David Gordon's The Philosophical Origins of Austrian Economics is a good summary of the underlying historical issues that lead to the development of Austrian Economics, generally recognized as having been founded by Carl (also Karl) Menger with the 1871 publication of The Principles of Economics, one of the earliest expositions of marginalist theory.
The Austrian School of Economics gathered in Vienna around Menger's innovative contribution and elaborated it differently than the British, of whom Alfred Marshall was a key early contributor to marginal theory. Whereas Neo-Classicalism took at objective stance characteristic of the British mindset at least since Locke and Hume, the Austrian School took a subjectivist one, more in the tradition of Goethe, Leibniz, Kant, Fichte, Shelling, and Hegel. The reasons become more clear based on an understanding of the philosophical underpinnings. The Austrian thinkers did not see their subjectivist position as lacking in objectivity since they take their principles to be grounded in self-evidence that is intuitively certain.
So if you want to understand the debate in a wider context than the economic controversies that led from Classical economics to the Marginal Revolution, which then bifurcated into objectivist and subjectivist schools, read Gordon's short article about the philosophical background. It is probably a bit challenging for those without prior knowledge of the field and the controversy.
However, the intelligentsia of the 19th and early 20th centuries were well steeped in a broad range of knowledge, including philosophy. Such issues were key contributors to the formation of contemporary knowledge, not only in economics but also the sciences. The developers of quantum mechanics were also influenced by similar issues, even though few people are much aware of the philosophical debate at present.
Gordon does a reasonably good job of summarizing the issues involved, although of course any summary of such a limited scope is necessarily greatly simplified. Moreover, authors taking a particular view generally have difficultly adequately representing opponents' views. That said, I think that the essential points are clearly made, regardless of these qualifications, so quibbling over fine points here would be a distraction.
Gordon confirms my previous statements about Austrian economics following Aristotle's method of deductive reasoning based on self-evident first principles (Greek αιτιαi), which Mises admitted are similar to mathematical axioms. Gordon quotes Mises:
In The Ultimate Foundation of Economic Science, [Mises] addressed the claim of Karl Popper that scientific propositions must be falsifiable. Although Popper was not a positivist, he intended his falsification criterion to separate scientific from non-scientific statements. Mises' comment was dismissive: "if one accepts the terminology of logical positivism . . . a theory or hypothesis is unscientific if it cannot be refuted by experience. Consequently, all a priori theories, including mathematics and praxeology are unscientific'. This is merely a verbal quibble."Well, it is not a "verbal quibble." It is a basic issue in philosophy at least since Emmanuel Kant distinguished between apriori, synthetic, and synthetic apriori propositions. Apriori propositions are either necessarily true as tautologies or necessarily false as contradictions, given the formation and transformation rules of a syntactical system, that is, by definition. This means that apriori truth is purely deductive. In contrast, synthetic propositions are empirical, based on either direct observation or inductive probability.
The philosophical question is whether there are synthetic apriori propositions that are necessarily true (probability equals one) and also provide knowledge about how things stand, must stand or ought to stand in the world. Logical and mathematical expressions are apriori propositions that have probabilities of one (tautology) or zero (contradiction), but they say nothing about how things stand in the the world. Rather they define the limits of language, establishing the boundary between sense and nonsense.
The philosophical question is whether there are self-evident propositions that are necessarily true that both say something about how things stand in the world as descriptive, or must stand as causal, or ought to stand as prescriptive, but depend on neither induction or deduction for their truth value. The way philosophers have put this is in terms of whether there is intellectual intuition in addition to sense intuition that provides information about the world, especially causal information or "natural laws" that can serve as the starting point for deduction. The answer of the Austrian School, at least the branch following Mises, is yes. The answer of scientific realists is no.
For scientific realists, mathematics is not scientific. Rather, mathematics is the language of science. As such it is neither scientific nor "unscientific." It is part of the methodology, not part of science as a general description of how things stand in the world. In this view, Mises fails to make the proper distinctions.
This is key because the philosophy of Aristotle and the method that he used was based on appeal to self-evident first principles held to be ontologically causal, hence, primary. Thus, metaphysics is "first philosophy," and ethical principles are considered in the same vein as being determinative. In this view, the positions of those who fail to recognize these first principles and what follows from them are erroneous, and argumentation against them is categorically rejected, since self-evident principles are irrefutable.
Scientific realism strongly opposes this view since its adoption in Christian theology led to what scientists since the Renaissance have seen as a needless delay in the development of the scientific method, not to mention the repression of early scientists and publication of scientific discoveries. It is a matter of historical record, that dogmatism was imposed on the justification of "first principles," "ultimate causes," and "natural law." What was deemed opposed to a dogma was declared to be "unnatural," regardless of whether it was found widely in Nature.
Therefore, it is not surprising to see scientists opposing the Aristotelianism of the Austrian School, as well as that of Ayn Rand's Objectivism, which Libertarians combine with Rothbardian Austrian economics into an ideological dogmatism of individual freedom without social responsibility on the basis of assumed "natural" processes.
The other historical influence on the development of Austrian economics was Hegelian historicism, which also stands in opposition to the timeless truth of first principles, in that it sees knowledge as unfolding though a dialectical process of testing. rather than through observation by experiment as in the experimental sciences, this testing occurs through the crucible of historical conflict among different views. While the Austrian school of economics rejects this view, it makes it historical appearance in this light. While its star it rose to brilliance for some time in opposition to historicism, it was later eclipsed by New Classical emphasis on objectivity, and the Austrian School became increasing marginalized or absorbed into Neoliberalism.
As Gordon observes, the evolution of the Austrian school was a reaction to the previously dominant philosophical school in German-speaking countries, namely Hegelianism. This implies that the original Austrian thinkers were part of the dialectical progression of thought and played a historical role that was at the cutting edge in their day, at least in their cultural environment.
During the post-WWI period in that environment, Logical Positivism of the Vienna Circle was also philosophically prominent, and it criticized the philosophical foundations of the Austrian school of economics as being apriori, hence, not "scientific" in the Positivist sense of being empirical grounded. Karl Popper, also from Vienna, continued criticism in that vein, emphasizing the lack of falsifiability.
As Gordon notes, the Austrian school of economics rejected that criticism, and they do to this day. Their problem now, however, is that science has greatly progressed since then, and a scientific epistemology has emerged that seriously calls into question previous views of philosophical epistemology. The dominant Austrian School has largely ignored subsequent discoveries (as has Neoliberal Economics). So the argument ended in disagreement over worldviews based on fixed principles as norms that provide unquestionable criteria. This is where the contemporary debate seems to be stuck.
Neither the initial Austrian subjectivist view nor the initial New Classical objectivist view that launched the Marginal Revolution in economics stayed abreast of relevant discoveries in related fields. Such theoretical assumptions used in model construction result in representations of how things are that describe imaginary worlds rather than how things actually are in this world of experience. Those assumptions, being largely philosophical and speculative, need to be updated with respect to scientific findings.
As far as I can see, the Austrian school of economics has not successfully refuted the Popperian criticism, let alone taken into consideration more contemporary scientific research into general systems theory, cognitive science, and behavioral psychology. For that reason, I have said that contemporary AE is dated — as is Neoliberal Economics — and both need to do some catching up with developments in knowledge. I don't see that either have done so, and as a result of this failing to keep up, fundamental features of both appear to be dogmatic and ideological rather than reality-based now that greater knowledge is available.
Related to this is the pitting of methodological individualism against Hegelian holism. This also applies to Neoliberal Economics. That debate has also moved forward by great leaps with the contemporary investigation into systems in general system theory, biology, cognitive science, systems analysis and computer science.
Based on newly discovered knowledge, methodological individualism is deficient, at least in any strict form such as the contemporary Austrian and Neoliberal schools use. So they need to revisit this in light of what's happened since the end of the 19th and beginning of the 20th centuries. Just because collective consciousness has not caught up is no reason to ignore the cutting edge, a lot of which is many decades old by now, and taking account of these advances in knowledge is long past due.
I personally understand where the Austrian schoolers are coming from with respect to Aristotle, since I was very much into Aristotle when I studied his works, and there is much to admire about his approach. I think that this orientation will get a rehearing in time, but for the present, it has been superseded by the scientific approach, which itself has surpassed narrow positivism. This stage is not the last either. However, the next step is not to be found by looking backward.
Knowledge is a growing endeavor, and my impression is that neither Austrian nor Neoliberal Economics have sufficiently kept up with contemporary developments to be taken seriously as major players. Proponents of AE need to get up to date and advance their discipline in light of the times, or it will go the way of phlogiston theory, and that goes for Neoliberal Economics, too.
(This is an amplification of a comment)