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.