The profusion of senses of justice in NE V.1–7 has left many readers with a general impression of chaos, but also gives rise to pressing questions about Aristotle’s conception of justice. Specifically, why does Aristotle claim that there are two parts to justice as equality, but go on to discuss three types of equality in the subsequent chapters? What is the relationship between political justice and the distinction between general justice and particular justice? I argue in this essay that the (...) notion of reciprocity, central to the first question, can also help us address the second. Specifically, I show that reciprocity is not a third species of particular justice, but rather a prior condition for political community and for political justice. Political justice is best understood as a redescription of particular justice that highlights how distributive and corrective justice maintain equality among citizens in an existing political community. In addition to explaining the unity of Aristotle’s thought in these chapters of NE V, I demonstrate a number of philosophical consequences for understanding Aristotle’s conception of justice. (shrink)

The purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a “mathematical mechanistic world picture” that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was (...) the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing, the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument, the most popular justification for subjective probability. The paper’s main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics of physica and practica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems. (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)

In just proportional exchange, under Aristotle's theory of reciprocal justice, superior sharers in a community materially assist the weaker, and receive honour as a reward. Aristotle's economic thought is represented with a system of 18 formulae. Explained are: (1) What Aristotle means when he says that it is impossible for two sharers or their erga to be commensurable; (2) The extent to which the variables in Aristotle's proportions can be quantified. (3) What diagonal pairing ( ?ατ δ? ??τ?o? σ ??????) (...) is; (4) How need makes sharers and their erga ?sufficiently' commensurable; and (5) Aristotle's theory of what is just in exchange. (shrink)

This article proposes an interpretation of the chapters of theNicomachean Ethicsconcerning exchange and friendship. Rejecting approaches where Aristotle anticipates modern labour or need-based theories of value, the article claims that those notions of labour and need are required for a satisfactory interpretation of the most obscure passages of Book V. Finally, Aristotle's texts on exchange and friendship are related in such a way that the latter, since it is free from any political considerations, allows us to better understand the philosopher's (...) view on exchange. (shrink)