The mathematics of Austrian School economics

[corpus_delicti]

Not knowing if and when Jon intends to reply, I suppose my reply will have to do for now.

[EDIT: Jon beat me to it I see. Sorry to reply with a watered-down version [:)]]

You asked the following

@Iain

Jon, you say that you can know that certain axioms are true, because if one assumes they are not true then one arrives at absurd conclusions. I disagree. I think that almost all axioms are in essence founded in empiricism. I would like you to give an example of an axiom which you think is self-evidently true because of this absurdity principle.

How about the axoim of human action?

• Human beings act by employing scarce means to fulfil ends.

To attempt to refute a hypothesis is to act with a given end in mind, i.e. the refutation of the hypothesis. Thus anyone attempting to refute the axiom/hypothesis of human action can be shown to do what they are trying to refute. The conclusion of such a refutation would thus be absurd. It would be absurd because the axiom/hypothesis is self-evidently true.

This is of course a rather crude and simplistic argument. One really needs to define what is meant by the terms action, means and ends. This is, incidentally, what praxeology encompasses.

On a different, albeit close-related, note: Why is it that no critic of the austrian school of economics simply refute the axiom of human action? If they could it would all fall to pieces. What could be more simple?

Instead they say as you say:

@Iain

Ultimately it is the role of theory to predict and explain the world, and if a theory cannot accurately predict phenomena then it is useless. if economic theories are not to remain topics of pure philosophical speculation, then they must usefully predict events of the real world.

Why is a theory useless if it cannot predict phenomena accurately? To me it seems quite obvious that a theory can be useful even though it can only explain a certain phenomena and the requisites for such phenomena to occur. It might very well be that in the real world these requisites are impossible to observe, thus making accurate prediction impossible. In any case present neo-classical macro-economics has an appalling hit record it seems. Maybe they should test their hypothesis some more and not be so doctrinaire. After all biased science is not science [;)]

[Austroglide]

This [http://www.econlib.org/library/Essays/LtrLbrty/gryHRC1.html] is an EXC-ELL-ENT paper that begins with a deeply penetrating and thoughtful discussion of Frederick Hayek’s philosophy of mind and knowledge.

Importantly, because the initial focus of the paper is on these foundational constituents of Hayek’s thought, one begins to gain a foundational understanding of why the Austrians might wish de-emphasize the empirical. I say merely BEGIN to gain an understanding, because the focus of the paper is not to fully explore methodology.

A couple of the non-philosophical highlights:

Hayek contends, as many of you already know, that social order - including intsitutions such as morality, law, and markets - results NOT from any kind of conscious design, but instead from evolutionary and spontaneous processes whereby the disparate bits of socially useful knowledge possessed by the various members of society are coordinated.

What’s especially apt about this in regards to the “Why” of Austrian methodology, is that Hayek believes that the coordination of social knowledge is so complex that the best one can hope to do when studying social and economic phenomena is merely identify general patterns.

Here’s Hayek:

“It is evident that this interplay of the rules of conduct of the individuals with the actions of other individuals and the external circumstances in producing an overall order may be a highly complex affair. The whole task of social theory consists in little else but an effort to reconstruct the overall orders which are thus formed… It will also be clear that such a distinct theory of social structures can provide only an explanation of certain general and highly abstract features of the different types of structures… Of theories of this type economic theory, the theory of the market order of free human societies, is so far the only one which has been developed over a long period.”

Indeed, the author posits, for purposes of studying social and economic phenomena, this complexity is “not just a problem of specific data, articulable in explicit terms, being dispersed in millions of heads: it is the far more fundamental problem of the practical knowledge on which economic life depends being embodied in skills and habits, which change as society changes and which are rarely expressible in theoretical or technical terms.”

And yet another highlight of the paper is the author’s surprising and perhaps controversial contention that Hayek doesn’t subscribe to the Austrian methodology of deducing ineluctable truths from sets of axioms. In fact, the author offers, “Hayek’s methodology of social and economic science does not belong to that Austrian tradition in which social theory is conceived as an enterprise yielding apodictic truths…It seems fair to hold that Hayek acknowledges that the proper method in social and economic studies, as elsewhere, is the hypothetico-deductive method of conjectures and refutations set out by Popper.”

So, a tension potentially emerges: On the one hand, to the degree that social phenomena become increasingly complex - and social phenomena are indeed very complex, according to Hayek - the models used to describe them must become less and less descriptive. On the other hand, however, if Hayek champions the hypothetical-deductive method, as the author contends, then one might be tempted to conclude that Hayek would then champion the use of mathematical modeling to describe the economy. I’ve indeed heard that some Austrians use ACTUAL math (lol), but I’ve never heard of any Austrians championing the use of mathematical modelling.

A quite dense but illuminating paper. I recommend it.

[Jon_Irenicus]

Hayek is a complicated case and the extent to which he really deviates from Mises is disputed (in fact I recall Long saying in a lecture that Hayek presented his arguments to Mises, expecting Mises to disapprove, and Mises just retorted “great, I agree”… which might suggest there was some talking past Mises.) At any rate, one can parse Austrian econ into math or formal logic without lapsing into the hypothetico-deductive methodology. The two are not synonymous.

[corpus_delicti]

@Jon Irenicus

(in fact I recall Long saying in a lecture that Hayek presented his arguments to Mises, expecting Mises to disapprove, and Mises just retorted “great, I agree”… which might suggest there was some talking past Mises.)

Any chance you could recall which lecture this is?

[Austroglide]

@Jon Irenicus

At any rate, one can parse Austrian econ into math or formal logic without lapsing into the hypothetico-deductive methodology. The two are not synonymous.

However, the author’s argument is precisely that Hayek is convinced of the necessity of the hypothetico-deductive method. And Hayek IS synonymous with the Austrian school.

Clearly we’re not going to settle this matter here. My point is that a somewhat compelling case is made by the author that Hayek indeed believed in the hypothetico-deductive method. If this is in fact the case, I imagine this should have important implications for how Austrians approach their subject. At the same time, however, we see that if this idea about Hayek is in fact true, it has to date had little to no bearing on the Austrian’s continued use of Misean methodology.

[Austroglide]

@Iain

Mr. Iian, having little familiarity with the philosophy of science, I don’t get this. Must truth, in all cases, spring from either a process of induction, a process of deduction, or not at all?

Yes, in the sense that philosophy of science usually takes induction to be all forms of reasoning which are not deductive. So to talk about inductive and deductive reasoning is to talk about all forms of reasoning.

Take the statement “All men are male in gender”. Please elaborate as to why the truth of this statement cannot be granted - i.e. without reference to the empirical.

This statement is definitional. A man is defined a someone who is male in gender, so this statement is true because it is true. That is, it is true because we have defined it to be so. Axioms can be definitions, and in mathematics they generally are. If we deduce a conclusion from a set of definitions, then it is true when applied to that set of definitions. Such conclusions only have any significance to the real world is we assume that some objects or phenomena in the real world have that set of properties.

For instance, define anything with properties A, B and C to be a P. Suppose we take these axioms A, B and C and arrive at a conclusion “All P are Q”. This is true by our definition of P. But P is simply a logical construct; it does not refer to any real world phenomena. But if we then say: a real world object N has properties A, B and C, therefore N is a P, therefore N is a Q, then we are making the inductive, empirical leap that N has properties A, B and C. Our set of axioms are now:

1. Something with properties A, B and C is a P

2. N has properties A, B and C

The first axiom is definitional, but the second is assumed, based on induction. We observe that N has these properties or otherwise assume them. No deductive statement can refer to the real world without such an inductive leap.

Excellent. Thank you.

[Jon_Irenicus]

However, the author’s argument is precisely that Hayek is convinced of the necessity of the hypothetico-deductive method. And Hayek IS synonymous with the Austrian school.

Not really. Hayek is just one of its more popular exponents. Menger, followed by Mises would be synonymous with the Austrian School.

Clearly we’re not going to settle this matter here. My point is that a somewhat compelling case is made by the author that Hayek indeed believed in the hypothetico-deductive method. If this is in fact the case, I imagine this should have important implications for how Austrians approach their subject. At the same time, however, we see that if this idea about Hayek is in fact true, it has to date had little to no bearing on the Austrian’s continued use of Misean methodology.

Why should it if Miseseans do not agree with him? Lachmann also had divergent views on methodology from Mises. I think Long occupies the more reasonable ground in this matter. If you mean to imply Miseseans simply dismiss Hayek, they do not; they simply agree with Hayek in his earlier phase.

Corpus, I think it was in his lecture on positivism. I don’t recall the exact title.

[Austroglide]

@Jon Irenicus

However, the author’s argument is precisely that Hayek is convinced of the necessity of the hypothetico-deductive method. And Hayek IS synonymous with the Austrian school.

Not really. Hayek is just one of its more popular exponents. Menger, followed by Mises would be synonymous with the Austrian School.

I see. I misunderstood Hayek’s place in the Austrian tradition. Thank you.

[Iain]

No, not without an empirical basis understood as a basis in the world. I’m going to try save you time here, to avoid talking at cross-purposes and getting bogged down in semantics: read the neo-Aristotelian documents I mentioned, especially the ones by Roderick Long, Geoffrey Plauche and Barry Smith. Hoppe is a Kantian. Their entire conceptual framework is different to what is in currency in the philosophical mainstream at the moment (so is the neo-Aristotelian one, but not by as much in a sense), and so there is bound to be confusion. If you would prefer to pause a discussion on the matter until you’ve had time to read up on this, that is fine.

Since one of those documents is 163 pages long, I don’t see myself reading them anytime soon, since I am not so much interested in neo-Aristotelianism. If an understanding of neo-Aristotelianism is necessary in any discussion of Austrian economics, perhaps you could give me a brief summmary of what it entails?

What do you mean by “empiricism”? Do you mean observation from the real world? That is not the same as saying something must be constantly testable and open to revision. Certainly not in the case of well-grounded empirical truths.

By empiricism I mean both observation and testing - in essence those two things are not dissimilar. Testing is simply a particular way of making an observation, usually in a more controlled environment. Certainly something does not have to be “constantly testable” to be considered scientific or meaningful. Astronomy is a science, but it is not necessary to replicate stars or planetary formations in the laboratory; it is enough to observe them. Just because empirical evidence was not obtained in a test does not render it useless. I think part of the disagreement here might be confusion about the meaning of empiricism. To remove any confusion, I take empirical evidence to be any observational evidence of the real world. To use an economic example, I might observe that in nations past and present, when there has been a high minimum wage, there has also been high unemployment, and use this as evidence for or against a particular hypothesis, without constructing a particular controlled experiment to show this.

Here’s the most common example in philosophy: “there is no truth”. The statement is, however, stating a truth. It is self-refuting in that sense, in that it denies the very premises it is founded upon. There are also performative contradictions, e.g. denying that man acts (i.e. behaves purposefully, in a goal-directed fashion.) The very denial constitutes an action. You can say these are “empirical” in a very broad sense and are not axioms, but well-grounded concepts, or whatever, but they’re not in need of constant testing.

I accept that you can make some logically correct statements about the world in a very limited sense - about the nature of truth or the self for instance. But to generalise these to real world observations requires an inductive leap. For instance, the there is nothing logically wrong with denying that man acts. It is impossible to deny that oneself acts, which is similar to the Descartes’ famous “I think therefore I am”. However, one cannot deductively generalise that to the people one meets in the real world. If I pass someone in the street, I cannot deductively determine whether that person is a conscious self or not, so I cannot logically determine whether that person acts or thinks or exists or is indeed a man or person at all.

Now, you might consider this a rather pathological objection - I doubt many mainstream economists will doubt that other people our conscious beings - but I believe problems with purely deductive logic like this mean that empirical evidence is necessary - although again that does not necessarily mean “constant testing”. It is possible to start with a set of what you think are quite reasonable axioms, or well-grounded conceptual truths or whatever you might want to call them, with just a few seemingly minor logical holes in them, which lead you to quite wrong conclusions. This has happened many times before in scientific history, and this is why science and economics require empirical or observational evidence to make sure we haven’t gone off onto the wrong track entirely. That is not to say that there is anything wrong with logical reasoning, just that the conclusions of such reasoning should be compared with observation of the real world.

In the social sciences? At best it may hint at an ommitted/misspecified conceptual truth (see Barry Smith on this.) If you’ve done any social science you’ll realize there is no such thing as observation of brute facts, especially considering how social science facts are multifaceted (and thus to regard something as an economic fact you need a theory that allows you to do so in the first place.) All social science is theory-laden, i.e. contingent on an appropriate interpretive framework. Otherwise one merely observes human actions, which may be interpreted in any number of ways.

Whilst I accept that eonomics deals with very complicated systems, where the interpretation of observational evidence can be very difficult, I do not believe that is enough to discount it entirely. The theory-ladeness of observation is never justification for abandoning empirical evidence altogether, because even theory-laden observation is better than no observation at all.

That is a view on this, and by no means an uncontroversial one. The instrumentalist view of science. Not everyone agrees with it, and outside of the context of deterministic objects, it becomes all the more untenable to base theories on their predictive as opposed to explanatory success. Economic theories provide good explanations, and qualitative predictions at best. Not quantitatively precise ones. This is not Physics, and humans do not behave in a deterministic fashion (this is a major problem for neoclassical theories based on prediction; they work for a while then break down utterly.) All one is saying is that different sciences merit different methodologies, something that should be obvious with the death of positivism.

I don’t think explanatory success is any means by which to judge a theory. “God did it” explains everything admirably, but it has no predictive power at all. I understand that the instrumentalist view is not without controversy, but I believe that the best way to tell if an explanation is a good one is to see how well it can predict phenomena. Now, there seems to be more confusion here between us about what it means to predict phenomena. I do not believe in any way that predictions must be quantitatively precise. I think a theory is more useful and stronger if it can make accurate and precise quantitative predictions, but certainly a theory that can make accurate qualitative predictions is better than a theory that can do neither. If my economic theory predicts that an increase in the minimum wage will cause the unemployment rate to go up, and this is observed, then this theory has successfully predicted a phenomenon. A theory that could predict the amount by which unemployment would go up to the nearest percent would be better, but as you say there are so many factors as to make this extremely difficult. As far as economics go, accurate qualitative predictions may be the best we can hope for.

[Jon_Irenicus]

Since one of those documents is 163 pages long, I don’t see myself reading them anytime soon, since I am not so much interested in neo-Aristotelianism. If an understanding of neo-Aristotelianism is necessary in any discussion of Austrian economics, perhaps you could give me a brief summmary of what it entails?

I wouldn’t say it’s necessary, but I would say it is valuable for getting an understanding of forms of empiricism that do not fall prone to the criticisms Hoppe mentioned and that can actually sustain the Austrian method. Plauche’s paper is short and worth the read, and so is Barry Smith’s, although the latter does write in a technical style. I do not disagree with you on a lot of the points you raised, but it’s important to take Hoppe’s view in with the proper background in mind.

By empiricism I mean both observation and testing - in essence those two things are not dissimilar. Testing is simply a particular way of making an observation, usually in a more controlled environment. Certainly something does not have to be “constantly testable” to be considered scientific or meaningful. Astronomy is a science, but it is not necessary to replicate stars or planetary formations in the laboratory; it is enough to observe them. Just because empirical evidence was not obtained in a test does not render it useless. I think part of the disagreement here might be confusion about the meaning of empiricism. To remove any confusion, I take empirical evidence to be any observational evidence of the real world. To use an economic example, I might observe that in nations past and present, when there has been a high minimum wage, there has also been high unemployment, and use this as evidence for or against a particular hypothesis, without constructing a particular controlled experiment to show this.

That is my point. When Hoppe criticizes empiricism he is criticizing positivism in particular, which has been the most predominant form of empiricism advocated by economists this last century. The Kantian system has its own obscure vocabulary, but essentially no one is rejecting the value of observational evidence. Of course, no economist would argue one can merely observe a minimum wage is destructive; they’d need to know that other factors were not in the way.

For instance, the there is nothing logically wrong with denying that man acts. It is impossible to deny that oneself acts, which is similar to the Descartes’ famous “I think therefore I am”. However, one cannot deductively generalise that to the people one meets in the real world. If I pass someone in the street, I cannot deductively determine whether that person is a conscious self or not, so I cannot logically determine whether that person acts or thinks or exists or is indeed a man or person at all.

And I cannot with absolute certainty preclude the possibility that I am a brain in a vat. Yet that does not lead economists to conclude there are no humans to study. No, their object of study is humans, and to take it further, they have absolutely no reason to deny they’re studying conscious beings. At best one can say what they have to say does not apply to zombies. As scientists, they’re in no position to entertain scepticism: only the possibility that they’re wrong. Arguments for the problem of other minds (aside from the non-solutions offered by the likes of behaviorists) are generally put aside by an inference to the best explanation.

Now, you might consider this a rather pathological objection - I doubt many mainstream economists will doubt that other people our conscious beings - but I believe problems with purely deductive logic like this mean that empirical evidence is necessary - although again that does not necessarily mean “constant testing”.

They can’t because the purpose of their discipline is to study human actions (and in this regard they are like natural scientists in that the latter will dismiss sceptical claims for the purposes of doing science.)

That is not to say that there is anything wrong with logical reasoning, just that the conclusions of such reasoning should be compared with observation of the real world.

Indeed - that is one way in which I disagree with Hoppe, and it’s a point Barry Smith raises regarding theories that repeatedly yield obscure explanations of the facts: that there might be something missing in them.

Whilst I accept that eonomics deals with very complicated systems, where the interpretation of observational evidence can be very difficult, I do not believe that is enough to discount it entirely. The theory-ladeness of observation is never justification for abandoning empirical evidence altogether, because even theory-laden observation is better than no observation at all.

Then there is no fundamental disagreement.

I don’t think explanatory success is any means by which to judge a theory. “God did it” explains everything admirably, but it has no predictive power at all. I understand that the instrumentalist view is not without controversy, but I believe that the best way to tell if an explanation is a good one is to see how well it can predict phenomena. Now, there seems to be more confusion here between us about what it means to predict phenomena. I do not believe in any way that predictions must be quantitatively precise. I think a theory is more useful and stronger if it can make accurate and precise quantitative predictions, but certainly a theory that can make accurate qualitative predictions is better than a theory that can do neither. If my economic theory predicts that an increase in the minimum wage will cause the unemployment rate to go up, and this is observed, then this theory has successfully predicted a phenomenon. A theory that could predict the amount by which unemployment would go up to the nearest percent would be better, but as you say there are so many factors as to make this extremely difficult. As far as economics go, accurate qualitative predictions may be the best we can hope for.

Okay, I think the problem is largely semantic then. I disagree on instrumentalism with regard to the social sciences, because the explanation you mentioned can be ruled out as backed by nothing but theology. It matters little though because you seem aware that the predictions economics offers are qualitative in nature.