Keynes's Treatise on Probability 100 Years Later: Small vs. large worlds and closed vs. open systems

The meaning and significance of Keynes’s Treatise on Probability has changed over the 100 years since its publication. Initially it stood on its own as an original contribution to probability theory. After The General Theory some saw the Treatise strengthening Keynes’s later arguments. Yet by the time New Classical Economics became dominant it became largely ignored. This paper attributes that later rejection to the mainstream economics’ reliance on Savage’s subjective expected utility restriction of probability thinking to what he called small worlds. It argues that his small worldslarge worlds distinction produces a small worlds-closed worlds conception of economics the mainstream employs, and that Keynesian economic thinking and the Treatise employ a large worlds-open worlds conception of economics. It frames this open-closed opposition in terms of two contrasting conceptions of science from 1930s system theory, and argues that in economics it is the basis for two conceptions of time: a static, before-after view of temporal sequences and a dynamic, past-present-future view of temporal sequences. The paper then shifts to how Sraffa explained the relationship between production and distribution as an interaction between a relatively closed production system open to distributional forces, shows an analogous view exists in the later thinking of Wittgenstein with whom Sraffa interacted, and then argues Keynes’s thinking in the Treatise employs a similar Cambridge understanding whereby our probability judgments are relatively closed but also open to fundamental uncertainty.