We know a great deal about what is possible, so modal knowledge must be possible, not just in principle but by ordinary methods. Christopher Peacocke’s leading thought in Chapter 4 of Being Known is that this fact places significant constraints on philosophical treatments of modality. Modal realism is ruled out on the ground that it renders modal truth “radically inaccessible”, and actualism is forced upon us. It goes without saying that any account of the modal facts must eventually dovetail with (...) some account of how we know them. But Peacocke’s approach is animated by the thought that there is a mystery about modal knowledge—a transposed version of Benacerraf’s puzzle about mathematical knowledge under Platonism. Peacocke clearly believes that modal realism renders the problem intractable. But what exactly is the mystery in the modal case? And why exactly does modal realism preclude a solution? Peacocke himself does not say. The ‘access problem’ for modal realism is clearly decisive for him; but it is very much in the background. Nonetheless, for several reasons, it will help to start here. (shrink)

ABSTRACTThe paper explores Stephen Yablo's suggestion that ‘If-Thenism’ in the philosophy of mathematics is best formulated as the thesis that the real content of a mathematical claim C is the result of subtracting the potentially problematic metaphysical commitments of mathematics from C [Yablo 2017]. Yablo's proposal assumes that some propositions make others true. The present discussion assumes that propositions are coarse-grained sets of possible worlds and asks what Yablo's proposal looks like on that assumption. The conclusion is that the adequacy (...) of the proposal turns on hard-to-settle questions about the truthmakers for propositions expressed by material conditionals. (shrink)

This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...) and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink)

The deepest beliefs’ about personal identity whose consequences Unger seeks to draw out are the beliefs of those who already share his theoretical convictions; and his pain-avoidance’ experiments show nothing unless one already assumes those convictions. If there is a risk’ that I may not survive a brain operation even though I know exactly which chunks of brain will be removed and replaced, that shows that I am a separate thing from my body and brain, about which the latter provide (...) normally reliable, but still fallible evidence. (shrink)