To: David S.

From: Geoffrey Klempner

Subject: Implications of Kreisel's dictum for moral 'objects'

Date: 7 December 2004 11:43

Dear David,

Thank you for your email of 26 November, with your second essay for the Moral Philosophy program, in response to the question, 'The mathematician George Kreisel once remarked that the problem for the philosopher of mathematics was 'not the existence of mathematical objects but the objectivity of mathematical truth'. How does the distinction between the question of objectivity and the existence of objects apply in the field of ethics?'

You give a careful account of the 'queerness' of moral 'forms', both in terms of their dubious authority and the equally dubious epistemology which would be required to explain how such forms make epistemic contact with the human mind.

How would this apply to mathematics? Clearly there is a problem for the full-blooded Platonist of giving an account of mathematical 'perception'. However, there are different degrees of Platonism. Consider, for example, the Russell/ Frege 'logicist' program of defining numbers in terms of sets. This involves a more modest Platonism than the pure, Platonic variety.

(Interestingly, in the Foundations of Arithmetic, Frege shows a way to analyse statements involving number contextually, in terms of existential quantifiers. E.g. 'There were two people in the room' becomes '(Ex)(Ey)(Ez)(x was in the room and y was in the room and x is not equal to y and if z was in the room then z=x or z=y). A good question for the mathematician/ philosopher of mathematics to ask is, Why wasn't he satisfied with this? Why did he feel the need to go on and give an account of numbers as set-theoretic objects?)

Or, consider two very different reactions to logicism: formalism and intuitionism. Your remark that '"triangle" is something that conveniently exists by definition, and mathematical truths are discovered by a process that starts and first principles and proceeds by reason step by step,' looks like a version of formalism. Far from capturing mathematical objectivity, however, the formalist program begins to reduce to a version of subjectivism in the face of the discovery of alternative, non-Euclidean geometries. While Godel's powerful proof that arithmetic cannot be finitely axiomatised put the nail in the coffin of the idea that truth can be reduced to provability within a system.

The intuitionist, by contrast, strongly emphasizes the role of a kind of 'perception' in mathematics, explained not in terms of metaphysical objects but rather in terms of the exercise of a capacity for mathematical judgement demonstrated by our ability to follow a constructive proof, guided by our native capacity for mathematical 'intuition'. In other words, numbers are not 'out there' but rather exist in the human mind itself.

Yet both formalists and intuitionists are equally vociferous in claiming to save the objectivity of mathematics in the face of scepticism over the metaphysical assumptions of Platonism/ logicism.

This points to a lacuna in your account of the alternative to moral Platonism. In your penultimate paragraph, you say, 'Morality with fixed objects and rules is often easier to understand and implement, but that might well be the reason for moral failure and moral relativity throughout human history.' What you seem to have done here is conflate 'objects' with 'rules'. Kant's categorical imperative surely looks like an account of morality with which Kreisel would agree. Yet this approach is very much at odds with the ethics of dialogue, where there are no fixed rules. In other words, as in mathematics, there is more than one way to pursue objectivity in the face of the rejection of Platonism. (I would not go so far as to compare Kantian ethics with formalism, or the ethics of dialogue with intuitionism - one has to be very careful in appreciating the limits of analogy here.)

You mention relativity, Mackie's other main argument against objectivism, but you don't really tackle the question Mackie raises, namely how we can possibly view moral statements objectively if relativity is admitted. What is the difference between an 'objective' approach which admits relativity, and mere inter-subjectivity? Why call morals 'objective' if you admit that two people can sometimes disagree and yet both be 'right'? This would hardly be acceptable in mathematics - or would it?

The relativity challenge does deserve to be met. A two-pronged strategy might be employed here. On the one hand, we need to scrutinise very carefully alleged cases of 'relativity' - many of which turn out on closer inspection to be differences of custom or different ways of applying a given rule, rather than disagreements over the rule itself. On the other hand, we can pursue the question of what underlying concepts are common to all 'moral' viewpoints, e.g. the notion of the dignity of human beings and the idea that 'the other person always counts'.

As you see, there are several lines which deserve further exploration. But a good essay nonetheless.

All the best,

Geoffrey