The debate between exceptionalists and anti-exceptionalists about logic is often framed as concerning whether the justification of logical theories is a priori or a posteriori (for short: whether logic is a priori or a posteriori). As we substantiate (S1), this framing more deeply encodes the usual anti-exceptionalist thesis that logical theories, like scientific theories, are abductively justified, coupled with the common supposition that abduction is an a posteriori mode of inference, in the sense that the epistemic value of abduction is (...) (and, indeed, must be) a posteriori. In past work, however, we have argued that this common supposition is incorrect: abduction is an a priori mode of inference, in the sense that the epistemic value of abduction is (and indeed, must be) a priori (Biggs and Wilson 2017a, 2017b, 2019). After sketching our two main argumentative strategies for this conclusion (S2), we go on (S3) to consider its import on the proper understanding of anti-exceptionalism about logic. (shrink)

Two related claims have lately garnered currency: dispositional essentialism—the view that some or all properties, or some or all fundamental properties, are essentially dispositional; and the claim that laws of nature (or again, many or the fundamental ones) are metaphysically necessary. I have argued elsewhere (On the metaphysical contingency of laws of nature, Oxford University Press, Oxford, 2002) that the laws of nature do not have a mind-independent metaphysical necessity, but recent developments on dispositions have given these ideas a new (...) vibrancy and made them the topic of more focused discussion. So I would like to revisit this, arguing that the new work, as interesting and important as it is to our understanding of fundamental properties, powers and dispositions, should not change our minds about metaphysical necessity. One should still think necessity is conceptually or conventionally grounded. I do not argue that laws of nature are not necessary, nor that properties do not have dispositional essences, but only that if these are the case, then, like other de re or empirical necessities, they have no metaphysical weight and are based in our rules or decisions about how to talk about the world. We may have excellent reasons to talk and think in this way—but these reasons do not include, require or provide evidence of mind-independent metaphysical necessity or essences. (shrink)

Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...) vindicates Countabilism. Our discussion dovetails with recent independently developed treatments of CT in Meadows (2015), Pruss (2020), and Scambler (2021), aimed at establishing the mathematical viability, and therefore epistemic possibility, of Countabilism. Unlike these authors, our goal isn't to vindicate the mathematical underpinnings of Countabilism. Rather, we aim to argue that, given that Countabilism is mathematically viable, Countabilism should moreover be regarded as true. After clarifying the modal content of Countabilism, we canvas some of Countabilism's many positive implications, including that Countabilism provides the best account of the pervasive independence phenomena in set theory, and that Countabilism has the power to defuse several persistent puzzles and paradoxes found in physics and metaphysics. We conclude that in light of its theoretical and explanatory advantages, Countabilism is more likely true than not. (shrink)