Mathematical Ethics

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Mathematical Ethics

Philosophers since antiquity have argued the merits of mathematics as a normative aid in ethical decision-making and of the mathematization of ethics a theoretical discipline. Recently, Anagnostopoulos, Annas, Broadie and Hutchinson have probed such issues said to be of interest to Aristotle. Despite their studies, the sense in which Aristotle either opposed or proposed a mathematical ethics in subject-matter and method remains unclear. This paper attempts to clarify the matter. It shows Aristotle’s matrix of exactness and inexactness for ethical subject-matter and ethical method in the Nicomachean Ethics. Then it probes a resultant puzzle from the matrix, namely, the HL model of the happy life without consideration of mathematical justice (Bk. III) and the HJL model of the happy life with such consideration (Bk. V). Finally, it examines Aristotle’s twofold rationale for differentiating these two models in his overall moral feedback loop system: differences in the intellectual virtue of good deliberation; the priority of friendship over justice for the happy life. This suggests Aristotle saw no objection either to using mathematics as an aid to ethical decision-making for a happy life, or to mathematizing at least some parts of an ethical theory of eudaimonism.

I. The problem of math ethics in modernity and antiquity

Mathematizing ethics to become scientific ethics has long been a dream of some philosophers, dating to both the Academy and perhaps the Lyceum. In modern philosophy Jeremy Bentham, (1) G.E. Moore, (2) and Nicholas Rescher (3) have tried to mathematize ethics. Such mathematizations square with Quine's view that mathematizing inexact things by way of exact methods marks a successful reduc...

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...participants. It misses the mark methodologically, or, as Broadie likens it, it is "playing at ethics" or even a "perversion." It is, as Aristotle sees in the Nicomachean Ethics, a deception, since the underlying longitudinal assumption is that someone thinks they can become good by talking about the good without doing good and without being impacted by doing what they have chosen in a moral feedback loop system. (1105b 13-17) Furthermore, such maturation theories overlook the iterative dimension of moral decision-making with feedback loops and filters in the development of moral character — including the possible use of mathematical ethics in the manner of Aristotle, who seems to have steered a middle course between complete reductive mathematization of ethics and an apriori resistance to even a partial mathematization of ethics. "Not too much and not too little!"
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