Keynes' criticism of ideal utilitarianism
Keynes did not espouse ideal utilitarianism, but he seems influenced by Moore's awareness that in practical application ethics meets some difficulties in prescribing duties which produce the greatest sum of good. Mathematical expectation, intended as the product of a judgement of goodness and a judgement of probability, is based on two assumptions that Keynes (1973a , pp. 343-4) finds unjustified: 'first, that degrees of goodness are numerically measurable and arithmetically additive, and second, that degrees of probability are also numerically measurable.'
Organicism justifies this belief, since the position of each element of the economic system, is (in some sense) dependent on that of the others. In fact, 'the atomic hypothesis which has worked so splendidly in physics breaks down in psychics. We are faced ... with the problems of organic unity, of discreteness, of discontinuity - the whole is not equal to the sum of the parts, comparisons of quantity fail us, small changes produce large effects, the assumptions of a uniform and homogeneous continuum are not satisfied' (Keynes, 1972c , p. 262).
As regards moral good, if organic relations are admitted, it has to be also admitted that quantities of goodness are not always subject to the laws of arithmetic. As regards the measurability of probability, Keynes in his 'The Principles of Probability' (1907: unpublished, ch. 4) distinguishes between risk (measurable uncertainty) and (non-measurable) uncertainty before Knight (1921), and in his Treatise on Probability (1973a ) he expresses his theory of logical or inductive probability and his doctrine of rational intuition, which admits that probabilities may be non-measurable and non-comparable. The lack of a scientific basis for computing probabilities would depend on the existence of continuous social interaction that can determine significant changes in the economic structure from the quantitative and qualitative points of view. This would determine the fundamental or true uncertainty of economic phenomena. Fundamental uncertainty means here that there is no scientific basis for establishing any calculable probability whatever, thus we also speak of non-measurable uncertainty (Keynes, 1973c , p. 114).
Therefore, mathematical expectations of alternative courses of actions are not always measurable and, 'even if a meaning can be given to the sum of a series of non-numerical "mathematical expectations", not every pair of such sums are numerically comparable in respect of more and less' (1973a , p. 344). According to Keynes (1972b , p. 284), the philosophical problems about the application of mathematics and statistics to human conduct are not satisfactorily solved by resorting to the maximisation of the expected value, which 'deals with the present without any consideration for the fact that agents know very little about the future; so it is very difficult to make predictions about future facts'. In particular, statistics are built by assuming that past cases are certain; while uncertainty, when it is true, cannot ever be purely statistical (see Roberto Scazzieri, chapter 5, this volume).