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:
- be able to express and determine the truth value of every single proposition, but allow contradictions
- 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.