My question is, have there been any critiques of Mises' praxeological
theory?
Sure. None have been successful though.
1 He who wants to attack a praxeological theorem has to trace it back, step by step, until he reaches a point in which, in the chain of reasoning that resulted in the theorem concerned, a logical error can be unmasked. But if this regressive process of deduction ends at the category of action without having discovered a vicious link in the chain of reasoning, the theorem is fully confirmed. Those positivists who reject such a theorem without having subjected it to this examination are no less foolish than those seventeenth-century astronomers were who refused to look through the telescope that would have shown them that Galileo was right and they were wrong.
— Ludwig von Mises, Ultimate Foundation of Economic Science, p.70
2 "The essence of logical positivism is to deny the cognitive value of a priori knowledge by pointing out that all a priori propositions are merely analytic. They do not provide new information, but are merely verbal or tautological, asserting what has already been implied in the definitions and premises. Only experience can lead to synthetic propositions. There is an obvious objection against this doctrine, viz., that this proposition that there are no synthetic a priori propositions is in itself —as the present writer thinks, false— a synthetic a priori proposition, for it can manifestly not be established by experience."
— Ludwig von Mises, The Ultimate Foundation of Economic Science, pg. 5
3 “The attempt to disprove the action-axiom would itself be an action aimed at a goal, requiring means, excluding other courses of action, incurring costs, subjecting the actor to the possibility of achieving or not achieving the desired goal and so leading to a profit or a loss.
And the very possession of such knowledge then can never be disputed, and the validity of these concepts can never be falsified by any contingent experience, for disputing or falsifying anything would already have presupposed their very existence. As a matter of fact, a situation in which these categories of action would cease to have a real existence could itself never be observed, for making an observation, too, is an action.”
— Hans-Hermann Hoppe, Economic Science and the Austrian Method
I would also like to know whether anyone has made an attempt to render
praxeological reasoning in symbolic form. Previous theories that were
claimed to be synthetic a priori later came to be regarded as
analytic. Kant thought that Euclidean geometry was synthetic, but then
the discovery of non-Euclidean geometry and the advent of rigorous
formalizations of Euclid's axioms by Tarski and Hilbert led most
philosophers to conclude that it was analytic. Similarly, Kant dubbed
arithmetic synthetic, but then Frege made a compelling case that it
was analytic by providing logical foundations to the subject (with the
help of Peano's axiomatization of arithmetic).
"The whole controversy is, however, meaningless when applied to praxeology. It refers essentially to geometry. Its present state, especially its treatment by logical positivism, has been deeply influenced by the shock that Western philosophy received from the discovery of non-Euclidian geometries. Before Bolyai and Lobachevsky, geometry was, in the eyes of the philosophers, the paragon of perfect science; it was assumed that it provided unshakable certainty forever and for everybody. To proceed also in other branches of knowledge more geometrico was the great ideal of truth-seekers. All traditional epistemological concepts began to totter when the attempts to construct non-Euclidian geometries succeeded.
Yet praxeology is not geometry. It is the worst of all superstitions to assume that the epistemological characteristics of one branch of knowledge must necessarily be applicable to any other branch. In dealing with the epistemology of the sciences of human action, one must not take one’s cue from geometry, mechanics, or any other science.
The assumptions of Euclid were once considered as self-evidently true. Present-day epistemology looks upon them as freely chosen postulates, the starting point of a hypothetical chain of reasoning. Whatever this may mean, it has no reference at all to the problems of praxeology.
The starting point of praxeology is a self-evident truth, the cognition of action, that is, the cognition of the fact that there is such a thing as consciously aiming at ends. There is no use cavilling about these words by referring to philosophical problems that have no bearing upon our problem. The truth of this cognition is as self-evident and as indispensable for the human mind as is the distinction between A and non-A.”
— Ludwig von Mises, The Ultimate Foundation of Economic Science, p.5
So an attempt to write out symbolically the reasoning of Mises (and his successors like Rothbard) might either reveal that it's totally incoherent or lacking in rigor, or it might remove the synthetic quality.
It is unnecessary.
Praxeology: The Methodology of Austrian Economics by Murray N. Rothbard
...Moreover, even if verbal economics could be successfully translated into mathematical symbols and then translated into English so as to explain the conclusions, the process makes no sense and violates the great scientific principle of Occam’s Razor: avoiding unnecessary multiplication of entities…
...Although himself a mathematical economist, the mathematician son of Carl Menger wrote a trenchant critique of the idea that mathematical presentation in economics is necessarily more precise than ordinary language:
Consider, for example, the statements (2) To a higher price of a good, there corresponds a lower (or at any rate not a higher) demand.
(2') If p denotes the price of, and q the demand for, a good, then
q = f(p) and dq/dp = f' (p) ≤ 0
Those who regard the formula (2') as more precise or "more mathematical" than the sentence (2) are under a complete misapprehension … the only difference between (2) and (2') is this: since (2') is limited to functions which are differentiable and whose graphs, therefore, have tangents (which from an economic point of view are not more plausible than curvature), the sentence (2) is more general, but it is by no means less precise: it is of the same mathematical precision as (2').
Mathematics versus Economic Logic by Ludwig von Mises
...The deliberations which result in the formulation of an equation are necessarily of a nonmathematical character. The formulation of the equation is the consummation of our knowledge; it does not directly enlarge our knowledge. […] No such constant relations exist, however, between economic elements. The equations formulated by mathematical economics remain a useless piece of mental gymnastics and would remain so even it they were to express much more than they really do.
...The mathematical method is at a loss to show how, from a state of nonequilibrium, those actions spring up which tend toward the establishment of equilibrium. It is, of course, possible to indicate the mathematical operations required for the transformation of the mathematical description of a definite state of nonequilibrium into the mathematical description of the state of equilibrium. But these mathematical operations by no means describe the market process actuated by the discrepancies in the price structure. The differential equations of mechanics are supposed to describe precisely the motions concerned at any instant of the time traveled through. The economic equations have no reference whatever to conditions as they really are in each instant of the time interval between the state of nonequilibrium and that of equilibrium. Only those entirely blinded by the prepossession that economics must be a pale replica of mechanics will underrate the weight of this objection. A very imperfect and superficial metaphor is not a substitute for the services rendered by logical economics...
