Justin Clarke-Doane*  Morality and Mathematics.

Abstract

This excellent book compares and contrasts morality and mathematics. Their similarities and differences are not what one might naïvely suppose, as the author demonstrates. The book is highly recommended to philosophers interested in both subjects, and to anyone who seeks a global understanding of how morality and mathematics fit into our belief system. In Chapter 1 the reader is introduced to the author’s understanding of two key terms: realism and objectivity. One overarching opinion presented in this book is that these notions are in tension, and here the motivation for this view is put forward. First, a general recipe for a ‘realist’ view of some subject matter F is devised, with candidate ingredients being examined one by one before being either included or rejected. In the end, the author advocates an understanding of ‘F-realism’ as the view that F-sentences should be interpreted at face-value, that they are commonly used to express beliefs and typically have truth values, that some atomic F-sentences (not merely tautologous compounds) are true, and finally that the F-truths hold independently of mind and language. Surprisingly, among the ingredients rejected by Clarke-Doane is objectivity. Though he denies that the term is being used here in a revisionary or technical sense, he also wishes to deny that ‘objectivity’ should be taken to mean the same as either intersubjectivity or mind-independence. Rather, objectivity here just means a kind of anti-pluralism: we can call the answer to a question an objective one just in case that answer is uniquely correct. Now the idea of treating a matter as objective just in cases where there is only ‘one right answer’ seems, at first blush, to accord with common usage. It is only when the author begins to push on this line that it shows itself to be rather more radical. To use his own example: it is not an objective matter whether the parallel postulate holds (as a pure mathematical conjecture), even if robust platonism is true, since it is true in Euclidean space but not in hyperbolic space (or rather, true of Euclidean lines, but not of hyperbolic lines). There is thus not a unique right answer to the question ‘Is the parallel postulate true?’ To go in for an illustrative moral example, error theorists about morality could plausibly be called moral objectivists (though importantly, not realists) in Clarke-Doane’s sense, given that they give one and only one answer — namely, ‘no’ — to any question at all of whether something is right, wrong, good, bad, etc. The idea of separating the notions of realism and objectivity, if cogent, is clearly one with a great deal of potential, ripe for application to more diverse areas of philosophical dispute. In one light, the present monograph might be seen as a proof-of-concept for a more general metaphilosophical project, the broader horizons of which are sketched in the Conclusion.