Wednesday, September 7, 2011
I really like my mathematical economics professor
Why? Because at least half a dozen times during the class he justified doing something because it was "useful", and he did it last week too. He was the one in the math review that said "being able to abstract in useful ways is useful", and at least twice he's said "I know this is wrong but it is very useful" (once talking about the equality of sets and another time talking about parallel lines). He's never propounded a philosophy of knowledge explicitly, but he is unapologetic about useful but potentially false premises that aid understanding.
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I believe, not making a pun that the use of such loose analogies is often useful and even an insightful teaching tool, as often pointing out the connections between otherwise disparate subjects almost maps the way in which as human beings we naturally adapt to the learning of new concepts, contrasting them with what we are already familiar. But at the same time it's important to be careful not too much into such things.
ReplyDeleteFalse assumptions are useful for instance in physics to the application and inference of physical theories, allowing one to move from an idealized abstraction by steps to an approximation of a given empirical situation while at the same time having a hold on the quantitative deviation between the 2. These assumptions only serve this comparatively limited purpose however, and are not the component propositions from which physical theories are built and it is the task of the scientific method to sift out.
The latter propositions are rather in essence hypothetical premises, whose truth character is unknown, and hence can only indirectly be inferred through the falsification of competing hyptheses based on the conclusions(and hence predictions of data) they imply.
Many economists seem to be the only ones who still mix up both types of propositions. Statistical corroboration of predictions based on a chain of logical deduction starting from false premises does not correspond to scientific justification of such theories, since the entire point of a falsificationist methodology is to determine whether premises whose truth character is uncertain can be shown to be false.
In any case, greetings from an interested follower of this blog.
Indeed - there's a difference between pure mathematics and applied mathematics. The Bourbakis (sp?) type didn't turn out so well in practice, while being very elegant in formal theory. Similarly, Richard von Mises's approach to probability, while mathematically elegant, it may be unrealistic in modelling decision-making. Judging from what I've read from certain critics, it's not so much formalism being the problem as much as how realisticly the mathematics can be applied and whether or not the mathematics is used correctly.(And yes, Richard von Mises and Ludwig von Mises were related - directly in fact, they were brothers.)
ReplyDeleteKeynes himself was not opposed to mathematics per se, he was more opposed to the misuse and incorrect use of mathematics. This journal article soundly argues that some economists have misunderstood Keynes's position.
http://www.springerlink.com/content/l5457w0721nhrrx5/
--Blue_Aurora
Thanks for the thoughts Blue Aurora. I've actually had a fan of Brady bring his work (including this article) to my attention recently. I haven't had time to read through any of it yet.
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