Conza

logicallypositive:

Within formal logic, there is a result known as Godel’s Incompleteness Theorems. I’ve written about them before, but basically what the important theorem says is that “Within a second-order or higher system of logic, it can be either consistent or complete, but not both.” So your formal system of logic can either:

1. be able to express and determine the truth value of every single proposition, but allow contradictions
2. not allow contradictions, but permit the truth-value of at least one proposition to be indeterminate using the rules of that system

In order to successfully symbolize Austrian economics, one would have to use set-theoretic concepts and functions, at least that is what my intuition tells me. Which means the logic of praxeology would be at least 2nd order, quite possibly even 3rd order.

So what this means is that within the science of praxeology, there exists a non-empty set of propositions which have an indeterminate truth value. Granted, they do have a truth value. HOWEVER, it is impossible to prove their truth within the confines of praxeological logic. In other words, there exist true statements which one cannot prove using praxeology.

This is certainly a less problematic conclusion that straight up admitting that the Austrian school is a clever and elaborate tautology, but it is still problematic. Specifically, it means that Austrians cannot use either verbal OR symbolic logic to prove at least one statement which is true. The methodology is incomplete, and thus necessarily lacking. Powerful, but still lacking.

A large part of the Austrian mission was to avoid the use of empirical evidence. Sadly, admitting this fact to be true necessarily means to prove that particular proposition, you’d have to resort to some sort of empirical, inductive reasoning. Some sort of econometrics or non-praxeological methodology. It’d be better than nothing, but it’s still a depressing result.

It’s always been admitted that there are a priori axioms from some empirical observations.

• “Actually, despite the “extreme a priori” label, praxeology contains one Fundamental Axiom—the axiom of action—which may be called a priori, and a few subsidiary postulates which are actually empirical. Incredible as it may seem to those versed in the positivist tradition, from this tiny handful of premises the whole of economics is deduced—and deduced as absolutely true. Setting aside the Fundamental Axiom for a moment, the empirical postulates are: (a) small in number, and (b) so broadly based as to be hardly “empirical” in the empiricist sense of the term. To put it differently, they are so generally true as to be self-evident, as to be seen by all to be obviously true once they are stated, and hence they are not in practice empirically falsifiable and therefore not “operationally meaningful.” What are these propositions? We may consider them in decreasing order of their generality: (1) the most fundamental—variety of resources, both natural and human. From this follows directly the division of labor, the market, etc.; (2) less important, that leisure is a consumer good. These are actually the only postulates needed. Two other postulates simply introduce limiting subdivisions into the analysis. Thus, economics can deductively elaborate from the Fundamental Axiom and Postulates (1) and (2) (actually, only Postulate 1 is necessary) an analysis of Crusoe economics, of barter, and of a monetary economy. All these elaborated laws are absolutely true.” ~ Murray N. Rothbard, In Defense of Extreme Apriorism.

• “It should be noted that for Mises it is only the fundamental axiom of action that  is a priori; he conceded that the subsidiary axioms of the diversity of mankind and nature, and of leisure as a consumers’ good, are broadly empirical.”  ~  Murray N. Rothbard, Praxeology: The Methodology of Austrian Economics, p3.