See also how the Austrian School of Economics does not fall in that category at all and has created sound, useful and correct economics without math, but only pure logic.
I will agree that it is extremely logical and extremely internally consistent - but it doesn't describe the real world (in a macro sense) at all. Much of the problem is that it tries to reason about the behaviour of individuals or individual companies and extrapolate it into a macroeconomic theory - classic fallacy of composition.
The austrian economists in turn don't pretend to know that macroeconomics work this or that way, they can make assumptions of effects that can happen due to policies, but don't attempt to quantify them.
I think the austrian school is largely ignored for two reasons:
- from it derives a very libertarian view of the world, which many people reject because of political views. after the WW2 libertarian views were not popular, so Hayek and Mises where largely forgotten. - because its philosophical approach is exhaustively researched and you cannot add more fundamentals, leaving economists with the problem of not having much to work on.
I think some of the most promising macroeconomic modelling I've seen has been Steve Keen's complex dynamic systems work, which is all derived from actual definitions and identities, rather than trying to scale up individual behaviour. It's all stock-flow consistent too, which means it ensures everything actually follows the laws of accounting (strangely this isn't necessarily the case in mainstream models).
"They are, like those of logic and mathematics, a priori. They are not subject to verification or falsification on the ground of experience and facts. They are both logically and temporally antecedent to any comprehension of historical facts."
Sounds more like ideology than a science to me....
Arguing that your subject, which most definitely is attempting to model part of the real world is actually a part of the a mathematical world and therefore not subject to the same rules as sciences seems a bit dubious to me.
It uses a priori truths and deduction from it to arrive at new results.
Additionally several branches of philosophy and logic use a priori facts to derive results from it.
Praxeology is one of different ways of scientific reasoning. Just because you cannot get quantitative results from it, doesn't mean its unscientific. It cannot get you very far in predicting concrete human action, because in its view, humans act based on a subjective value "function" that has a discrete scale (you can only say: A is better than B, not by how much). and since every human is unique with their own values, which are simply not objectively comparable, there is just no way to make predictions or qualitative assumptions from this approach to science.
Praxeology as defined by wikipedia, "is the deductive study of human action". Deduction is deeply rooted philosophy, mathematics and logic. A very valid way of scientific reasoning.
It is a different way of doing science, than the "scientific method", which uses observation and quantitative methods.
The Austrian school derives consequences from human action, allowing to describe what can happen in an economy, qualitatively. But their method doesn't allow to make quantitative statements, which makes it "useless" to politicians wanting to change the economy.
Edit: A lot of the stuff around praxeology sounded rather like Marxism in that its proponents argue that it can't be refuted. Turns out that Hayek actually reached a similar conclusion and favoured a Popperian view that "any system which claimed that it was irrefutable was by definition not scientific".