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I find David Glasner's blog post at Uneasy Money interesting for his discussion of (1) the role of axiomatic reasoning - much hailed by libertarians especially in the praxeological tradition (von Mises, Rothbard), (2) the aberrations of neoclassical economics, and (3) the concept of precision which is not infrequently used to rule out by denigration methods more appropriate to the social sciences, especially economics, than methods preferred because they yield the spurious appearance of supporting an "exact science".
The way I read Glasner, he is saying that axiomatization in economics has become a fetish, a misguided promise of more profound and more certain knowledge, and that modern economics in its immature ambition to be considered "an exact science" and by overemphasising mathematical formalization has lost the subject-matter of economics out of sight.
Glasner summarises:
[...] that it is important to understand that there is simply no scientific justification for the highly formalistic manner in which much modern economics is now carried out. Of course, other far more authoritative critics than I, like Mark Blaug and Richard Lipsey (also here) have complained about the insistence of modern macroeconomics on microfounded, axiomatized models regardless of whether those models generate better predictions than competing models. Their complaints have regrettably been ignored for the most part.
I like the way in which Glasner looks beyond the foreground and middleground, probing into the remoter roots of fetishistic illusions about precision and exactness in science.
Thus, the author argues
[...] the concept of precision is itself hopelessly imprecise, and to set precision up as an independent goal makes no sense.
He backs up his view with quotes from Karl Popper's
enlightening discussion of the historical development of calculus despite its lack of solid logical axiomatic foundation.
And concludes:
[...] However, the absence of a rigorous and precise definition of the derivative did not prevent mathematicians from solving some enormously important practical problems, thereby helping to change the world and our understanding of it.
Writes Popper, the terms "exact" or "precise"
[...] strongly suggest that there exists what does not exist – absolute exactness or precision – but also because they are emotionally highly charged: under the guise of scientific character and of scientific objectivity, they suggest that precision or exactness is something superior, a kind of ultimate value, and that it is wrong, or unscientific, or muddle-headed, to use inexact terms [...]
[...] the demand for precision is empty, unless it is raised relative to some requirements that arise from our attempts to solve a definite problem. [...]
[...] the attribute of exactness is not absolute, and that it is inexact and highly misleading to use the terms “exact” and “precise” as if they had any exact or precise meaning [...]
[...] a lesson taught by the whole history of science: that absolute exactness does not exist, not even in logic and mathematics (as illustrated by the example of the still unfinished history of the calculus); that we should never try to be more exact than is necessary for the solution of the problem in hand [...]
The source.
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