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.

Arqiduka said...

Happy to be corrected if wrong, but I think the examples made are instances of "an assumption made that appeared trivial is no longer so trivial, and may need to me relaxed in the real world" instead of instances where a priori knowledge turns out to be wrong. Ex. Is now usefull to model non-flat space etc. If some trivial assumption ofthe Austrian framework is likewise relaxed tomorrow (ex. Emergence of AI as an actor) all the best.

But I also think Austrians make too kuch of these differences. A better interpretation in my view would be that there are far fewer degreez of freedom to economic analysis than many non-Austrian economists think, not that there is nothing usefyll to be gained by models and math.

David Friedman said...

It's a case where what someone thought was a priori knowledge was wrong because he didn't realize that it depended on an assumption that could be false. My point is that after such striking examples of that pattern, one should assume that anything you believe is obvious a priori might turn out to be similarly false. Obviously it might not, but you should not treat it as certain even if it seems to be because you cannot think of any way in which it could not be true.

I think most non-Austrian economists believe in the same laws of economics, but as things partly based on a priori argument, partly on evidence, and things you expect to be true but cannot be certain are. Diminishing marginal utility is one example.

I discuss a good deal of this in a recent chapter draft, will add a link to my post.
http://www.daviddfriedman.com/Ideas%20I/Economics/Critique%20of%20a%20Version%20of%20Austrian%20Economics.pdf

naivetheorist said...

"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.". Walter Block told me that economics is a branch of logic and being a theoretical physicist, a field where the worth of a theory is determined by its ability to agree with experiment, i immediately lost all interest in the subject.

David Friedman said...

My interaction with the Austrians started as an online debate with Walter, continued by email correspondence with him and several others. Mostly I am trying to figure out what difference in substance there is between my approach to economics and theirs and the answer still isn't clear. My chapter is mostly a critique of Rothbard's _Man, Economy and State_, which is easy since much of it is wrong on its own terms and much of the rest consists of rejecting conventional Marshallian economics with no good reason and no attempt to explain the arguments he is rejecting.

The hard part is figuring out what Austrians in general, as opposed to Rothbard, believe that distinguishes them from Marshallians, and still isn't clear to me.

Arqiduka said...

Not wanting to sound like the motte to some Austrians' bailey,I understand the key difference to be that Austrians do not allow some questions to be asked because they make no sense in the model. An example, you wish to study whether (not by how much) an increase in minimal wage impacted employment at all. An Austrian would not even try, as the theory tells that the impact must be there and it must be negative. If your model is calibrated and comes out as finding no statistically significant effect on employment, to an Austrian that'd be bunk. Go add another varibale until this coefficient is negative and material, they'd say.

Critiquing this comes down to disproving the logical chain of reasoning, but all science relies on some a priori framework. The Austrians just go nuts with theirs, but a difference of degree.

naivetheorist said...

Arqiduka:

The fundamental difference lies in treating economics as a branch of science or as a branch of logic. We are still arguing about the relevnce of Godel's Theorem to physics (eg., Penrose thinks that Godel places limits on the status of theories in physics while many other think that Godel is not at all relevant to theories in physics.

Arqiduka said...

@naivetheorist,

I don't think that's a fair assessment of the School, and am aware that Block and others go into those flight of fancy at times (not implying you are willfully misinterpreting what Block said at all). The method itself - as fair as I remember it - is simply saying that there is layer of a priori laws you are not allowed to challenge based on empiricism, no matter how much your model explains. You only challenge these based on logic. A question of philosophy if such an approach qualifies as a branch of logic or not.

The practical difference then, is that most other schools would consider the edifice of a priori laws erected by the Austrians to be a combination of trivial and already included, and just plain wrong.

naivetheorist said...

the idea that economics is a branch of logic rather than of science is not just a flight of fancy. it is a fundamental core of the Austrian school.

Richard Feynman said of physics theories:

"If it disagrees with experiment, it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is, it does not make any difference how smart you are, who made the guess, or what his name is — if it disagrees with experiment, it is wrong.".

Walter wrote:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1879610

"Methodenstreit is a debate in economics concerning the philosophy of social science. It involves the issue of which is the property method to pursue in the dismal science. Although this type of debate had its origins two centuries ago, the present paper is a contribution to a more modern Methodenstreit begun by Caplan (1999). It addresses some of the fundamental issues in economics: is this discipline best to be thought of along the lines of an empirical science, such as physics or chemistry (the view of the logical positivist school), or is it more properly described as a branch of logic or mathematics (the perspective of Austrian economics)? "

Arqiduka said...

By such standards yes, there's an obvious difference between the Austrian approach and the modern physics approach. Not sure the gap is so great with other schools of economic thought though. If I propose a model which derives some predictive power from assuming upward sloping demand curves, what happens? Am I laughed out of the room or do they take me seriously?

naivetheorist said...

i don't know. i gave up on talking economics to either theoretical physicists (in the field of econophysics) or economists.
you might want to look at "the end of theory" an intertesting, easy to read, book on economics methodology.

https://www.amazon.com/gp/product/0691169012/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

as Isaac Marcosson said:: “lf all the economists in the world were placed end to end they would not reach a conclusion."

note: when i praise theoretical physics, i asm excluding the fields of theoretical cosmology and interpretations of quantum mechanics where the authors are disconnected from experiment (and often, from sanity).

Arqiduka said...

You cannot apply the method of physics to economics, and this much is right with the Austrians. You cannot generate controlled experiments at will that allow you to rely entirely on empiricism in looking for the simplest model that explains. Where theoretical physics stops being able to generate experimental data it freezes and goes off in a million directions until we make a bigger collider.

You have to make sense of a real-life situation in econ, with no ability to control variables. Hence, you have to rely on an a priori framework that precedes you empirical work. Austrians take their ability to create chains of reasoning for granted where they should not, but the basic idea remains and is sound.

It is true that if you line up all the world's economists they would not reach a conclusion, but this is the nature of the field.

Brandon Berg said...

I don't disagree with the broader point, but this strikes me as an unfortunate example, given that relativity was worked out a priori before it was experimentally verified.

naivetheorist said...

"Where theoretical physics stops being able to generate experimental data it freezes and goes off in a million directions until we make a bigger collider.". i suggest you read the blog "Backreaction" by Sabine Hossenfdelder. Bee is a quantum gravity theorist and a leader in the fight against building bigger colliders. you might also read stuff by P.W. Anderson, a leader in condensed matter theory, who was most responsible for stopping construction of a supercollider in Texas.

James said...

The example about the triangle is not a case of a priori reasoning being wrong at all.

It can be proved from axioms that the Pythagorean theorem holds for any triangle in any Euclidean plane. That is an a priori claim and it is entirely correct.

There is also the incorrect belief, held by most people even today, that Euclidean geometry is a correct description of the material world. This is based on the senses and not on a priori reasoning from some set of axioms.

James said...

I no longer would call myself an Austrian, but when I did claim the title I frequently had the experience that non-Austrians were extremely inconsistent on the importance of methodology.

When challenged to defend their approach, the response was that methodology is not that important and Austrians need to quit talking about methodology all the time. When Austrians would present some economic idea based on a priori reasoning, the response was that methodology is incredibly important and that the only valid approach was building models based on algebra and then fitting the parameters of those models using econometrics software.

To be fair, that inconsistency is not what I am detecting here.

Anonymous said...

Are you holding in reserve any specific thoughts on David Harriman's work "The Logical Leap: Induction in Physics" (2010)?

naivetheorist said...

Harriman's book is, imo, totally useless.it is obvious that Harriman "(as well as Peikoff) is not a theoretician and has no familiarity with, or understanding of, the practice of doing theoretical physics research. btw: the same can be said for Thomas Kuhn who misdescribes scientific research). my personal view is that you can't talk the talk if you haven't walked the walk (ie., only theoretical physicists are qualified to have an opinion on the nature of theoretical research.).

Matteo Pastrello said...

After watching the debate it strikes me as clear that in Austrian economics, even though i agree with much of the conclusions and policy interventions (or lack of policy interventions better) that they arrive to, there is one fundamental problem and misunderstanding of what testing and experiments are supposed to do. If I construct a mathematical model given certain assumptions, and manage to prove in that framework all of my conclusions, there is no questions that I was able to arrive to some form of a-priori knowledge, and that doesn't need to be tested for it to be correct. The point of testing, in my opinion, is to control that the "real" world (leaving aside various epistemological inconsistency and assumptions in the world "real") really reflects the assumptions that I took for granted. So testing isn't really about testing the conclusion of a theory, but rather to test the assumptions made for that theory to work. Given that the theory is well constructed and free from internal logical or mathematical errors.

Amrit said...