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2/10/2017 3:23 am  #1

An Aristotelian Philosophy of Mathematics

Reading through Redeeming Economics yet again. Thought this quote might generate some good discussion (p. 375n13):

Economics is (and has been since Aristotle) a mathematical as well as moral discipline. But Alfred Marshall once gave another economist this excellent advice: “(1) Use mathematics as a shorthand language, rather than an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics.” In other words, mathematics cannot say any more than can be said in English. “Twice two equals four” means the same as “2 x 2 = 4.” But the math does serve some very useful purposes: checking whether a theory is logically complete, discovering its implicit assumptions, and quantifying and testing its predictions. Once you realize this, math loses any mystique and becomes no more exciting (though it remains no less necessary) than proper spelling and grammar. The practicing economist is a man of simple pleasures, like Charles Dickens’s Mr. Micawber: “Annual income twenty pounds, annual expenditure nineteen nineteen six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.” Or rather, for the practicing economist: four unknowns, four equations, result happiness. Four unknowns, three equations, result misery. As an empirical practitioner, I began to suspect that most of the misery in modern economics results from the simple error of starting with more unknown variables than explanatory equations. All varieties of modern neoclassical economics have no more than three kinds of equations to explain the four essential facets of human economic decisions. Each missing equation or explanation forces economists either to resort to circular logic (thus making their descriptions unverifiable) or else to replace missing variables with assumptions (and thus to prescribe and falsify rather than describe the facts). The explanatory equation missing from classical and neoclassical economics is the one that describes gifts (and their opposite, crimes) at the personal level and distributive justice at all social, e.g., family and political, levels. Marshall to Bowley, 27 February 1906, in Memorials of Alfred Marshall, edited by A.C. Pigou (London: Macmillan, 1925), 427.

The sacred rights of mankind ... are written, as with a sunbeam, in the whole volume of human nature, by the hand of the divinity itself; and can never be erased or obscured by mortal power. (Alexander Hamilton, The Farmer Refuted)

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