This argument seems to outline and defend the notion of rationality using the basic axioms as a defense. I ask what the value is in this? Will monetarists and Keynesians disagree that people act? How does this axiom validate the Austrian school over the others? Rather than being solely an Austrian confirmation it seems to be an Economic confirmation. I do however understand it is more in line with the Austrian perspective.
I will assert that rather than using these axioms to attack or defend against other economic schools their value is placed against outside attack. This is an excellent defense on the core of economics from the people who will question it due to lack of scientific rigor or empirical reenforcement. People who only tout the hard sciences will attack things like economics and anthropology due to the inability to test the core foundations.
What happens in Hoppes text is an invalidation of the empiricalist argument. Even in the hard sciences there is a reliability on logical assumptions. These logical assumptions can be equated to the economic axioms. When a physicist relies on mathematics he is allowing a relative margin of irrelevance.
This can be equated in a theoretical problem. How many digits of pi would one need to know the circumference of the universe within one hydrogen atom?
24. Despite the fact that we would be ignoring the infinitesimal amount of digits remaining in pi they become irrelevant.
This is where I see the hubris in Hoppe and Mises' argument. Priori knowledge does not invalidate empirical knowledge just creates a separation. Rather than using this to show a relative balance of the accuracy and value of Austrian economic theory Hoppe tries to argue that praxeology is the only "pure" form of knowledge.
I find the use of the axiom of action to have great utility in defending the rationalist argument but not in solely defending the Austrian method.