Pure and Applied Economics

Oscar B. Johannsen

[Reprinted from The Gargoyle, November, 1961]

Inasmuch as the principles of economics are based on deductive reasoning, it would appear that possibly in the interest of arriving at a greater understanding of the world of reality, economics might be divided into two categories - pure economics and physical or applied economics - much as modern mathematics is divided into two phases, pure mathematics and physical or applied mathematics.

Pure mathematics does not deal with any particular subject matter of reality and has nothing to say about such items of interest to men, as space. The theorems which are derived are true and certain because they are analytical and not empirical. This means that the truth of a theorem is derived by logical deduction from certain so called undefined terms, usually called primitives, and some axioms. These axioms are more or less arbitrarily enunciated. The theorems are true as related to these primitives and axioms because they are merely explicit statements of what is implicit in the primitives and axioms.

To put it simply, the primitives and axioms contain hidden meanings. These meanings (theorems)are uncovered by means of logic. The theorems do not assert anything which is theoretically new as compared with the axioms and primitives from which they are derived. They are said to be psychologically new in that we did not realize they were implicitly contained in the initial assumptions.

Whether a theorem is factually correct in the world of reality is a problem of empirical science, that is, it is a problem of applied mathematics. Man can never be absolutely certain about empirical results as the discovery of new facts may alter the results. However, if all the evidence confirms the applied theorems, then they are accepted "until further notice". This is all summarized in a famous statement of Albert Einstein who said, "As far as the laws of mathematics refer to reality they are not certain; and as far as they are certain they do not refer to reality".

Inasmuch as in economics we are dealing with logical deductions from fundamental definitions and axioms, could not the same approach be taken? Can we construct a pure economics which would be certain as long as it does not refer to reality, but as far as it does relate to reality is not certain?

This writer believes it could be done, although it might be a rather arid approach.

Such concepts, as man, land, labor, wealth, etc., which are our initial terms, might be the primitives or undefined terms. In mathematics such primitives are terms as line or point. (However, while they are undefined, nonetheless, conceptually man does give them the definitions which we usually visualize them to be,) There is no question of the "truth or falsity of these terms, any more than there is about the terms in a game of chess. In Chess, the primitives might be the pieces, as the King, Queen, etc. The axioms would be the rules of the game which were arbitrarily set up thousands of years ago. The theorems would be the possible moves which could be made, and are all implicit in the rules. these would be discovered by the players by applying their deductive reasoning to the rules. The discovery of these moves (or theorems) would not be theoretically new as they are all implicit in the rules. However, as it has been estimated that the possible moves in chess are in the order of billions, it is obvious that no one could possibly discover all of them no matter how many lifetimes he lived.

What value would it be to divide economics into pure and applied parts? It might prove as valuable as it has in mathematics. Knowledge was advanced. Originally mathematics started as physical math, as men were interested in making physical measurements of areas. From these considerations, mathematics in the abstract evolved. And this pure mathematics proved invaluable to man. For example, Einstein as he pondered his theory of relativity, looked for some mathematics that he could use to deal with his concepts of space. He found it in Riemann's geometry. This non-Euclidian geometry had been developed by Riemann with no concern for any relationship which it might have with reality, and yet, when Einstein needed a tool, there it was at hand, and with tremendous practical value.

If man will try to do this in the field of economics, probably many of the disputes among economists will disappear. The disputes usually apply to the physical application of the theoretical laws. Today, these "pure" economic relationships are not carefully systemized, as the "pure" mathematical ones are. If they were, then it could be shown that they are true in the abstract, and there could be little or no dispute about them. As one of the great problems in economics is that no two economists use the terms in the same way or have quite the same understanding of the fundamental axioms or assumptions, there is little meeting of the minds. Should we not at least give this method a trial?