Kenneth Boulding is one of my favorite authors in economics. In 1948, Boulding reviewed Samuelson's *Foundations* in the *JPE*. Samuelson had argued that mathematical economics would rid economics of the ambiguities that plagued its pre-scientific era as a branch of moral philosophy. Confusion results from natural language because people use the same words to mean different things, or different words to mean the same thing. Mathematical reasoning would eliminate this problem and force all the hidden assumptions to be stated explicitly.

Boulding countered Samuelson's confidence in the unambiguous advance of mathematical reasoning in economics. Boulding concluded that mathematics operates by abstracting from any heterogeneity or complexity in the structure of economic relationships. This is mathematics great strength and weakness when applied to economics. Its strength is that by abstracting from the complexities in the internal structure, mathematics is able to eliminate inconsistency and provide precise statements. Its weakness is that by abstracting the complexities of the internal structure of economic relationships is neglected. If the structure is important this neglect means that mathematics will lead us to ignore precisely that which we are supposed to be examining. Boulding sums this up by stating that: "mathematical economics will remain to flawless in its perfection to be very fruitful."

The awarding of the Nobel Prize to Robert Aumann raises this issue of the relationship between mathematical reasoning and the art of political economy. Aumann has thought deeply about many issues in economics and philosophy with the aid of mathematical tools. On the discussion list sponsored by Mises Institute, Richard Ebeling, the President of The Foundation for Economic Education, has written insightful comments to remind us on the limits and potential of abuse with mathematics in the discipline of economics:

Mathematics is a rigorous way of reasoning, that follows fairly strict rules of logic. So, yes, it is possible to have a degree of confidence about any conclusions from starting premises.

But it also has its limits in a subject-matter such as economics. Karl Menger, Jr. (an internationally respected mathematician who taught at the University of Chicago) discussed a number of these limits in his contribution, 'Austrian Marginalism and Mathematical Economics,' in J. R. Hicks and Wilhelm Weber, eds., "Carl Menger and the Austrian School of Economics" (Oxford: Clarendon Press, 1973) pp. 38-60.

Some of these limits were also discussed earlier by George J. Stigler in his "Five Lectures on Economic Problems (London: Longmans, Green, 1949 pp. 37-45, in the chapter on 'The Mathematical Method in Economics.'

In addition, Oskar Morgenstern pointed out many of the limits and shortcomings in modern mathematical general equilibrium and microeconomics in his article, 'Thirteen Critical Points in Contemporary Economic Theory: An Interpretation' [1972], reprinted in, Andrew Schotter, ed., "Selected Economic Writings of Oskar Morgenstern" (New York: New York University Press, 1976) pp. 267-293.

More generally, I would suggest that the criticism that have been leveled against reliance upon the mathematical method by the Austrians still has general validity. Natural language has the ability to capture, express, and explain the nature, content, and unique properties of conscious human conduct in ways that reduction of "action" to functional, interdependent relationships between "variables" cannot convey or fully incorporate.

To analyze an economic (or any social) interactive situation requires the economist to look "beneath" the interdependent "variable" surface of things to try to determine the "meanings" of the situation as seen through the eyes of the human actors themselves. It is how the actors define the situation, including the meaning they see in their own actions and that of others with whom they may interact, that determines just what kind of interaction it is. What is a voluntary act of exchange and what is a coerced transfer of goods may externally look the same, but certainly is not, when understood from the perspective of the actors.

Also, reflection upon and thinking through the meaning and nature of "action" also reminds us of the limits to any mathematical modeling, including game theoretical approaches. I.e., how an essential aspect of real action is thinking, creatively outside the matrix. "Given that the actors in the game operate with the following assumptions, then. . ." But the essence of the real world is that individuals devise new ways of thinking about the situations they are in, which modifies and transforms the elements and values in the initial assumptions made by the analyst for his "exercise."

That is why the "laws of economics" remain logical relationships, and not "empirical" ones. But they are logical relationships with properties and characteristics distinct from a merely mathematical analysis of such interdependent relationships. It would be like trying to study man by only looking at the skeleton, and ignoring the flesh, the blood, the muscles, the nerve endings, and most especially the creative and imagining mind that guides what the body does.

This, of course, is what drives so many mainstream economists crazy. They want determinate "solutions" in a real world of unending process with unpredictable change due to what man is. They want to confine man within a "define" that will satisfy their desire for "answers" they feel most intellectually comfortable with.

In other words, they define the shape of man to fit the theoretical suit into which they want him to fit, rather than to design the theoretical suit to conform to the shape of the human subject they claim to want to study and understand.

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