on the Fregean conception. I also argue that the Fregean conception motivates a functional individuation of properties, which we can use to extend the Fregean justification for β-Equivalence to cover a more general principle, β-Conversion.