http://stickmanscorral.blogspot.com/2010/10/why-we-need-maths-in-economics.html
"I'm not a fan of Murray Rothbard." -- David D. Friedman
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?
@Student
both the neoclassical and keynesian schools of though were formed before the mathematical revolution in economics.
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.
"If we wish to preserve a free society, it is essential that we recognize that the desirability of a particular object is not sufficient justification for the use of coercion."
@JCatalan
If you read what you quoted completely, you'll notice the differentiation between statistical econometrics and mathematics.
Yes, thanks. I understand this.
Mathematics qua mathematics has nothing to do with empiricism or positivism.
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.
Any problems with mathematics is not necessarily methodological.
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.