Wednesday, July 15, 2009

On science, mathematics and economics

A typically succint and lucid review in this month's Quadrant by David Armstrong of James Franklin's What Science Knows: And How it Knows It. Such a good review of have the book on order and Franjklin's two preceding works.

The idea I gather is that the book provides a riposte to the quartet of philosophers of science who gave postmodernism a big leg up (being Popper, Kuhn, Lakatos and Feyerabend).* The flavour of postmodernism here is that version that suggests any perspective is usful, that all knowledge is relative.

I personally think that the leap between these philosophers and that position is much greater than generally considered. Firstly these philosophers were being positive not normative - describing how they think science DOES operate, not how it ought to. And secondly all of them required that theories have at least some performance as means of "explaining things"...typically of relating historically observed potential causes with historically observed potential consequences.

Franklin's "magic" I think is to make the "explains" part of this stronger. An explanation is not just a "model" that relates the inputs to the outputs but some plausible structure, and observation supports a theory under what is a test of "the inference to the best explanation". One of the current criticisms of string theory is contained in a book called Not Even Wrong but not only does it fail the falsification test it fails an explanation test - there is nothing about current string theory that makes it attractive.

This also leads to some interesting discussion on the relationship between science and maths. The discussion revolves around the idea that maths itself is the study of "structures or patterns". As a consequence it provides an incredibly useful tol set for constructing scientific theories. The interesting part is that this view of mathematics means that there is no ontological commitment inherent in the maths itself. It is noteworthy that almost all modern science has borrowed pre-existing maths. I think the last time the scientist had to build his own maths was Newton building the calculus, and even it was developed at the same time by Leibnitz as a piece of "pure" mathematics.

This all relates to economics in two ways. The first is that it punctures Milton Friedman's conception of the philosophy of economics - his positvist version. Put in more standard philosophical terms Friedman was a straightforward instrumentalist - it doesn't matter what the machinery is in the middle so long as the theory relates the inputs to the outputs in the observed way.

But it also goes to the debate about the use of mathematics in economics. The maths doesn't bring any ontological commitment in and of itself. It is just a way of doing things. The biggest criticism of the use of maths in orthodox economics is the way the theory and facts are forced into the maths. In the same Quadrant issue such a theorist refers to markets saying that "there are differences in the speeds at which markets clear". It is a nonsense in the maths of the theory which assumes instantaneous clearing of the market. Once a lag is admitted between a signal and efect it is almost certain that the market will never actually clear, merely oscillate around a path that reflects something that might have bee an equilibrium point in a hypothetically instantaneously clearing market!

Still I plan to remain a fan of Feyerabend - the importance of his contribution is to the idea that it is okay at any time to try to find another theory - even if the one you are using "seems to work". It is a plea for lateral thinking, it is a plea for creativity, it is a plea for escaping bounded rationality. Real scientists do that says Feyerabend. They are not, however, anti-empirical nor merely relativist. They are, however, inquisitive and deeply suspicious.

* For those who don't know the title of this blog is taken from both a position ascribed generally to Feyerabend, and used by David Stove as the title of a book in response.

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