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 aand 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.
John Quiggin 
@Hank
Hank, if I might give a couple of quotes from you:
“In fact, no evidence can prove or disprove whether Euclidean geometry applies to the real world or not.” “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.” “There is no evidence that denies Euclidean geometry from applying to the real world”
To me, this sounds like you are denying the validity of the statement “the universe is non-Euclidean” because Euclidean and non-Euclidean are abstract geometries and not empirical things like the universe, and therefore there is a category error in the statement. This, to me, is getting hung up on terminology. If there is some different interpretation of your words, please supply it.
You also seem to think that whether space is curved has in some way not been tested (“There is no evidence that denies Euclidean geometry from applying to the real world, because nothing says its impossible for you to describe space and light as Euclidean.” – “Saying its possible, doesn’t make it possible.”). I assure you it has been. The GPS system incorporates corrections for the time dilation caused by the gravitational field of the earth, as predicted by General Relativity – that is, for the non-Euclidean curvature of space. If it didn’t incorporate those calculations, GPS-supplied coordinates would be completely erroneous. Frame dragging has been observed around Black holes and similar massive stellar objects.
““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.”. First, the question was not whether we “see” a fourth dimension, but whether we can mentally visualise it. Second, I (and you) see a fourth dimension whenever I see something change with time. Third, prove it.
A lot of your post consists of slipping, sliding, and changing definitions. Do you agree with Mises that economic propositions are a priori or not? If they are a priori, they are not empirical. That is what a priori means.
How are you going to draw a line between introspection and imagination? How can you tell that what is introspectively valid for you is introspectively valid for others? Keep in mind that a defining characteristic of cognitive distortions and mental illnesses is that they usually prevent you from recognising that your thinking is distorted. Or by “introspection” do you mean mental exercises in deductive logic from axioms/premises, such as geometry?
The rest of your argument assumes what has to be proved, namely that Mises’ HIGHLY SPECIFIC economic nostrums follow from some very vague and general axioms/propositions. The idea that all people seek monetary profits, for example, is quite clearly false.
PS If you think that the law and its application is not fundamentally shaped by race, class, gender, culture, wealth, power, and many other social realities besides, then I have a bridge to Terabithia to sell you.