Euclidean geometry is pretty solid, I think. But Einstein showed it was not an adequate deductive system for building up theories related to relativity and so on. In a sense one could argue that Euclidean geometry was *a priori* and maybe true. But so what?

The same can be said of any system we use to describe economics. It may appear as solid as Euclidean geometry, but if in the end it continuously fails to stand up to tests … we have to start asking ourselves about our basic premises.

I don’t see where Popper’s ideas conflict with Austrian theories, per se. It’s mostly neutral. It does conflict with what a lot of Austrians say about epistemology. Here though, I’ll note, Hayek quickly took Popper’s criticism on board and never bothered to look back. It’s a pity most Austrians see Popper as an enemy such that arsenals are needed to be used against people who think he got it right.

How did you manage to spin this from the bit you read, precisely? He is referring to the conditions referred to in the theorem obtaining in the “real” world. As for whether a truth is “analytic” or “synthetic”, how about you give Henry Veatch’s Two Logics a read for a demolition of the arbitrary dichotomy? BonJour in his In Defense of Pure Reason also subjects the dichotomy to a conceptual dissolution.

“I am not sure whether you think the human axiom is synthetic a priori, but if not what is it? True by introspection? (as Kirzner). Is it analytic? How can you get non-vacuous inferences from an analytic proposition true only by definition”

True by virtue of the fact that its denial leads to contradiction. It isn ot a matter of mere “definition”.

“Every theorem of praxeology is deduced by logical reasoning from the category of action. It partakes of the apodictic certainty provided by logical reasoning that starts from an a priori category. Into the chain of praxeological reasoning the praxeologist introduces certain assumptions concerning the conditions of the environment in which an action takes place. Then he tries to find out how these special conditions affect the result to which his reasoning must lead. The question whether or not the real conditions of the external world correspond to these assumptions is to be answered by experience. But if the answer is in the affirmative, all the conclusions drawn by logically correct praxeological reasoning strictly describe what is going on in reality” (Mises,1978 [1962]. The Ultimate Foundation of Economic Science: An Essay on Method, 2nd edn, Sheed Andrews & McMeel, Kansas City. p. 44).

But once you introduce synthetic propositions as premises in deductive arguments, you have given up apodictic certainty. Unless you can show that ALL of your synthetic propositions introduced as premises are justified, the inferences deduced can be subject to doubt.
I am not sure whether you think the human axiom is synthetic a priori, but if not what is it? True by introspection? (as Kirzner). Is it analytic? How can you get non-vacuous inferences from an analytic proposition true only by definition?
And once the synthetic premises come in, you must start invoking empirical evidence as relevant to your arguments.

See further:
H. Albert, H. 1999. Between Social Science, Religion and Politics: Essays in Critical Rationalism, Rodopi, Amsterdam. p. 131ff.

Not sure whether you know the work of Meyer:

Meyer, W. 1981. “Ludwig von Mises und das subjektivistische Programm,” Wirtschaftspolitische Hätter 4: 35–50.