Abstract This book explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. It argues that our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified. It is also incorrect that reflection on the “genealogy” of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral anti-realist on the basis of epistemological considerations, then one ought to be a mathematical anti-realist too. And yet, the book argues that moral realism and mathematical realism do not stand or fall together – and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense in which mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. It follows that the concepts of realism and objectivity, which have been widely identified, are actually in tension. The author concludes that the objective questions in the neighborhood of questions of logic, modality, grounding, nature, and more are practical questions as well. Practical philosophy should, therefore, take center stage.
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