You make good points, the main reason these tools don’t exist , however, is that I thought Mises and others felt that economics was about logical deduction from the axioms of human action - Praexology. and thus there was no need for math or empiricism to validate the theories - they were Prima facie correct.
Indeed. And it is a good thing in my layman's point of view because we better explain things in a simpler way and reach conclusions with math only if it is really required. It's like qualitative vs. quantitative.
That said, no one would judge you for doing math. However, the important pieces (axioms) don't require it.
Lack of math doesn't mean anything bad. See Frédéric Bastiat and Gustave de Molinari. Both are amazing and no math required :)
Everything boils down to mathematics one way or another, even logic.
The trouble with praxeology is not the lack of math, though; it is the notion that results need not be validated empirically because they're based on logic. However, your assumptions (i.e. axioms) need not hold in nature and any number of mistakes could had been made in the reasoning process. This is why being based on logic does not make a model magically free of errors.
Marxism took the same approach--attempt to derive absolute truths about the empirical world using pure logic. I don't know if Mises actually applied Hegelian dialectics, but the fundamental approach seems similar. It's all very German--compare Einstein's approach where he generates imaginary paradoxes and then finds higher truths in their resolution.
Problem is, the real world is messy. Some aspects of the world are susceptible to logical reductionism, but not all of it. Enough of it is arbitrary that you very quickly fall off the rails, even when it's not obvious. A theory can often seem superficially more consistent than it really is simply out of coincidence, insufficient precision, or insufficient predictive power. In the real world the proof is in the application.
I believe what they try to achieve is beyond what we currently have. And if Mises was born in this age, he would've probably go to the biology level or even deeper to start his work. The tooling and data to connect the dots in his mind was simply not there. To me, he wanted something that is not approximate. For those purposes, what you mentioned might be the best tools one can have at starting stage. I think some work in micro-economics has something similar to Mises'. They can work on simulations now to have fact-based and measurable discoveries. In the end, most likely what human can do is limited to the tooling, not the understanding and educated imagination.
>I believe what they try to achieve is beyond what we currently have. And if Mises was born in this age, he would've probably go to the biology level or even deeper to start his work.
This isn't really true. When Human Action was written there already was a fair bit of literature on behavioural psychology and other fields, but Mises made a conscious choice to not base his theories on them. In the first part of Human Action Mises does bring this point up but makes a clear distinction between investigations into human behaviour that are rooted in the natural and empirical sciences (i.e. biology) and his own flavour which is rooted in a Kantian-esque introspection. This concept is referred to in Mises' work as well as in the works of his successors as methodological dualism, and is a core tenet of Austrian social analysis.
How would they measure from simulations, if he can't have the exact set of same people on different situations and your results might vary?
Social science isn't "experimentable" as biology or physics... And if you try hard to force it you will end up with what's called social engineering instead...
W. Brian Arthur is an economist I like. Complexity theory is also very exciting for me. I do not have any experience in those, but they and other things inspired how I perceive the world.
I probably did not deliver what I think clearly. The link above might be helpful to deliver what I mean.