John Arbuthnot's celebrated but flawed paper in the Philosophical Transactions of 1711-12 is a philosophically and historically plausible target of Hume's probability theory. Arbuthnot argues for providential design rather than chance as a cause of the annual birth ratio, and the paper was championed as a successful extension of the new calculations of the value of wagers in games of chance to wagers about natural and social phenomena. Arbuthnot replaces the earlier anti-Epicurean notion of chance with the equiprobability assumption of (...) Huygens's mathematics of games of chance, and misrepresents the birth ratio data to rule out chance in favour of design. The probability sections of Hume's Treatise taken together correct the equiprobability assumption and its extension to other kinds of phenomena in the estimation of wagers or expectations about particular events. Hume's probability theory demonstrates the flaw in this version of the design argument. (shrink)

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results (...) from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice. (shrink)