In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions (...) between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems. (shrink)

Modal rationalism is the claim that for all p, if it is ideally conceivable that p, then there is a metaphysically possible world, W, in which p is true. This will be true just if there are no strong a posteriori necessities, where a strong necessity (for short) is a proposition that is conceivably false, but which is true in all metaphysically possible worlds. But are there any strong necessities? Various alleged examples have been proposed and argued over in the (...) literature, but there is no consensus on whether any is genuine. In this paper, I aim to move the debate forwards by proving that there are in fact no strong necessities. I argue that there are no strong necessities because they are impossible; they are impossible because the very notion of a strong necessity is – despite prima facie appearances – ultimately incoherent. Thus, I argue, it is an a priori truth that there are no strong necessities, and that modal rationalism itself is true. (shrink)