This axiom, the proposition that humans act with a purpose, fulfills the requirements precisely for a true synthetic a priori proposition. It cannot be denied that this proposition is true, since the denial would have to be categorized as an action and so the truth of the statement literally cannot be undone.
This distinguishes the New Austrian School from all other schools. Keynesianism in all its strands (pure, post, new, neo, etc.), neo-Classiscism, Monetarism etc. are replicating the search for a needle in a haystack by trying to statisically link cause and effect the way natural sciences try to discover relationships. In human sciences, people are not objects (euphemistically referred to as "agents") that simply respond to Benthamite stimuli like pleasure or pain. So do animals. Normal people act with a purpose and have goals. They have a will and above all they have a high level of self-consciousness, setting them apart from animals.
Although it sounds a lot easier then trying to discover a cause with statistical probability under conditions of radical uncertainty, it was recognised by Prof. Menger that people always act in complex ways that can be deducted from the processes in which they are involved such as e.g. the pricing process in which there are two prices: the (higher) bid and the (lower) offer.
Purposeful acting people are both competing and co-operating with each other at different levels. It is the basis of complexity theory. Nothing is linear anymore.
The New Austrian School has the benefit of the work of Prof. Fekete who already developped a disequilibrium model, not only for pricing goods and services at different levels, but also on the level of interest and discount formation. Read our MANIFESTO for more on the difference with the traditional Austrian School.