I aim to understand whether apriority entails necessity, aposteriority entails contingency and conceivability entails possibility; that is, the relationship between, and the nature of, rationality and modality. The thesis is split into two parts: one on apriority and modality (chs. 2-4), and another on conceivability, apriority/aposteriority and modality (chs. 5 to 7).\ud \ud In Chapter 1, I discuss ‘two-dimensional modal semantics’, arguing that it is ill-equipped to provide a substantive account of rationality and modality, before setting out the basis of such an understanding.\ud \ud I begin the first part of the thesis (in Chapter 2) by outlining a preliminary account of the a priori: it is, strictly, not defeasible by empirical evidence; it involves a kind of necessity (‘rational necessity’); and it is (at least in its prima facie variant) fallible. In Chapter 3 I discuss the contingent a priori, arguing that genuine apriority entails necessity, before placing apriority qua ‘rational necessity’ (and ‘rational modality’ more widely) with respect to other kinds of modality (in Chapter 4). I conclude Part I of the thesis, by arguing that the a priori is not coextensive with, but is grounded in, metaphysical necessity.\ud \ud Part II of the thesis begins with a discussion of the necessary a posteriori (Chapter 5), where I argue that there are no genuine cases, thus aposteriority entails contingency and conceivability entails possibility. I then deal with Frege’s and Kripke’s puzzles (Chapter 6), which I claim (as with the necessary a posteriori) pose no genuine problem for conceivability-possibility reasoning. Finally (in Chapter 7), I offer a deeper account of rational modality together with a tentative account of metaphysical modality (and essence). I then conclude that genuine apriority qua rational necessity entails metaphysical necessity; similarly, strictly, aposteriority (rational contingency) entails metaphysical contingency and, (in)conceivability (rational (im)possibility) entails metaphysical (im)possibility.\u
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