Mathematics and Ethics

Several philosophers have recently been seeking analogies between mathematics and ethics. For example, Brendan Larvor (University of Hertfordshire) has given talks on 'Particularism and the exact sciences', stressing how both the mathematician and the moral agent cannot rely on general principles to conduct their reasoning, and Jim Franklin in his On the parallel between mathematics and morals argues that relativist objections to an objectivist ethics would work equally well against an objectivist mathematics. For both of these philosophers, the important parallels between mathematics and ethics do not support the mathematicisation of ethics. Indeed, Franklin makes the interesting observation that: "It is a strange fact that whereas objectivist ethics has tended to avoid mathematics, reductive attempts to replace ethics by something else have been highly mathematical." (p. 109)

Time and again, I'm struck reading Alasdair MacIntyre's writings on ethics, by the parallels between his account of moral enquiry, and my account of mathematical enquiry. For example, the final sentence of 'The Magic in the Pronoun "My"', a review of Bernard Williams, Moral Luck (CUP, 1991) in Ethics 94: 113-125 (available on JSTOR),

although premature systematization is always the enemy of truth in philosophy, delaying systematization for too long can be equally injurious. (p. 125),

perfectly encapsulates the conclusion of chapter 7 of my book, in which I criticise Lakatos for overemphasising the equivalent of the first half of MacIntyre's sentence at the expense of the second half.

As for the quest to understand Lie algebroids, Kirill Mackenzie has dedicated a page to them, and has made available the very interesting Introduction to his forthcoming book 'General Theory of Lie Groupoids and Lie Algebroids', Cambridge University Press.