## Thursday, January 20, 2022

### A Priori Certainty vs Physics

I have recently had an extended conversation with some supporters of the Austrian school of economics about the differences between the way they do economics and the way I do. One thing they offered as part of what distinguished their school of thought was the idea that one can determine economic laws by logical reasoning based on axioms known with certainty, just as one could know facts such as the Pythagorean Theorem without measuring any triangles.

The interesting thing about that example is that it isn't true. Space is not flat,  not perfectly described by Euclidean geometry. If you measured sufficiently large triangles you might  find that the Pythagorean Theorem was false or that the angles did not add up to 180 degrees. That is one of several ways in which modern physics is inconsistent with things that seem to us certainly, even obviously, true.

A second example is the way in which velocities add. If I am in a train going north at 50 miles an hour and walk towards the front of the train at four miles an hour I am moving at 54 miles an hour relative to the ground. That not only is obvious, it seems to be something that one could easily prove. It is not, however, true. At those speeds it is very close to true, but if the velocities are a significant fraction of the speed of light it is not.

That example is from special relativity but quantum mechanics offers others. The closest one can come to an ordinary language description of the double slit experiment is that a single electron, beamed at a barrier with two slits in it and a detector behind them, goes through both slits. The closest one can come to describing tunneling is that a particle can get from one place to another even though it is impossible for it to be between them.

These are all cases where our picture of reality, based on large objects moving slowly, turns out to be wrong. The only one of them where I can, with some effort, get the correct picture to make sense to me is the first. Once the implicit assumption (that simultaneity is defined independent of reference system) is pointed out, it becomes possible to understand why what seems obvious might not be true.

As these examples show, something can appear to be known with certainty and yet be false. However clear the a priori claim, one should believe it with less than certainty. That is an argument for the importance of testing the implications of economic laws against real world data.

Many, perhaps all, Austrians would agree that even if an economic law is known with certainty its implications for the real world depend on uncertain real world facts, so the point may not matter much for the implications of Austrian economics, but I think it is relevant to the way in which many Austrians think about the difference between the schools. Recognizing that even one's most solidly held beliefs might turn out to be mistaken is, in that context and many others, a good thing.

I beseech you, in the bowels of Christ, think it possible that you may be mistaken.(Oliver Cromwell

P.S. My current views on Austrian vs Chicago school are in a webbed chapter draft. Comments welcome.