Aristotle's Geometrical Accounting

Aristotle’s analysis of economic exchange in the Nicomachean Ethics involves two paradigms which he addresses separately but then he stresses that there is no difference between them: barter and monetary exchange. Each one of them is rendered here separately but in a mutually consistent way by using geometrical methods which were well established and widely used in Aristotle’s intellectual surroundings. In this framework Aristotle’s ‘monetary equivalence’ in exchange appears as an application of Euclid’s proposition Elements I,43 about the equality of geometrical complements in a rectangle. Aristotle repeatedly refers to ‘own production’ when mentioning exchange between two artisans, say, ‘builder’ and ‘farmer’. The accounting worth of the quantity of ‘own production’ in terms of money is then Aristotle’s “worth” of an artisan. This interpretation helps to make sense of Aristotle’s statements of the type: ‘as builder to farmer, so food to houses’. We show that this statement is logical and plausible provided that the goods in question are measured as proportions of sales out of own production. This result solves one of the major riddles of Aristotle’s text on exchange. Accounting of exchange should be seen in connection with Aristotle’s critique of the Pythagoreans’ concept of justice. He claims that they wrongly equate justice with ‘reciprocation’. The paper does not speculate about Aristotle’s alternatives. It just shows that his text on ‘reciprocation’ can be interpreted with reference to a consistent and interesting system of geometrical accounting. This might not be his own invention, but Aristotle’s writings are the sole literary source for systematic geometrical accounting of economic exchange. This definitely merits listing Aristotle’s passages on exchange as being among the most interesting texts of ancient economic analysis