The mathematics of Austrian School economics

I’ve only just started learning about the Austrian School of economics, after reading an article claiming that it successfully predicted both the Great Depression and the current crisis. I’m currently a few chapters into von Mises’ book “The Theory of Money and Credit”. In fact I only found this site because Wikipedia links to an online version of the book hosted here. While I was reading about the Austrian School on Wikipedia, it claimed that the main criticism of this school of economics is that its theories are too qualitative and imprecise, and not mathematical enough. This means that its claims cannot be easily tested in the real world. That is, that this school relies on logic and reasoning instead of empirical testing, making its theories more philosophy than science.

My questions are:

  1. What are the mathematics and econometrics behind Austrian economics, if there are any?

  2. Are there any good books or articles on this subject you could recommend?

Cheers,

Iain

Welcome Iain

A good lecture about reasoning in austrian economy can be found here. Just a short remark, if only empirical testing counts as science, we would have to give up math altogether basically, as math is at its core axiomatic :slight_smile: And I would strongly disagree to say philosophy is not science.

A good starting point might be the reading list found here.

Regarding the critisism of austrian economy being to qualitative and imprecise, because they are not mehtematical enough, one quick argument.

Economic actions are simply action of individuals. How an individual act at a given time in a given environment can not be expressed in mathematical terms. Without offering a proof here, each individual strives to achieve his goals. One does so by choosing means he employs to get there. What action is taken depends on the preferences a person has at the time of the action. The end with the highest preference that seems attainable with means thought to be at hand will be choosen. In fact people do no only have one goal at a time. So you have a list of preferences of wich you always choose the one you regard highest. You show that by acting accordingly. All other preferences are lower on the list. Yet, they are simply rankings. This means they are ordinal. You can not use ordinal numbers to calculate anything, this can only be done with cardinals. If the basis of economy is human action and the action is based on picking the one with the highest preference which, at any time, are a list of rankings,e.g. ordinal, you can not possibly build any mathematical system on that no matter how complicated the equations are you use.

If you do not accept that 1 and 1 is two than you can not have any useful discussion about calculus at all.

That does not mean austrian economics doesn’t use math. It just means any math based on preferences humans have counterdicts itself right from the start.

Have a lot of fun researching

Wait, that’s the criticism of Austrian economics? Yeah, so sorry to the mainstream dolts for not wanting to apply mathematics to an area that does not admit of quantitative precision. But, you know, we might as well gloss over these problems and pretend they don’t exist!

Whom do you refer to? Me?

No, the “criticism”. It’s blatant scientism, and it isn’t even true of the natural sciences, strictly speaking.

I agree, yet he refered to an article I think and I tried to point him to some arguments. In fact the Hoppe lecture copes exactly with “scientism” ehmm positivism I mean :slight_smile:

Have a great day

Yes, perhaps I should’ve just responded to his post directly. At any rate, good reading on the topic, in addition to what you mentioned, is Martin Hollis’s Rational Economic Man and Hayek’s The Counter-revolution of Science. If he’s feeling amibitious, Laurence Bonjour’s In Defence of Pure Reason and Brand Blanshard’s Reason and Analysis are also excellent, although not focused on economics. Finally, these articles and books are worth reading too:

-Economic Science and the Austrian Method

-Antipsychologism in Economics

-Wittgenstein, Austrian Economics, and the Logic of Action

-Reason & Value

-On Praxeology and the Question of Aristotelian Apriorism

-The Question of Apriorism

These are all good supplemental readings (with the first being primary.)

This point was made by Jeffery Tucker I believe, but I’m not sure: If mainstream economics is so “accurate” with all of the mathematical non-sense and econometric “forecasting”, why did they not predict the current situation? Just look at the history of what Austrian economists/theories predicted. Quite accurate if you ask me, and they didn’t use bogus mathematical models or ridiculous equations. Thus, I would tend to take what Austrian economics predicts over false economists’ predictions any day.

(1) As per your 1st question, I’d be interested in the answer myself. I’m sort of in the same position you are.

(2) As per your 2nd question, here is an article providing a quick overview of the main reasons why Austrian method is deductive instead of empirical.

Spoiler: Surprisingly, the author doesn’t dismiss empiricism as useless, as one might suspect an Austrian would be tempted to do. However, he presents an argument as to why a deductive methodology in studying social affairs is far superior.

My linking skills need polishing apparently. Here’s the url: http://mises.org/daily/1304

I listened to the lecture by Hoppe (http://media.mises.org/mp3/MU2008/4_Hoppe.mp3) and I disagree with some of his defences of Austrian reasoning, and some of his attacks on logical positivism.

For instance, he says that if he deduces an economic statement from certain axioms, such as law of marginal utility, then he knows that this statement is true. Hoppe claims that he knows with absolute certainty that the conclusion of any deductive argument is true, and so there is no need for empirical testing. To use another of his examples, he knows that having a minimum wage of $1000 per hour would lead to a rise in unemployment, and there is no need to test this. Hoppe’s mistake is not realising that we must be certain that the axioms of a deductively valid argument are true if we are to be certain that the conclusion is true. However, we cannot know that our axioms are true with certainty, because all axioms are in essence assumptions. An a priori statement is one which we take to be true for the purposes of argument; the mistake here is assuming that this means that an a priori statement is in fact true. Hoppe claims that some a priori are self-evident truths, which are ‘unfalsifiable’.

(By the way, he uses the term ‘unfalsifiable’ incorrectly; he takes it to mean that a statement is unfalsifiable if it cannot be shown to be untrue because it is true, whereas the correct usage would be that a statement is unfalsifiable if it cannot be shown to be untrue in principle; that is, because there is no observation or experiment that could even attempt to show that it is false.)

However, there is no justification for assuming self-evident truths, or that a priori statements are true. There is by definition no deductive basis for an a priori statement, so how can we be certain that it is true? The only possible justification we can have for assuming the truth of a priori statements, if we have any at all, is inductive. That is not to say that a priori statements are inherently unreasonable, merely that we cannot be certain of their truth, in the same way that all conclusions of inductive reasoning are inherently uncertain, even if reasonable.

An example is Euclidean geometry, which is in fact mentioned in one of the articles defending Austrian reasoning (http://mises.org/daily/1304). With the axioms of Euclidean geometry, one can deduce all sorts of results, which are all true as long as the axioms underpinning Euclidean geometry are true. But we do not know that these axioms are true. People believed they must be true for a long time, because they were taken to be self-evidently true. However, if you take different axioms you end up with different spaces and different results. Indeed, modern science believes that the space we inhabit is in fact non-Euclidean, so the laws that people like Hoppe might have been absolutely certain about, like that the shortest distance between two points is a straight line, are not necessarily true.

I also disagree with his main attack on logical positivism, which is that it relies on an assumption of constancy. He then argues that it is impossible to obtain constancy, and so logical positivism is inherently flawed. His argument is as follows:

Suppose I have a hypothesis, if A then B. I then observe A, followed by B. This observation ‘confirms’ the hypothesis, but only in the strict sense of confirmation which Hoppe defines. I then, at a later date, again observe A followed by B. I would then argue that this second observation confirms the first observation. Hoppe says that this is only the case if there is a constancy over time between the two observations; if the nature of A or B has changed between the two observations, then the second observation can neither confirm nor falsify the first. The argument then continues that any observation or experiment must be made by an observer, who must learn from his observations, otherwise what is the point of observing? Because the observer learns after each observation, there is therefore no constancy between observations, and so logical positivism is flawed.

However, there are a number of problems with this argument. To begin with, he uses confirm in the wrong sense, indeed contradicting his own definition of confirm, which is reasonable from Popper’s perspective. That is, he talks about confirming or falsifying observations, but that is nonsensical. One can only talk about confirming or falsifying hypotheses. When one makes an observation, then another observation, these observations neither confirm nor falsify one another; they are merely separate observations. One observation may confirm a hypothesis, whilst the other falsifies it, or vice versa for another hypothesis, but it doesn’t make any sense to talk about observations confirming or falsifying one another.

Furthermore, Hoppe makes the logical mistake of assuming that if A changes, then A is still A, when this is by definition false. If A changes it is not A, but rather something else, which we can label A’. Returning to the original hypothesis of if A then B, and we observe A’ followed by B’, then this is a different phenomenon from A followed by B, and so neither directly confirms nor falsifies the hypothesis. Thus no assumptions about constancy are necessary at all. Furthermore, if the rule governing relation between A and B changes, that is the hypothesis is ‘true’ at one point in time but false at another, then the hypothesis, is, strictly speaking, false, because it requires A to always be followed by B.

As an aside, I don’t think Hoppe is strictly speaking about logical positivism, but rather mixing elements of Popper’s philosophy with that of the logical positivists. He takes Popper’s view that hypotheses cannot be verified; one can only fail to falsify a hypothesis, which is the definition he takes of ‘confirm’, whereas the positivists thought that meaningful statements could be determined to be true or false. Also, I suspect Hoppe is confused by the concept of causality. Causality has no place in logic; to say A implies B in no way implies a causal relation between A and B.

No, Hoppe understands it quite well.

Whence this notion of axioms? Even granting this, an assumption can be either true or false. Those that cannot be denied without contradiction are true. So where is the problem?

Or perhaps because any attempt at denying the truth in question is self-defeating.

There are definitely ways to know if it is true or not.

I think you’re confusing things here. Hoppe has a Humean notion of causation in mind, whereby all man observes in nature are correlations between certain events A and B. It is the interpretation of his own mind that views this as a causal, necessary relationship. I don’t have this view of causality, but positivists do subscribe to it. The problem being that causality is presupposed in empirical observation to begin with… if one does not assume it all one observes are random events following other random events temporally. Nothing more.

No, the point is that intervening factors can be the cause of an observed factor. For example there is no way to rule out that some other factor, C, caused B as opposed to A. Moreover, to deduce any laws from this, that instances of B following A obtain, we have to assume that there is such a thing as lawlike constancy in relations between factors. Hoppe’s point is that the positivist has no ground to stand on here. This is a real problem for positivism.

Yeah, except in practice one needs to be careful not to toss out well-confirmed theories for the smallest of problems. This links to what I said before and is another problem positivism (and falsificationism) faces. Kuhn’s account of science is better than the nonsense dreamed up by positivists.

Not sure about this, but it’s been a while since I heard the lecture. I wonder if it has to do with a Kripkean notion of necessity. E.g. if water has X properties, then we should expect it to cause iron to rust. Water has X properties thus, as a matter of logical necessity (the conditional being satisfied), water can cause iron to rust.

Being an Aristotelian I don’t agree with Hoppe 100%, but he is solid on this much.

The notion of axioms is essential to any deductive reasoning. It is impossible to deductively reason anything without axioms. Hoppe claims that he knows with absolute certainty that the conclusions of his deductive reasoning are true, for instance about the law of marginal utility or about the effects of a high minimum wage on employment. He is therefore saying that the axioms underpinning that deductive reasoning are true, and that he is certain they are true.

Now, an axiom or assumption is either true or false, yes. But one cannot deductively determine whether an axiom is true or false, because by definition axioms have no deductive basis; they are the starting point from which all deductive reasoning follows. Since the truth of axioms cannot be determined deductively, one must do so inductively, which means resorting to empirical methods. To have any justification for an axiom, one must either have direct empirical evidence for it, or else have empirical evidence for its conclusions. The former is a stronger justification, because it is possible for a conclusion of an argument to be true without the premise being true. But either way, one must resort to empirical, inductive methods. Not only does this contradict Hoppe’s own position that empirical analysis is unnecessary in the face of deductive logic, but it introduces uncertainty into the truth of all deductive claims.

That is Hoppe’s argument, yes, but it doesn’t alter the fact that he misuses the definition of falsifiable.

What are these ways?

Causality is not presupposed in empirical observation. To state that an event A is always followed by an event B does not in any way imply causality, unless one defines causality as “B is caused by A if B always follows A”, but in the intuitive sense of causality this is not the case. If B is followed by A, it could be that B is causing A, or else that a third event C is causing both A and B, or else that the two events are unrelated and only happen to coincide at similar points in time. All of these possibilities are real and cannot be discounted. If I empirically observe two events A and B close together in time, I cannot make any statement about a causal relationship between A and B, or even if there is one. But just because one cannot make any causal statements does not mean that all one observes are “random events following other random events temporally”. While this is a possibility, to state so is to make a claim about the causal relationship between two events, which cannot be done. The only thing an empiricist can say is that B has been observed to follow A closely in time, or to formulate a hypothesis that if A occurs, then B occurs. A concept of causality is indeed not even necessary.

Again, the concept of causality is entirely misplaced. The hypothesis is not that “B is caused by A”. This hypothesis is unfalsifiable in the correct sense of the term. The hypothesis is “if A, then B”. It is irrelevant what causes A or what causes B; what matters is whether, when we observe A, we then observe B. If we observe A and then B we fail to falsify the hypothesis, and if we observe A and fail to observe B, we falsify the hypothesis. Again, the causality plays no role here, indeed has no relevance to the question at all.

This is the problem of induction, that any laws derived from repeated empirical observation are only certain to be true if there is constancy in time. I don’t know if this is exactly what Hoppe was getting at; if it was I missed his point somewhat. The problem of induction is indeed intractable, and it does indeed mean that it is impossible to deduce laws from instances of B following A. But no one claims to be able to deduce laws from empirical observation; Hoppe himself mentions the distinction drawn by logical positivists between empirical statements and logical statements. One can deduce logical statements from other logical statements, but one cannot deduce a logical statement from an empirical statement. They are separate things. That is why no empiricist worth his salt will claim, quite unlike Hoppe, that his laws of nature or economics are absolutely certainly true. The problem of induction means that one cannot know that any empirically founded law is true. That is why the testing of a hypothesis does not verify it; it either falsifies it or fails to falsify it. This is a limitation on empiricism. Hoppe however fairs no better, since he is certain that his statements are true when he has no justification for such certainty.

I would agree that Kuhn’s description of science is better than logical positivism. However, Kuhn, unlike Hoppe, does not deny the importance of empiricism. Hoppe claims that true statements can be made about the world with absolute certainty without any empirical basis. I am arguing that that is nonsense. I agree that logical positivism has its problems and limitations, but I would say it’s more sensible than what Hoppe is arguing.

What you’re referring to here is a weakness in the Kantian system with regard to concept-formation: they lack a satisfying account of it. Nonetheless, it does not follow that axioms require constant empirical testing. And moreover, if an axiom’s truth is such that denying it leads to absurdities, it is guaranteed.

What do you mean “misuses”? Falsification has multiple meanings, one of which is the one he offers.

I mentioned one above, i.e. facts of which their denial is self-defeating and logically absurd.

Except for the “minor” problem that positivists hope to discover scientific laws from such observations.

Yeah, I phrased that poorly. At any rate, why should that falsify the hypothesis? What if some intervening factor caused B not to appear? This is one area where positivism needs to make a theoretical, non-observational assumption to the effect that ceteris remain paribus. And if the hypothesis is to be in anyway interesting, i.e. not just recounting correlations but in fact trying to reveal causal relations between various facts, then one most certainly must impose the category of causality on observed facts. Otherwise one is not dealing with laws; just correlations. And positivists are interested in laws. Martin Hollis lists the ten tenets of positivism here, on page 10. The problem is with vii), i.e. that it is a non sequitur to infer from correlation that there is causation. His subsequent discussion of the problem of induction is relevant too.

Hoppe is mentioning a distinction positivists posit by way of pure assertion: that the only statements knowable a priori are syntactic and logical truths, i.e. analytic truths. All others are knowable a posteriori and are synthetic. The problem, being, this assertion is itself non-trivial, about the real world, yet it is not testable in anyway. I.e. it falls into neither category (because it is a truth that is a priori and synthetic.) Positivists certainly hope to uncover scientific laws involving causal relations between events; mere correlations will not suffice, and it takes further assumptions on their part to transform correlations into causal links.

And how would you know he has no such justification?

Hoppe denies the dogma called positivism. Not the value of empirical observation. Nor is he an infallibilist with regard to truths other than the axioms.

If by “empirical” you mean constantly “testable”, then sure, Hoppe is arguing one can have knowledge of the sort that is about the world and does not need constant testing. You’ve done nothing to demonstrate this is nonsense. I think maybe you should give Plauche’s paper a read, perhaps it will be more to your taste. Perhaps it is the Kantian verbiage that is getting in the way.

The specific experience with which economics and economic statistics are concerned always refers to the past. It is history, and as such does not provide knowledge about a regularity that will manifest itself also in the future. - Epistemological Problems of Economics, p. xiv

As a method of economic analysis econometrics is a childish play with figures that does not contribute anything to the elucidation of the problems of economic reality.
The Ultimate Foundation of Economic Science, p. 63

The objection that axioms ultimately must rest on an empirical foundation seems to me to be an important objection, in the present discussion, to the Austrian case - if by the Austrian case we mean a method of learning that supposes to deduce incontrovertible facts about human economic behavior from a priori, and ONLY a priori axioms.

Here’s a rundown of what’s been said about this so far:

Let’s take the Austrian axiom that humans act - specifically, that they exercise volition with the goal always to better their material condition (I hope I’m representing the Human Action axiom accurately here - please correct me if not). This to me seems an empirical statement. While difficult to imagine how anyone might reasonably object to it as a premise to a deductive argument about the economy, I can’t see how this would raise the Human Action axiom to the level of being an a priori statement.

And then there is also Mr. Iian’s foundational objection that " there is no justification for assuming self-evident truths, or that a priori statements are true."

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?

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.

I don’t want to get too bogged down in philosophical and semantic nitpicking, so I’ll try and get to the core of my problem with Hoppe’s views. Hoppe says that one can make statements about the world, in particular about economics, which we know to be true, and moreover that one can make such statements without any empirical basis, and that such statements do not need to be empirically tested.

My first problem is that all deductive arguments rely on axioms, and that these axioms are assumptions, which we cannot know to be true, so we cannot know that our deductive statements about the world or economics are true, even if these conclusions were arrived at by deductively valid arguments. 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. I also would like to know how we judge such conclusions to be absurd. If we take a set of axioms and arrive at a contradictory conclusion, then we know that not all of them are true, but absurdity does not necessarily disprove an axiom, since what we think is absurd could easily be true. Indeed our notion of what is absurd and what is reasonable is ultimately inductive. If at our conclusion we determined that everyone walks around on their heads, we would call it absurd, but only because we observe that this is not the case.

My second problem is this apparent distrust of empiricism. If statement is true, then surely testing it against the observed reality would confirm it, so why not empirically test even these deductive statements about the world? I don’t quite understand what your and Hoppe’s problem with empiricism is. I’m not talking about ‘constant testing’ - no theory, scientific or economic, is tested ‘constantly’. I’m merely saying that if Hoppe makes a statement which he is certain is true, but observation contradicts it or regularly contradicts it, then why would this not force a reformulation or abandonment of the contradicted statement? 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.

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.

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.

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.

Call them well-grounded conceptual truths, if the word axiom bothers you.

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.

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.

No, this isn’t a matter of psychology. It’s a matter of whether the principle in question affirms what is attempting to deny (i.e. entails a rank contradiction.)

There is a (reasonable) distrust of the hypothetico-deductive methodology as applied to the social sciences. Not of empiricism, though, as in knowledge gained from the senses, i.e. in the traditional Aristotelian sense (its take on induction also differs from that prevalent in modern philosophy.) The view Hoppe is putting forward accommodates both inductive and deductive truths, in a way that positivism fails to, even if his view has its problems.

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. Hollis and Mises are good reading on this. You’re not dealing with deterministic objects, you’re dealing with goal-oriented beings. As an example, if prices do not fall in spite of an expansion in supply this may be due to any number of intervening factors which pure observation will not reveal, and which, strictly speaking, do not contradict the theory. Even the fact that something is a price requires an understanding from an agent-centric point of view, i.e. the study of a thing with motives and intentions.

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.

By the way, Hoppe draws on Kripke a lot, whose discussions on necessary “empirical” (i.e. synthetic) truths are illuminating (in his Naming and Necessity.) To clear up any misunderstanding on Hoppe: he is a fallibilist (he believes deductive arguments are prone to error, hence subject to revision; I’d go further and say concept-formation is too, though to varying degrees) and he is not against the hypothetico-deductive method in the natural sciences (though even here there is debate; Feyerabend for example argued there is no such thing as one “scientific” method, just methods.)