Bcyclwutztht,
On second pass, I think you are not arguing the above—i.e. scientific validity of empiricism. It looks to me like you are saying that it’s ok to use math, as long as one is willing to sacrifice theoretical precision.
No, I said math follows the same rules of logic that verbal logic does. Math, in many ways, is more precise than verbal logic (and I think verbal logic in some ways can be more precise than mathematics, by the way).
@JCatalan
Yea, sorry. I was grunching. I have since gone back and read your original posts. I see that you are against the use of “empiricism” to derive economic theory, but not against the use of “math” to do so.
I’m not an expert in methodology. However, if the use of mathematics is proper for deriving economic theory, why do Mises and Rothbard discuss at length both (1) the distinct desirability of a causal-realistic method; and (2) the distinct UNdesirability of a quantitative method?
Seems to me this is why Austrian economics (1) is distinct from all other contemporary systems of economic theory; and (2) insists on the importance of an a prioristic and deductive method; and (3) is so damn baller:
Mises:
The Free Market and Its Enemies, p. 16
However, for a full appreciation and interpretation of Mises’s statement, I imagine a reading of Epistemological Problems of Economics; and The Ultimate Foundation of Economic Science; and Theory and History would be quite useful*.
*According to Hoppe, the bulk of Mises’s methodological work is contained in these three works. See Hoppe Economic Science and the Austrian Method.
bcyclwutztht,
We’re not talking about methodology.
@JCatalan
Oh?
Surely you are correct, sir. That is, if marching—to the drumbeat of neoclassical and Keynesian empiricism—to our social and economic demise more efficiently and rapidly counts as progress. Thank goodness for the maths.
^ both the neoclassical and keynesian schools of though were formed before the mathematical revolution in economics.
bcyclwutztht,
If you read what you quoted completely, you’ll notice the differentiation between statistical econometrics and mathematics. Mathematics qua mathematics has nothing to do with empiricism or positivism. Any problems with mathematics is not necessarily methodological.
Mises:
“The mathematical method must be rejected not only on account of its barrenness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile; they divert the mind from the study of the real problems and distort the relations between the various phenomena.”
[…]
"As there exist constant relations between various mechanical elements and as these relations can be ascertained by experiments, it becomes possible to use equations for the solution of definite technological problems. Our modern industrial civilization is mainly an accomplishment of this utilization of the differential equations of physics. No such constant relations exist, however, between economic elements.
The equations formulated by mathematical economics remain a useless piece of mental gymnastics and would remain so even it they were to express much more than they really do."
Mathematics Versus Economic Logic
This article’s original title is “Logical Catallactics Versus Mathematical Catallactics.” It is excerpted from chapter 16 of Human Action
I agree with Mises that economic relationships are rarely mechanistic. The best mathematics can do, in my opinion, is model a simple relationship in a theoretical environment similar to Mises’s own ERE. I think mathematics has been overused, in the sense that it is consistently used to derive conclusions that are applied to real life. A simple expansion is MV = PQ; Austrians recognize this mechanistic relationship as false.
What I think Mises overlooks (perhaps due to a weak background in economics) is that mathematics is bound by the same basic logic as verbal logic is. So, the problem with mathematics is one of application, rather than a fundamental difference in the form of derivation. In other words, mathematical rigour itself might be mathematic’s fatal weakness, in that it’s rigour makes it difficult (or even impossible) for it to consider the non-mechanistic and dynamic relationships which exist in a market.
The overall conclusion I think we should make is that while the use of mathematics is limited, it is not entirely worthless. In any case, I have always considered mathematics as a better tool for modelling relationships that have already been derived through verbal logic, rather than deriving relationships from pre-established relationships purely mathematically. In other words, I have seen mathematics of simplifying theory into a model. The caveat is that, as outlined above, this can hide the dynamic nature of real economy.
Good points Jonathan. I think we agree, except maybe I may be more skeptical of mathematical models, even those based on logically deduced premises, on the grounds that quantitative predictions are still not possible, only general qualitative predictions at best.
Has anybody found an economic mathematical model (quantitiative) applicable to the real-world which provides consistent correct, testable predictions with published results over time?
I came across the following quote from Paul Samuelson:
“In principle, mathematics cannot be worse than prose in economic theory; in principle, it certainly cannot be better than prose. For in its deepest logic […] the two media are strictly identical.”
I disagree with it.
It seems prose can describe mathematics but not vice-versa. There is a lot said in prose which knows no mathematical equivalent or where math does not apply, although all mathematics can be described in prose.
In other words, mathematics is a subset of prose (and language) and only useful in certain circumstances. Therefore, mathematics has a smaller domain of applicability in deriving knowledge than prose, which would be a point in favor of using prose to describe a qualitative model (from deduced logical premises).
On utilitarian grounds, is math easier or simpler to use than prose? I find prose easier and more accessible. Although assumptions can be made explicitly in math notation, assumptions are often hidden in them as well.
The case for mathematical models on predictive grounds - has using mathematical models in economic theory resulted in a better ability to predict peoples’ economic behavior?
Nonetheless, both have since dressed their theories in ever more brilliant and elegant mathematical expressions. Problem with this, however, is (1) Keynesian and neoclassical theory—especially when compared with Austrian theory—nevertheless remain feeble and vacuous; and (2) This impotence continues to be hidden from view—in no small part precisely because of the false scientific authority conferred by all the dazzling mathematics.
My biggest problem with the use of mathematics, in economics at least, is that it complicates inherently intuitive concepts and oversimplifies inherently complicated and dynamic phenomena (abstracts from too many relevant variables). Quick example: consumer choice.
@JCatalan
Yes, thanks. I understand this.
I agree, but with the small caveat that mathematics has nothing (necessarily) to do with empiricism and positivism. To be clear, however, empiricism and positivism DO NECESSARILY have much to do with mathematics.
Yes, I agree. Empricism and positivism = methodology. Mathematics != methodology (necessarily).
I only emphasize the differences for those readers who may not be clear on the distinction. Sorry for any unnecessary confusion.