One of the striking features of (propertarian) libertarianism, especially in the US, is its reliance on *a priori* arguments based on supposedly self-evident truths. Among[^1] the most extreme versions of this is the “praxeological” economic methodology espoused by Mises and his followers, and also endorsed, in a more qualified fashion, by Hayek.

In an Internet discussion the other day, I was surprised to see the deductive certainty claimed by Mises presented as being similar to the “certainty” that the interior angles of a triangle add to 180 degrees.[^2]

In one sense, I shouldn’t be surprised. The certainty of Euclidean geometry was, for centuries, the strongest argument for the rationalist that we could derive certain knowledge about the world.

Precisely for that reason, the discovery, in the early 19th century of non-Euclidean geometries that did not satisfy Euclid’s requirement that parallel lines should never meet, was a huge blow to rationalism, from which it has never really recovered.[^3] In non-Euclidean geometry, the interior angles of a triangle may add to more, or less, than 180 degrees.

Even worse for the rationalist program was the observation that the system of geometry (that is, “earth measurement”) most relevant to earth-dwellers is spherical geometry, in which straight lines are “great circles”, and in which the angles of a triangle add to more than 180 degrees. Considered in this light, Euclidean plane geometry is the mathematical model associated with the Flat Earth theory.

The discovery of non-Euclidean geometry led to the rise of formalism as the dominant philosophical approach in mathematics. The key point of formalism is that axioms like Euclid’s parallel postulate are neither true nor false. They are merely sentences in a formal language that can be combined and manipulated to form new sentences (theorems). A set of axioms may be useful if the theorems it yields turn out to provide a good model for some real world phenomenon, but this is not a mathematical question (though it helps keep mathematicians in work).

Mathematical formalism reached its high point with the Hilbert program in the early 20th Century. Despite the negative results of Godel, who showed that the more ambitious aims of the program could not be fulfilled, it was still dominant when I was taught mathematics in the 1970s.

I believe mathematical formalism has lost some ground since then, but if so, the effects have yet to filter through to economics. Mainstream (neoclassical and Keynesian) economics, since its mathematical reformulation by Samuelson and Arrow in the 1940s and 1950s, has been entirely formalist in its approach. Its axioms are not treated as self-evident. Rather the standard justification is that of modus tollens: if the theorems are descriptively false, we can trace our way back to work out what is wrong with the axioms.

The formalist program in economics hasn’t lived up to its expectations. It turns out to be much trickier than was hoped to work out what is important and what is not, and the formal clarity of deductive argument doesn’t necessarily translate into clear thinking. Still, this program is in far better shape than that of the Austrian School, and the methodological failure of a priori reasoning is a large part of the reason.

Having written this piece, I did a better Google search and found, as usual, that much of it is not new a~~and indeed goes back to Keynes. (Mises reply to Keynes seems entirely unconvincing)~~. But the point that Austrian economics is genuinely related to Flat Earth geography (as opposed to the use of this term as simple abuse) seems to be new.

**Update** The reference to Keynes above was the result of reading too quickly. The “Lord Keynes” in question isn’t John Maynard, but the contemporary blogger to whom I linked. And the weak reply is not from Mises but from one of his epigones, Hans-Herman Hoppe.

[^1]: As I read him, Nozick is equally extreme. An ethical theory that disregards consequences seems just like an economic theory that disregards data. Nozick seems to me to get more respect from other philosophers than Mises gets from economists. Reader

[^2]: Some presentations are more careful, referring to a triangle on a Euclidean plane. But that only shifts the problem one step back. Without the empirical proposition (false for the surface of the earth) that the subject of inquiry is a Euclidean plane, we don’t know (as Russell said) what we are talking about when we refer to Euclidean triangles. And, as Einstein showed, the situation isn’t improved by thinking of the earth as an object in three-dimensional Euclidean space.

[^3]: The most famous name here, immortalized by Tom Lehrer, is Nikolai Ivanovich Lobachevsky.

The parallel postulate is an axiom, and the real world is more easily described by non-Euclidean geometry. This is not to say that Euclidean geometry doesn’t apply to the real world.

To say that only Euclidean or non-Euclidean geometry applies to the real world are both metaphysical statements. There is no evidence that denies Euclidean geometry from applying to the real world, because nothing says its

impossiblefor you to describe space and light as Euclidean.In fact, no evidence can prove or disprove whether Euclidean geometry applies to the real world or not. It would be silly to attempt this. Its an arbitrary designation made for modeling.

However, to say that the mind perceives things as Euclidean is correct. You cannot visualize any non-Euclidean geometry, without visualizing it as Euclidean geometry. That is mental capacity of our mind, and is an inductive observation.

I can prove this by asking you to draw an instance where the parallel postulate is invalid. Since its not possible for you to draw this, then its sufficiently proven.

Schopenhauer had similar arguments shown here: http://en.wikipedia.org/wiki/Schopenhauer%27s_criticism_of_the_proofs_of_the_Parallel_Postulate

So when people say the universe is Euclidean, it is the same as saying the mental capacity of the human mind only perceives Euclidean space. Objectively, the universe is not necessarily Euclidean, non-Euclidean, or any geometry at all. Any geometry is a mental analytical conception.

This is where the confusion arises. Mises never used the term “axiom” because the basis of praxeology is formed of statements about the nature of how humans perform actions, which is inductive.

Everything derived from this is a priori, and is based on the analysis of the causal factors of human actions.

This isn’t like geometry because these are not constructions for the purposes of modeling reality. They are observations about reality itself. They are inductions from introspection that are validated by literally asking any person.

Mises did not invent the a priori. John Stuart Mill, in fact, explained why the the a priori method is valid in “On the Definition of Political Economy and the Method of Investigation Proper to It,” written in 1836. And Cartwright defended this method in “Nature’s Capacities and their Measurement,” written in 1989.

The Austrian position is simply that no economic statistics can possibly measure all the causal factors involved in society. These types of econometric statistics can in no way invalidate basic a priori economic laws because these tests simply don’t address the content addressed by the a priori laws.

Bollocks.

Visualise this. Take an orange. Draw an equator around it. Draw two lines at right angles to the equator. Since they are both at right angles to the equator, they are parallel with each other. Extend the lines all the way around the orange. They cross at the poles. Euclid’s parallel postulate does not hold in this everyday visualisation/drawing. QED.

For further applicability to the real world, imagine you are living on the surface of something spherical. It shouldn’t be too hard, unless you are Austrian.

The claim that a bunch of white male elderly privileged anglo-saxon-austrian-american economists could derive universal laws of human behaviour by contemplating their navels is even more ridiculous. I refer you to this well known paper, “The Weirdest People in the World?”, which documents just how little the findings of actual psychological tests (not just introspections) about very basic things (like, inter alia, concepts of “fairness”, “work”, “space” and “geometry”), which were taken to be universal, apply to people who aren’t residents of US university campuses.

PS If real spacetime could be correctly described as Euclidean then both General and Special Relativity would be falsified. You could still

describeit that way if you wished, much like conservative economists keepdescribingUS inflation as an imminent danger and/or already here, but being covered up by the FED; it’s just that you would be wrong.@John Quiggin

This reply to Pete is a nice reply about were people have honest disagreements.

Nevil, that’s a dumb argument. There is no reason special and general relativity must be “falsified.” This is based on what? Yes, it would require a difficult and impractical model, but this is not to say its

impossible.To you, it seems impossible because you have a difficult time visualizing it, and so do I. However, look at Eddington’s experiments. The light beamsdobend according to how our mind interprets them.As further evidence of your confusion, economists and scientists don’t

describeanything as dangerous. This is normative. Its not descriptive, its prescriptive.@Hank

I’m not sure this is correct. I can certainly visualise a triangle on the surface of a sphere, which I’m led to understand is non-Euclidean.

@Tim Macknay

…although I note that this could be a terminological issue as, on a brief scan of online material, some sources identify spherical geometry as being non-Euclidean, whereas others say that it is ‘not truly a non-Euclidean geometry’. At this point I’ll hand the discussion back to trained mathematicians (!).

@Tim Macknay

Spheres are Euclidean. There are also 4 dimensional spheres which are non-Euclidean impossible to visually construct.

@Hank

The predictions of general relativity would be falsified if spacetime was not curved. There is no internally consistent way to calculate the curvature of light around Mercury (etc) which is consistent with a Newtonian/Euclidian universe.

Quibbling about adjectives is a red herring. “an imminent event” if it makes you feel better (ps I note that Peter Boettke describes inflation as “socially destructive” in his encyclopedia definition of Austrian economics quoted earlier, so maybe you should take this up with him).

I noted earlier, but it seems to be stuck in moderation:

“Visualise this. Take an orange. Draw an equator around it. Draw two lines at right angles to the equator. Since they are both at right angles to the equator, they are parallel with each other. Extend the lines all the way around the orange. They cross at the poles. Euclid’s parallel postulate does not hold in this everyday visualisation/drawing. QED.”

@Nevil Kingston-Brown

Nevil, it is important. Many economists have opinions. Its perfectly fine to have opinions. “dangerous” is not a scientific term.

You are conflating Euclidean and non-Euclidean. Yes the two lines cross because they are were not straight (according to Euclid’s definition). You simply redefined straight to what normally means curved. There’s nothing wrong with that, but you are conflating it.

@Nevil Kingston-Brown

Regarding mercury, just because it doesn’t follow the laws of Newtonian gravity doesn’t mean its impossible to derive new equations explaining its motion.

Even if you can’t derive these equations, then the movement of Mercury would merely be unpredictable according to a Euclidean universe. There is nothing

wrongwith this, its just not very satisfying.@Hank

I think you will find that elliptical (eg on the surface of a sphere) and hyperbolic geometry are usually referred to as “non-Euclidean geometry”. You can come up with your own personal definition – much as Austrians have recently attempted to redefine the word “Inflation” – but you are unlikely to convince anyone.

On your second point, its hard to see this as anything but a flat rejection of Occams razor and enlightenment thinking generally. Consider this restating from a comparable paradigm shift: “Regarding Cholera, just bwvause it doesnt follow the wind patterns of miasma doesn’t mean that we can’t derive a new miasma to explain it. Even if we can’t, outbreaks of cholera would just be unpredictable by miasma theory. There is nothing wrong with this, it’s just not very satisfying”.

To expand on Nevil’s point, you can’t as a matter of empirical fact, rescue the actual geometry of the Earth for Euclid by treating it as a spherical object in Euclidean 3-D space. That’s because, thanks to Einstein, we know that space isn’t Euclidean, any more than the surface of the earth is a plane.

It might be worth reading Feynmann on armchair philosophers who claim to derive relativity theory from a priori argument rather than observation. The Austrians are exactly in this position.

@J-D

Well, maybe Tom Lehrer is not a popular as he used to but he made Lobachevsky far more famous, at least in the English speaking world. Mind you when I first heard of Lobachevsky I did not even know he was a mathematician. But the lyrlcs are great, and worthy of describing a Wegman.

“worthy of describing a Wegman.”

Gold. It’s a pity his name doesn’t scan

@Nevil Kingston-Brown

Nevil, first of all, you are missing the point. But I’ll follow up on your point regardless.

I agree with Occams razor. Occams razor is a normative statement about how scientist’s OUGHT to do science. I agree that non-Euclidean geometry is better applied to the universe and can probably describe more than what the rules of a Euclidean universe allow for. I’ve said that numerous times, so to say I “reject” Occams razor is patently false.

To say whether any geometry exists in the physical universe makes no sense, because geometry only exists as an analytic concept. It exists in the human brain, not in the physical universe.

So you are once again confusing two things. You can say its “correct,” as in the analytic concept is correct, or you can say its “correct” as in it follows the normative principle of Occams razor. One is a scientific statement, one is not a scientific statement.

However, as I already stated, the economic a priori principles are not axioms, like in geomtry. They are inductive observations. These causal factors exist in our physical universe. Therefore, you’re arguments about geometry don’t necessarily apply to what I was trying to say in my original comment.

@John Quiggin

“thanks to Einstein, we know that space isn’t Euclidean.”

Einstein was a physicist, not a metaphysician. To say that the outside universe is “Euclidean” is a metaphysical statement. No evidence can possible “say” that the universe is any geometry because geometry only exists conceptually.

Einstein developed a non-Euclidean model that can be accurately applied to the universe. Strictly speaking, this isn’t even accurate! The measurements of galaxy rotation contradict his model. Do you come to the conclusion that the “universe” is not “non-Euclidean”? No, because your statement about geometry “existing” in the physical universe is made arbitrarily, without any demonstration.

@jrkrideau

Among Lehrer fans — in which category I include myself — Lobachevsky must be one of the most famous mathematicians ever.

On the other hand, if I do a Web search for ‘famous mathematicians’, my top hit is a list somebody has compiled of the greatest mathematicians, on which Riemann is ranked 5th and Lobachevsky 110th. Obviously that’s a single observer’s opinion, but what I wrote was not about what everybody thinks, but rather about what some people think, an observation I stand by: some people rate Riemann higher than Lobachevsky. (And if Lobachevsky’s name is a bigger one than Riemann’s because of the Lehrer song, then it’s not because of relative contributions to non-Euclidean geometry.)

If you love Tom Lehrer’s work, you will know Lobachevsky’s name and don’t need to know Riemann’s. But if you’re interested in the history of non-Euclidean geometry, you should know Riemann’s name.

@Jim Rose

Between alternatives presented to them and based on their budget constraint. In other words the system determines how individuals choose. Public expenditures are examples where social groups choose.

Exchange behaviour is determined by budget constraint and is impacted by anti-competitive behaviours.

The facts of social sciences are objective facts of wealth and poverty and of working poor arrangements and unemployment.

Injustice is an objective standard essentially based on the “Golden Rule” or its breach.

Utility is subjective, costs are objective.

The price system corrupts the information needed to make sustainable decisions. If a market event occurs due to price there is no information whether the price figure was constructed of real sustainable value or in part of unsustainable debt.

Capitalist private property of means of production can never produce rational economic calculation. In the absence of additional debt, capitalist prices always exceed society’s final consumption expenditures. In the presence of additional debt – the economy is driven to catastrophe.

Monopolists, government agencies and planners produce discoveries.

This makes no sense. Who claims that money is natural.

Capital only has to earn the same rate of profit in the long run. Nothing needs to be aligned except capital and profit rate.

All social institutions operate within the law and therefore well and truely are the result of deliberate design.

@Hank

It would seem that part of our dispute here is terminological, and part is philosophical.

Terminological: I (and I think JQ) am using “the universe is non-Euclidean” as a sort of shorthand for “the universe can most accurately be described using the mathematical framework of non-Euclidean geometry” and you are objecting to this, or rather, you are inferring from it that I think of “geometry” as an empirical thing. I agree that geometry per se, whether euclidean or non-euclidean, is a formal mental construct not susceptible to empirical proof or disproof. Indeed that was part of the point of JQ’s original post.

However, the accuracy, precision and “scientific beauty” in the form of the least number of rules explaining the widest range of events, with which the physical universe can be described using various geometries is very much an empirical question, and claiming that the universe can’t be described as “non-Euclidean” because “non-Euclidean” is the name of a formal geometry is to mistake the terminological for the ontological. Your statement “In fact, no evidence can prove or disprove whether Euclidean geometry applies to the real world or not.” is simply wrong. No empirical evidence can prove or disprove the formal internal consistency of Euclidian geometry, but empirical tests of whether physical space is accurately described by Euclidean geometry, or in other words whether Euclidean geometry “applies”, are very much possible. Saying “the universe is non-Euclidean” is a shorthand for “the universe can most accurately be described using non-Euclidean geometry”, deal with it.

Getting back to the more philosophical issues, the question “what can the human mind visualise” is ALSO an empirical question. Just because you (or, my physics degree being long behind me, I) have difficulty visualising four-dimensional space-time curvature doesn’t mean that someone else with a better imagination and more mathematical training can’t do it. This so-called induction from introspection is really nothing more than an argument from incredulity, similar to people who say that they can’t possibly imagine all life evolving from a single cell 4 billion years ago and therefore Darwin must be wrong, or (in the normative sphere) that they can’t imagine homosexual sex in any positive way, therefore it must be evil.

Moving on to the next steps of your argument, you appear to be trying to have your cake and eat it. When you say “This [Mises’ premises from inductions] isn’t like geometry because these are not constructions for the purposes of modeling reality. They are observations about reality itself.” you appear to be a) contradicting Mises (“Its [praxeology’s] statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori.”) and b) claiming that they are simultaneously

a priori, which is, by definition,notderived from observations and experience, and empirical, whichdoesconsist of observations of reality. You can’t have it both ways – synthetic a priori is an empty box, as Lord Keynes elucidated.Claiming that various premises are embedded in the structure of the human mind is not a justification for a priori-ism, but an

empiricalclaim about the structure of the human mind. Enough research has been done on how widely minds vary across cultures, genders, classes, ages, etc (see the Heinrich et al paper I linked to above in post 27) to make any claim to universality of human understanding of economic action (and, for that matter, geometry) extremely dubious. Unless you are also going to adopt mysticism and claim that the human mind can never be empirically studied or understood (in which case, how would introspection work?), and by implication dualism, then this attempt to provide a non-empirical connection to the real world fails.You appear to then claim that Austrian economics is a formal system not susceptible to empirical proof or disproof (although your argument that Austrianism is not a formal axiomatic system but some kind of set of non-axiomatic statements and deductions appears to undermine this – how can you have deduction without axioms anyway?) but then you have to accept that Austrianism has no more relevance to the real world than Euclidean geometry as a formal system does. It is not about the actual economy, it is about an imaginary economic system that Mises introspected out of his navel. It may be very interesting to join him in contemplation, but it’s not anything that can guide study of the actual economy in any way – as you appear to admit when you say that economic statistics have no relevance to it. In which case, what’s the use of it except as a subset of abstract art, and why do Austrians keep making claims about what economic policy should be followed?

@Nevil Kingston-Brown

“Euclidean geometry “applies”, are very much possible.” Saying its possible, doesn’t make it possible.

“Saying “the universe is non-Euclidean” is a shorthand for “the universe can most accurately be described using non-Euclidean geometry”, deal with it.” Again, I never once disagreed with this statement. You pretend I disagreed with this for some reason. I don’t think I even attributed the view to you, yet you feel as if you need to defend yourself against nothing.

“ALSO an empirical question.” Correct. In addition, it has never been falsified.

“imagination and more mathematical training can’t do it.” Again, it has nothing to do with math or imagination. Its a simple (and empirical) fact that you, nor anyone, sees a fourth dimension.

“introspection is really nothing more than an argument from incredulity,” Here, you are denying empirical evidence as valid. Introspection is empirical. Psychologists frequently draw from introspection.

“they can’t possibly imagine” Introspection and imagination are completely different things.

“have your cake and eat it.” I would if I could.

Yes, I admit its hard to comprehend. Mises says, “Its [praxeology’s] statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori.” He’s saying that economic propositions made from basic praxeological concepts are a priori. These statements are the analysis from PRIOR concepts, aka a priori.

“claiming that they are simultaneously a priori” I didn’t claim that basic economic postulates are a priori. In fact, as you already noted, I said they were inductive.

“Enough research has been done on how widely minds vary across cultures, genders, classes, ages, etc (see the Heinrich et al paper I linked to above in post 27) to make any claim to universality of human understanding of economic action (and, for that matter, geometry) extremely dubious.” This is easily demonstrated as false.

Action has been a topic of research by cognitive science, psychology, and philosophy for decades. http://plato.stanford.edu/entries/action/

“But the view that reason explanations are somehow causal explanations remains the dominant position.” You see? This is precisely the same causal mechanism described by Mises in Human Action. These causal mechanisms are universal for all deliberative actions. This is an inductive argument and has never been falsified by any evidence.

Again, read Nancy Cartwright in

Nature’s Capacities and Their Measurementfor a full explanation on the reasons why singular causes, not general causes, are the important starting point in science.“how can you have deduction without axioms anyway?”

This horse is white.

This different horse is white.

This horse is the same color as the other horse.

This is a deduction without axioms. Is there some sort of logical law preventing deduction without axioms I am unaware of?

“imaginary economic system that Mises introspected” Again, equivocating introspection and imagination seems fundamental to your argument.

“guide study of the actual economy in any way” Every economist who studies the economy relies on basic fundamental postulates. You literally cannot use the term “value” without defining what “value” is. Once you understand that “value” is a completely subjective phenomenon, you must accept that the causal mechanism is the purpose these valuations have. Otherwise, you must unscientifically, arbitrarily, objectively determine value, or cease to use the term whatsoever.

@Nevil Kingston-Brown

In addition, the idea behind intentional an unintentional action is relied on in courts of law. In your world, there would be no difference between first degree murder and manslaugher. If deliberate action was really subject to “cultures, genders, classes, ages, etc” then you can live in a world where there is no legal concept of mens rea: http://en.wikipedia.org/wiki/Mens_rea

@Hank

If geometry only exists conceptually and not in the physical universe, then any system of economics that is analogous to geometry in this respect also only exists conceptually and not in the physical universe.

“Some presentations are more careful, referring to a triangle on a Euclidean plane. But that only shifts the problem one step back. Without the empirical proposition (false for the surface of the earth) that the subject of inquiry is a Euclidean plane, we don’t know (as Russell said) what we are talking about when we refer to Euclidean triangles.”

True, we cannot be certain that human beings act. Therefore, we can only be as certain of any conclusions we deduce from this axiom as we are in the correctness of the axiom and of our logical reasoning. The relevant question is then, are we more or less confident that human beings act than we are in the outcome of the latest regression analyses?