J B Say's Critique of Mathematical Economics

Today's mainstream neoclassical economics is in a deep trouble because of its inability to explain the reality of our economy and society at large. Most mainstream economists have no idea about how an economy actually functions e.g., take Nobel prize winner [sic] Paul Krugman who keeps on saying that destruction of wealth is somehow going to generate more wealth (see here his space alien threat strategy of fixing the ailing US economy)! He thinks that inflation will bring the economy out of recession! Most of them failed to anticipate even the 2007 world financial crisis e.g., at the height of US housing bubble in 2006, US Federal Reserve bank chairman Ben Bernanke was saying, that the housing prices will keep on rising when the bust was just around the corner (see here). The main reason for this failure to understand the economic reality is their faulty methodology of doing economic science. The heavy use of mathematics has ruined mainstream economics to such an extent that most mainstream economics textbooks look like math books more than economics e.g., see the picture below.

A Typical Mainstream Microeconomics Textbook

Abstruse mathematical and econometric models have created a big gulf between the reality of economic life and mainstream economic theories. This trend of mathematization of economics is at least 150 years old. It started mostly in the middle of the 19th century when many engineers, mathematicians and physicist started developing their mathematical theories of economics. It picked up speed in the 20th century and today it is so off the track that, as Sutter and Piesky's papers showed, even Adam Smith won't be able to publish in today's mainstream econ journals! Many brilliant minds of olden times tried their best to warn economists against this use of mathematics for developing economic theories. Jean Baptiste Say was one of those brilliant minds. I am reading his Treatise on Political Economy where in the Introduction he discusses some of the major problems with the use of mathematics in economics. Below I am reproducing some paragraphs and one lengthy footnote where Say discusses these issues.

Say begins by stating what the science of political economy i.e., economics is, and he contrasts it with statistics stating latter's limitations. Here is Say:

Political economy, from facts always carefully observed, makes known to us the nature of wealth; from the knowledge of its nature deduces the means of its creation, unfolds the order of its distribution, and the phenomena at tending its destruction. It is, in other words, an exposition of the general facts observed in relation to this subject. With respect to wealth, it is a knowledge of effects and of their causes. It shows what facts are constantly conjoined with; so that one is always the sequence of the other. But it does not resort for any further explanations to hypothesis: from the nature of particular events their concatenations must be perceived; the science must conduct us from one link to another, so that every intelligent understanding may clearly comprehend in what manner the chain is united. (emphasize mine)  

The founder of the Austrian School of Economics, Carl Menger, in the very first line of his treatise also said, All things are subject to the law of cause and effect. All economic phenomenon like inflation, unemployment, price, interest, wage etc., etc., have their definite cause(s) which sound economic theory should investigate. But, today's mathematical economists think that everything is simultaneously determined - their use of simultaneous equations - and so they never give proper attention to this causality in the economic life. This is one of the prime reasons why they are clueless about the present economic crisis! Say, after discussing what economics really is, talks about the limitations of use of statistics in economics. Most mainstream economists and other pundits are obsessed with economic data. They continue to compile one data set after another, and most importantly, they use these data (wrongly) to test economic theories. Here is Say on this issue:

The study of statistics may gratify curiosity, but it can never be productive of advantage when it does not indicate the origin and consequences of the facts it has collected; and by indicating their origin and consequences, it at once becomes the science of political economy.   

Just like Say's above statement, Ludwig von Mises's work informs us, that economic data are history, and they have nothing to do with the economic theory. 

Say then goes on and warns us about the misuse of mathematics in economics. I reproduce the paragraphs and that lengthy footnote below: 

It would, however, be idle to imagine that greater precision, or a more steady direction could be given to this study, by the application of mathematics to the solution of its problems. The values with which political economy is concerned, admitting of the application to them of the terms plus and minus, are indeed within the range of mathematical inquiry; but being at the same time subject to the influence of the faculties, the wants and the desires of mankind, they are not susceptible of any rigorous appreciation, and cannot, therefore, furnish any data for absolute calculations. In political as well as in physical science, all that is essential is a knowledge of the connexion between causes and their consequences. Neither the phenomena of the moral or material world are subject to strict arithmetical computation. (emphasize mine) At this point he then inserts the following footnote:

We may, for example, know that for any given year the price of wine will infallibly depend upon the quantity to be sold, compared with the extent of the demand. But if we are desirous of submitting these two data to mathematical calculation, their ultimate elements must be decomposed before we can become thoroughly acquainted with them, or can, with any degree of precision, distinguish the separate influence of each. Hence, it is not only necessary to determine what will be the product of the succeeding vintage, while yet exposed to the vicissitudes of the weather, but the quality it will possess, the quantity remaining on hand of the preceding vintage, the amount of capital that will be at the disposal of the dealers, and require them, more or less expeditiously, to get back their advances. We must also ascertain the opinion that may be entertained as to the possibility of exporting the article, which will altogether depend upon our impressions as to the stability of the laws and government, that vary from day to day, and respecting which no two individuals exactly agree. All these data, and probably many others besides, must be accurately appreciated, solely to determine the quantity to be put in circulation; itself but one of the elements of price. To determine the quantity to be demanded, the price at which the commodity can be sold must already be known, as the demand for it will increase in proportion to its cheapness; we must also know the former stock on hand, and the tastes and means of the consumers, as various as their persons. Their ability to purchase will vary according to the more or less prosperous condition of industry in general, and of their own in particular; their wants will vary also in the ratio of the additional means at their command of substituting one liquor for another, such as beer, cider, &c. I suppress an infinite number of less important considerations, more or less affecting the solution of the problem; for I question whether any individual, really accustomed to the application of mathematical analysis, would even venture to attempt this, not only on account of the numerous data, but in consequence of the difficulty of characterizing them with any thing like precision, and of combining their separate influences. Such persons as have pretended to do it, have not been able to enunciate these questions into analytical language, without divesting them of their natural complication, by means of simplifications, and arbitrary suppressions, of which the consequences, not properly estimated, always essentially change the condition of the problem, and pervert all its results; so that no other inference can be deduced from such calculations than from formula arbitrarily assumed. Thus, instead of recognizing in their conclusions that harmonious agreement which constitutes the peculiar character of rigorous geometrical investigation, by whatever method they may have been obtained, we only perceive vague and uncertain inferences, whose differences are often equal to the quantities sought to be determined. What course is then to be pursued by a judicious inquirer in the elucidation of a subject so much involved? The same which would be pursued by him, under circumstances equally difficult, which decide the greater part of the actions of his life. He will examine the immediate elements of the proposed problem, and after having ascertained them with certainty, (which in political economy can be effected,) will approximately value their mutual influences with the intuitive quickness of an enlightened understanding, itself only an instrument by means of which the mean result of a crowd of probabilities can be estimated, but never calculated with exactness.

Cabanis, in describing the revolutions in the science of medicine, makes a remark perfectly analogous to this. 'The vital phenomena,' says he, 'depend upon so many unknown springs, held together under such various circumstances, which observation vainly attempts to appreciate, that these problems, from not being stated with all their conditions, absolutely defy calculation. Hence whenever writers on mechanics have endeavoured to subject the laws of life to their method, they have furnished the scientific world with a remarkable spectacle, well entitled to our most serious consideration. The terms they employed were correct, the process of reasoning strictly logical, and, nevertheless, all the results were erroneous. Further, although the language and the method of employing it were the same among all the calculators, each of them obtained distinct and different results; and it is by the application of this method of investigation to subjects to which it is altogether inapplicable, that systems the most whimsical, fallacious, and contradictory, have been maintained.'

D'Alembert, in his treatise on Hydrodynamics, acknowledges that the velocity of the blood in its passage through the vessels entirely resists every kind of calculation. Senebier made a similar observation in his Essai sur l'Art d'observer, (vol. 1, page 81.)

Whatever has been said by able teachers and judicious philosophers, in relation to our conclusions in natural science, is much more applicable to moral; and points out the cause of our always being misled in political economy, whenever we have subjected its phenomena to mathematical calculation. In such case it becomes the most dangerous of all abstractions. 

Indeed, what dangerous of all abstractions today's mathematical economics has become! It has lost its way so much that most mainstream economists have become a laughingstock amongst the people. Not only J B Say, but many other eminent economists warned against this mindless use of mathematics and econometrics in economics. I reproduce some quotes from  Boris Ischboldin's paper below. First Alfred Marshall: 

Afred Marshall himself, who was originally a teacher of  mathematics, would have decisively rejected such treatment of his mathematical contributions. Many times he emphasized that an academic economist should give all the outlines of his theory in ordinary language and that to read lengthy translations of economic doctrines into mathematics is unreasonable.  In his correspondence with the famous British statistician, Bowley,  Marshall stated that if an economist arrives at some hypotheses by mathematical means, he should translate them into ordinary language and burn his mathematical notes. (emphasize mine) 

Here is Joseph Schumpeter:

Joseph Schumpeter who, toward the end of his life  manifested a distinct interest in historical generalizations and an increasing reluctance to use mathematical symbols in economic theory, came to the conclusion that an outstanding mind is able to find its way through  the maze of an intricate theoretical problem without recourse to the formal devices of mathematics.(emphasize mine)

Paul Samuelson once said, that an economist can become a great theorist without using mathematics but one must be more clever and brilliant.

And, finally, as Ludwig von Mises said, As a method of economic analysis econometrics is a childish play with figures that does not contribute anything to the elucidation of the problems of economic reality!

Despite all these warnings, mainstream economists continue their way in the wrong direction. Unless they change their methodology, it won't take long for their pseudo-science to become junk in the dustbin of history.