The case against formal methods in (Austrian) economics: a partial defense of formalization as translation

ABSTRACT Mainstream economics has been accused of excessive mathematization, whereas the rejection of mathematical and other formal methods is often cited as a crucial trait of Austrian economics. Based on a systematic discussion of potential benefits and drawbacks of formalization, this paper corroborates legitimate concerns that predominant types of mathematization induce a shift of attention away from the key concepts of Austrian economics. Taking this shift to the extreme, predominant modes of mathematization tend to accompany a detachment from ‘reality’ incompatible with Austrian pleas for realisticness. Contrary to popular prejudice however, the most prominent representatives of the Austrian School including Carl Menger, Ludwig Mises, Friedrich Hayek, Israel Kirzner, and Peter Boettke neither provide a justification for a wholesale rejection of formalization nor actually reject it. Adequate formalization can serve as a remedy for lacking logical and semantic rigor in standard mathematical economics as well as in murky verbal chains of reasoning.

Is over-mathematization and formalization the source of the perceived failures of mainstream economics? Would heterodox schools which employ formal methods less frequently or not at all fare better? Or does the perceived chasm between different schools itself disqualify the discipline? Far from settling all these disputes, my case study appraises Austrian economics' arguments against formal methods in economics. Other considerable merits of these arguments notwithstanding, I conclude that they do not suffice to reject formalization entirely. In doing so, my paper clarifies some misconceptions implicit in many arguments for and against formalization. The wholesale dismissal of formalization which a few Austrian economists seek could be obtained by recourse to an extremely essentialist conception of languages ('Sprachgeist') as defended by the early Wieser (1884).

Austrian economics as a paragon of anti-formalism
Among heterodox approaches to economics, the Austrian School has always been regarded as a staunch opponent of the use of formal methods. The Stanford Encyclopedia entry on 'Philosophy of Economics' spends only one on sentence the Austrian School yet mentions that its proponents are 'skeptical about the value of mathematical modeling' (Hausman, 2021). The skepticism or dismissal of formal methods is not only attributed to contemporary Austrian economists. Jaffe distinguishes the founder of the Austrian School, Carl Menger, from other protagonists of the marginal revolution because he allegedly 'avoided the use of mathematics in his economics […] out of principle ' (1976, p. 521). Similar to Hausman's and Jaffe's external assessments, a self-description in the Advanced Introduction to Austrian Economics maintains: 'The Austrian school is much less reliant on mathematical and statistical analysis, and is often suspicious of the economic analyses that rely on them.' (Holcombe, 2014, p. 109) Mathematical formulas or diagrams are rare not only in scholarly publications by Austrian economists, the anti-formal identity of the School is also perpetuated by its textbooks. The most prominent Austrian textbook contains several scattered diagrams, graphs, and tables but no algebraic formulas whatsoever. For the most part, it consists of text in plain English. The authors seek to accomplish more 'with less emphasis on formal modelling' (Heyne et al., 2013, p. xiv) without watering-down the content.
In some instances, especially since the 'revival of Austrian economics', Austrian economists' stance towards formalization has surpassed skepticism and reached rejection or utter hostility. Such examples are most frequent within but not limited to the praxeological branch of the Austrian School (see e.g. Wutscher et al., 2010). 1 Invoking Mises and Rothbard as the principal originators of their methodology, praxeologists proclaim that there is an a priori true starting point for economic theorizing, the axiom 'Man acts.', from which purportedly all economic theory can be obtained by deduction. In order to guarantee the truth and uphold the a priori character of all the attained theorems as intended, the correctness of each deductive step is crucial: Praxeologyand consequently economics toois a deductive system. […] No economic theorem can be considered sound that is not solidly fastened upon its foundation by an irrefutable chain of reasoning. (Mises, 1949(Mises, / 1998 Given the pivotal role of deduction, one would expect logic to play a central role in the methodological teachings of praxeologists. Indeed, the most prominent and engagingly written contemporary textbook in the praxeological branch of Austrian economics (Gordon, 2000) devotes the entire first chapter titled 'The Method of Economics' to deductive logic. Not to modern symbolic predicate logic though, but to verbal logic in the vein of Aristotelian syllogisms. This is in line with Rothbard's programmatic claim for praxeology that 'mathematical logic is uniquely appropriate to physics' (1956/2011, p. 292) whereas 'verbal logic permits each law to be meaningful as it is deduced' (1952/2009). Admittedly, the extreme stance towards formalization held by Rothbard is not representative of the current Austrian School as a whole. The research practice of many working economists sympathetic to the Austrian School has moved beyond wholesale rejection of formal methods and many Austrians might implicitly hold a nuanced and defensible position with respect to formalization. Yet, non-scholarly portrayals of the Austrian School almost always exaggerate the methodological claims regarding formalization. These overstatements exert considerable influence on the public image of Austrian economics. Leaving such distortions of public discourse aside, Rothbard's stance vis-à-vis formalization has remained largely unopposed by scholarly Austrian methodologists too. One of the purposes of this paper is to make explicit what in practice already seems to be the predominant methodology of the Austrian School and to vindicate it on Austrian grounds.
It is indeed by no means obvious on what grounds the possibility of useful formal methods in the social sciences should supposedly be dismissed entirely by a 'proper Austrian'. Which arguments do Austrian economists or other opponents of formalization provide? Backhouse responds that 'no Austrian, to my knowledge, has ever explained why mathematics cannot be used alongside naturallanguage explanations ' (2000, p. 40).
This paper provides several partial replies to Backhouse's query: First, it calls attention to the often-neglected professions of sympathy for formal methods in the history of the Austrian School (section 4). Second, the paper surveys potential benefits and drawbacks of formalization from an Austrian perspective (section 5), thereby corroborating legitimate concerns that predominant types of mathematization induce a shift of attention away from the key concepts of Austrian economics (section 6.1). Taking this shift to the extreme, predominant modes of mathematization tend to accompany a detachment from 'reality' incompatible with Austrian pleas for realisticness (section 6.2). Third, none of the customary Austrian and non-Austrian criticisms of formalizations justify a wholesale rejection of formal methods. Wieser's questionable notion of Sprachgeist could be exploited to develop such a knockout argument (section 7).

In defense of formalization as translation
Before appraising the Austrian stance, some clarification of the term 'formalization' is called for. Predominant meanings of terms like 'formal', 'abstract', and 'rigorous' changed in the course of history and moreover their usages in mathematics and economics differ (see Weintraub, 1998). Accordingly, some criticisms which on a literal reading dismiss formalization or mathematics tout court, could be interpreted charitably as merely considering the formal methods available them at the time. Rothbard, for instance, seems to falsely assume that all formal languages are uninterpreted calculi. Thus, according to him, any formalization would 'strip economics of all meaning ' (1952/2009, see also 1976/2011). In comparison, Mises might at least have had a point when he accused game theory of neglecting the cooperative core of a market economy in 1962 (pp. 87-90), not anticipating cooperative game-theory at it.
If one adopted certain definitions of 'formalization', it would be obvious that the praxeologists among Austrian economists hold no objections whatsoever, indeed they wholeheartedly embrace some forms of formalization. Consider for instance Loasby's characterization of formalist economics as a research program which 'seeks to emulate mathematicians by the careful construction of watertight logical systems from a brief but comprehensive axiom set ' (1976, p. 13). In this sense, formalism has nothing to do with formal languages but closely resembles praxeology. Backhouse outlines a helpful disambiguation of three variants of formalization: [A]xiomatisation, mathematisation and methodological formalisationare very different and should not be confused. What they have in common is the breaking down of a complex chain of reasoning into an explicitly stated series of steps, each of which is sufficiently simple for there to be an agreed procedure for dealing with it. (Backhouse, 1998(Backhouse, , p. 1849 Many Austrian economists champion the first component, axiomatization; many praxeologists even deem it the only acceptable way of economic theorizing. The contentious component is what Backhouse refers to as mathematization, in which statements of natural language are translated into a formal language such as mathematics or some logic. Then the inference rules of the formal system are deployed and yield certain conclusions in the formal language. These conclusions are then translated back into the natural language. One of the major advantages of formal systems is that their inference rules, which ideally are purely syntactic, facilitate the creation of deductions and other steps of reasoning. Moreover, controlling deductive steps for validity becomes almost trivialeven computers can usually do it. 2 The ill-intentioned ascertainment that 'mathematics is a substitute for thinking', sometimes attributed to Robinson, seems to miss this point of formalization. Austrian economists, by contrast, should be naturally inclined to welcome the idea of limited capacity of individual human reasoning and the potential of partially delegating rationality to an external process, be it a well-understood algorithm, an abstract rule, or market processes.
The notion of formalization the remainder of this paper will primarily be concerned with is formalization as translation into a formal language as described above. Indeed, many statements regarding the use of formal methods in economics made by Carl Menger, Karl Menger, Mises, Machlup, Rothbard, and other Austrian economists bear upon formalization as translation.

Sympathy for formal methods in the heyday of the Austrian school
Contemporary Austrian economics usually esteems the main ideas and figures in the historical development of the School, especially Mises and Hayek. Surprisingly, a closer look at some institutions and networks in the heyday of Austrian economics in interwar Vienna casts serious doubts on the School's protagonists' alleged hostility towards formalization.
The Austrian Center for Business Cycle Research, founded by Mises and Hayek as well as headed by Hayek and Morgenstern produced empirical studies (which already clashes with some accounts of the Austrian approach) and relied heavily on mathematical and statistical methods. The Mathematisches Kolloquium was organized by Karl Menger in part as a platform for exchange between the Austrian School of economics founded by his father and mathematical economics. Karl Menger also published a decision theory for ethical norms and social associations as one of the first highly formalized monographs in the social sciences outside economics (1934/1974). Many of the scholars who attended the colloquium regularly participated in Mises's Viennese private seminar too. There, Alt, Menger, Morgenstern, Schlesinger, and Wald discussed economics together with Kaufmann who published on philosophy of mathematics and Tintner who was co-responsible for the establishment of econometrics. These champions of uses of formal methods in the social sciences gladly spent their Friday evenings attending the non-university Mises Circle, and the host willingly admitted them to this private discussion group in his office at the Chamber of Commerce. Perhaps Mises was not a dogmatic adversary of all forms of mathematical economics after all.
Another incident does not square well with Mises's purported hostility against formalization. Reacting to a paper by Karl Menger (1936/1979a in which translations between natural language and mathematical language are a reoccurring constituent, Mises sent the author a personal letter. Instead of methodological criticism or a lack of interest expected from a key figure of Austrian economics, Mises replied that he 'read [the paper] with great benefit and learned a lot from it' (Mises, 1936, my translation). 3 It was the chief editor Mayer, the protege of Wieser, who blocked the publication of papers using formal methods in the Zeitschrift für Nationalökonomie until Morgenstern joined the editorial board (see Menger, /1979b).
On a less anecdotal level, Mises's methodological writings about the use of formal languages are quite explicit. He affirms that mathematical equations of equilibrium analysis 'say no more and no less' than what can be said in natural language (1938/2000, p. 28). Similarly, the algebraic expressions of probability calculus are perfectly legitimate, according to Mises. Probability calculus does not add anything new to the previous knowledge of a gambler, but 'it translates it into mathematical language ' (1949/1998, p. 108). Analogously, Mises explains the formation of prices in natural language but concedes the equivalent possibilities of drawing and intersecting curves and 'to express it in mathematical symbols ' (1949/1998, p. 330). The highly formalized nature of game theory serves as another, albeit circumstantial, clue that Austrian economics can be conciliated with formal methods.
Like most Austrian economists, Hayek hardly used mathematics in his writings. His slightly timid steps towards mathematization by means of graph theoretical explorations of the general meansends relationship (see Caldwell, 2016) or by means of triangles depicting the capital structure and the process of production were hampered by Hayek's lack of the respective mathematical skills. He later acknowledged that had he wanted to continue trying to engage people like Kaldor that it was 'a serious mistake' not to have acquired the command over mathematics needed to do so (see Caldwell & Klausinger, 2022, p. 365-381). Hayek did supervise and appreciate a mathematically advanced doctoral thesis, in which Lerner integrates the rate of interest to Hayek's triangles by adding a third dimension (Giraud, 2021, pp. 12-19). In any case, Hayek had no principled objections against formalization in economics. On the contrary, as one would expect from somebody keenly interested in complex systems, Hayek declared mathematics probably 'absolutely indispensable' for certain purposes in economics (1952/1964, p. 214).
Given Mises's, Morgenstern's, and Hayek's acceptance of partial formalization as well as Machlup's (1991, p. 330) encouragement of 'polylinguistic scholarship', i.e. economists should strive for fluency in natural as well as in formal languages, it becomes increasingly dubious whether the Austrian School provides any grounds for the wholesale rejection of formalization sometimes ascribed to it.

Potential benefits and drawbacks of formalization
Formalization as translation facilitates several consequences which constitute benefits from an Austrian perspective. Reviews of those potential 4 benefits identify prospects for improved communication across disciplinary boundaries, a potential for more precision and clarity, and increased efficiency of expression (Hudik, 2015;Linsbichler, 2021b;Menger, 1972Menger, /1973. Moreover, formal systems with syntactic rules enable and simplify scrutiny of arguments, criticisms, and purported proofs. Rules for manipulating diagrams might be interpreted as an intermediate step between syntactic rules of inference and verbal reasoning. Since even sympathetic interpreters like Caldwell (1984) highlight severe problems with 'verbal chains of logic', I maintain that improved control of deductive arguments is highly relevant for the praxeological branch of Austrian economicsbut not restricted to it. All of these traits of formalization as translation constitute benefits from the Austrian perspective: Austrians want to communicate with non-Austrians and with non-economists; Austrians seek to be precise, clear, efficient, andmost emphatically praxeologistsaim for deductive arguments without gaps or hidden assumptions. 5 In contrast, Austrians and non-Austrian methodologists identify several potential drawbacks of formalization. Most of the ensuing warnings of misguided over-mathematization are justified and deserve to be taken seriously. Having said that, I submit that none of the prevalent arguments suffices to underpin the wholesale rejection of formalization which some contemporary Austrian economists and other heterodox critics endorse.
Austrian and non-Austrian economists provide a plethora of arguments that specific formal methods involve an error or are inappropriate for the given purpose (Hudik, 2015;Linsbichler, 2021b). Granted. Economists should not commit errors of any kind, whether they use formalizations or not. And if certain formalizations are inadequate for a given purpose, then one should refrain from them. An important special case of possible inadequacy is the question of legibility for the intended audience. Since understanding formal languages requires training which not every intended reader might have, the potential benefits of formalization for communication mentioned above carry a flipside as well. An abundance of formulas in the language of symbolic logic or mathematics, while perhaps sometimes perceived as a seal of scientificity, may undermine the goal of reaching a policymaker or the general public. Even intra-scientific communication can be compromised by over-formalization. 6 The balance of pros and cons of formalization with respect to communication are often non-trivial. Since no ultimate standards are available, these and other discussions regarding the appropriateness and adequacy of a specific formalization can only be engaged pragmatically on a case-by-case basis.
6. Potential drawbacks continued 6.1. Shifts of attention A discipline can develop an appetite for formalizationand mainstream economics arguably has. Such a self-reinforcing tendency manifests itself in academic training and in requirements for publications in high-impact journals. If formalized work is considered the most prestigious or the only path to tenure, marginal scholars will shift their attention away from problems they consider relevant towards problems the concepts of which are easier to formalize or give rise to more intellectually stimulating formal systems. As a special case, quantitative methods shift attention to phenomena which can be measured. 7 By granting formalization the role of a threshold which respectable scientific work must pass, a discipline implicitly distorts its focus on relevant issues.
The case of shifts of attention is particularly pressing from an Austrian perspective because many pivotal components of the research agenda of Austrian economics indeed pose obstacles to formalization. Concepts such as meaning assignments, entrepreneurship, subjective interpretative knowledge, radical uncertainty, non-physicalist time, heterogeneous capital structures, and institutional considerations demarcate Austrian investigations from other schools' but seem to resist straightforward formalization or meaningful quantitative measurement. It creates even more misunderstandings when appropriations by mainstream economics substantially alter Austrian concepts, as in the transformation of Austrian 'knowledge' to mainstream 'information' (see Boettke, 2002;Boettke & O'Donnell, 2013). While variants of the mainstream's 'information' are pruned for handy mathematization, they do not permit conceptual space for real surprises and other phenomena which Austrian economists deem indispensable for a proper understanding of entrepreneurial action and the market process.
Another example for problematic appropriation, posed by a trend in Austrian economics, concerns 'culture'. 8 Extending upon an existing body of thought in the Austrian tradition and especially upon Lavoie (1986), 9 some Austrian economists aim to organically integrate economics with cultural studies in order to achieve and explore a pervasive theory of economic culture (Berger, 1991;Chamlee-Wright, 1997;Harper, 2003;Lavoie & Chamlee-Wright, 2000;Storr, 2013). 10 The most developed aspect of this branch of Austrian economics insists on taking the culturedependent subjective interpretation on the part of entrepreneurs seriously. Lavoie argues that Kirzner's theory of entrepreneurship, its other merits notwithstanding, disregards the role of culture and of interpretation in entrepreneurship because a neoclassical concept of equilibrium plays an overbearing role in Kirzner's reasoning (Berger, 1991;Chamlee-Wright, 1997). It is worth noting that Kirzner does not use mathematical or other formal language in his theorizing. So, in accordance with the argument in this paper, the content of equilibrium analysis is problematic from Lavoie's perspective, not the language in which it is formulated.
One objection to the inclusion of 'culture' into economic analysis demurs that the concept is too vague or nebulous to be useful (Storr, 2013, p. 9, pp. 15-17). As a prima facie sensible reaction, various (mostly non-Austrian) economists tried to define 'culture' in a mathematically manageable manner. An extreme case of this would be to reduce the culture of a community to two indirectly measurable, well-defined magnitudes, such that a given community may score 57,4 on an index of mutual trust and 36,2 on an index of collective-mindedness. These two values are then inputs into formulas which animate predictive models of economic activity of the community. This and somewhat more sophisticated definitions of 'culture' are obviously deeply unsatisfying from the hermeneutical Austrian perspective. Accordingly, Austrian economists in the hermeneutical tradition continue employing non-formal strategies for incorporating culture into economic analysis, including ethnographic case studies and interpretative understanding. In any case, weighing the benefits and drawbacks of this approach is a pragmatic matter. The Austrian literature on economic culture does not contain a convincing argument for a wholesale principled rejection of formalization, nor does it maintain to do so. In fact, Kaufmann (1931) defends a by no means simplistic theory of interpretative understanding ('Verstehen'), yet upholds its compatibility with formal methods in principle.
The examples of 'knowledge' and 'culture', however, do substantiate the legitimate Austrian worries that the prevalent mathematizations shift attention away from the crucial problems of (Austrian) economics. Restraint from eagerly employing the currently prevalent or available formal methods thus seems epistemically and strategically warranted for Austrian economists. I take this to be the most plausible interpretation of Boettke's (1996) assertion that 'mathematical economics cannot capture the essence of the economic problem individuals confront in the world' since 'the language of mathematics is not designed to deal with issues of semantic meaning'. 11 A convincing indication of hazards and limitations of certain types of mathematical formalism should however not be conflated with the wholesale rejection of formalization championed by Rothbard and some others. Perhaps, as Morgenstern (1963, p. 3) heralded 'altogether new mathematics has to be invented in order to cope with manifold forms of economic problems '. 12 Given that, for example, meaning assignments of the individual actors play a crucial role in Austrian economics and considering the resulting need for a social scientific language capable of describing meaning assignments, even a more sophisticated form of mathematics will likely never be sufficient. Yet, intensional logics and highly formal methods can be and are, e.g. by linguists, successfully utilized to express or study meaning assignments. It is equally dubious why natural language statements about heterogeneous capital structures, about entrepreneurs, about culture, or about institutional arrangements should place any excessive burdens on a determined formalizer. Arguably, creating adequate formalization of characteristically Austrian concepts and theories is a highly intricate problembut not much more complicated than adequate formalization of the concepts and theories used by mainstream economists in the natural language passages of their papers. The internal rigor of mathematical passages of papers is of no avail if the meanings of the mathematical terms are unclear or the relation between the mathematical and the natural language part is hazy. Formal predicate logic has in fact been employed to criticize semantic ambiguity and a blatant lack of deductive rigor in standard mathematical economics (Dennis, 1996). 13 Regardless of the merits of the specific tool set and strategy proposed by Dennis (2002) as a remedy, such criticisms of prevalent modes of mathematical economics should be embraced by Austrian economists and advocates of (adequate) formalization as translation alike.

Detachment from 'reality' -the Austrian plea for realisticness
A shift of attention to less relevant issues is already regrettable. Even worse from the perspective of prior priorities, economists might become completely detached from 'real world problems'. Induced by the beauty of the formal apparatus or by career considerations combined with the disciplinary incentives of an overblown prestige of mathematical methods, an economist might become fully absorbed by the investigation of the formal systems themselves and by the search for elegant proofs of theorems while paying no heed to empirical data. Similar concerns, especially about general equilibrium theory, have been raised by many non-Austrian economists as well. 14 Many criticisms of the use of formal methods advanced by Austrian economists are in effect merely criticisms of the detachment from realisticness incidentalbut not inherentto formalization, or so I will argue. Consider for instance Mises, who after praising the mathematically advanced economics of Auspitz and Lieben (1889) as 'brilliant' puts the Austrian School in contrast to their equilibrium analyses: The Austrian School aims to account for prices actually paid in the market, and not just prices that might be paid under certain never-realizable conditions. It rejects the mathematical method, not because of ignorance or an aversion to mathematical accuracy, but because it does not place importance upon the detailed description of the condition of a hypothetical and static equilibrium. (Mises, 1940(Mises, /2009 More recently, Peter Boettke aptly subtitled a paper 'Modern economics as a flight from reality' (1997), thereby enunciating the Austrian plea for realisticness. Austrian economists regularly claim that their School 'has consistently adhered to the postulate of [realisticness]' (Hülsmann, 1999, p. 3). In theories and models targeted at explaining the 'real world', many Austrians reject idealizations, i.e. assumptions known to be false. 16 In contrast to idealizations, Austrian economists acknowledge the necessity of abstractions in which certain factors are deemed irrelevant and are thus left unspecified (see Mises, 1929Mises, /2011Long, 2006).
Unrealistic assumptions of mathematical economists have been criticized by Austrian economists for almost 150 years. Carl Menger rejected the simplifying assumptions which allowed Auspitz and Lieben a mathematical and graphical treatment of price theory as 'inadmissible' (1889, p. 4). 17 Half a century later, Mises discards at least three types of mathematical economics. Econometric quantifications of elasticities of demand, price theory without consideration for the use of money or the market process, and quantitative utility analysis are all rejected for resting on untenable assumptions (Mises, 1949(Mises, /1998. More recent critics of mathematical economics, e.g. Kirzner (1973Kirzner ( , 1976 and Shackle (1973), expand on their Austrian predecessors and identify unrealistic assumptions of general equilibrium theory and their arguably detrimental consequences for economic analysis. In particular, vastly exaggerated assumptions about the knowledge and the computational capabilities of economic actors and the presupposition of regularity of economic systems lead mathematical price theory astray and mainstream economics 'into an unfortunate direction' (Kirzner, 1973, p. 3).
These are just a few of the most prominent examples of Austrian criticisms of unrealistic assumptions in mathematical economics. The scientific and extra-scientific context of the various debates changed. Likewise, the criticisms target different unrealistic assumptions and different mathematical tools, from differential calculus to probability theory to statistical methods. However, for the narrow purposes of this paper, all these distinctions can be provisionally discounted. For the sake of argument, I concede that, first, the assumption in question is indeed unrealistic, and second, all unrealistic assumptions ought to be avoided. Now suppose an economist seeks realisticness and suppose she adopts the definition of formalism from the Elgar Companion to Austrian Economics, according to which 'the formalist approach starts with the formulation of simplifying assumptions' (Klamer, 1994, p. 48). If idealization is directly linked to formalization, then she must indeed reject formalization. Contradicting his own assertions cited above, Mises seems to commit the same error of assemblage: '[The mathematical method] is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms […] divert the mind from the study of the real problems ' (1949/1998, p. 347).
Given that mathematical economics typically involves idealizing assumptions, the generic Austrian reflex against formalization is relatable but sometimes misses the real targetthe theories and ideas expressed in mathematical terms. One problem of neoclassical models is that they depict markets as frictionless and instantaneous to adjust, thereby concealing a market process that has transaction costs, error, discovery, and arbitraging actions through time. The prima facie problem is not that these potentially misleading models are presented in mathematical language. While it might in fact be typical for mathematizations to involve idealizing assumptions as the examples above strongly suggest, the association is by no means necessary. True natural language statements can be formalized just as well as false ones. Conversely, false assumptions can be expressed in natural languages or in formal languages. A few pages after his misapprehension, Mises seems to realize that the potential problem lies with the content of the propositions and not with their translation from one language to another (1949/1998, p. 352).
If the goal is realisticness, then idealizing assumptions are to be avoided, regardless in which language they are stated. Austrian economists caution against certain, perhaps typical, uses of formal methods, but a repudiation of simplifying assumptions of specific manifestations of mathematical economics does not entail an outright rejection of formal languages.

Friedrich Wieser: invoking Sprachgeist against formalization tout court
Critics provide ample argumentative resources to emphasize detriments of formalization. Yet, none of the arguments so far suffices for the dismissal per se which many praxeologists, most notably Rothbard (1952Rothbard ( /2009Rothbard ( , 1956Rothbard ( , 1976, advocate. According to him, a translation between English and a formal language 'would be likely to lead to grave errors'. Since Rothbard does not account for the superior proof checking properties of many formal languages he contends that a translation 'makes little sense' and should 'have to fall with one slash of Occam's Razor ' (see 1952/2009, 1956/2011, pp. 292-293). 18 Mises', Hayek's, Kirzner's, Boettke's, and arguably Carl Menger's 19 arguments mainly target re-conceptualizations and unrealistic assumptions instead of the introduction of formal or semi-formal languages as such. These key figures of Austrian economics do not qualify as authorities for a wholesale rejection of formalization. I submit one unlikely candidate in the history of Austrian economics who could provide the argumentative resources to do so: Friedrich Wieser. 20 In his first monograph (1884), he sets up what I will, using Wieser's term, call a Sprachgeist ['spirit/essence of language'] argument. 21 Wieser's protege Mayer's turndown of Menger's formal paper (1936Menger's formal paper ( /1979a) corresponds with the anti-formalist underpinnings of their research program.
Resembling German historicist Ranke's notion of Volksgeist ['spirit/essence of a people'], Wieser maintains that over centuries, a people, e.g. the German people, accumulates and stores knowledge in the essence of its natural language. In contrast to the natural sciences, the knowledge laid down in the Sprachgeist tends to be more reliable than observation of phenomena as far as the social sciences are concerned. In some areas, such as theory of value, Sprachgeist even provides necessarily true knowledge, according to Wieser. Consequently, the economist investigating the theory of value need not bother with empirical data but can remain in her armchair, study the German language, and still learn about empirical laws: [We should] reawaken the great sense of the basic words of our mother tongue. Some names, i.e. some notions associated with the sound of the names, are so correct and sound so pure in us, that the scientific investigator is allowed to restrict herself to the analysis of language in order to determine the essential characteristics of a phenomenon.
[…] The ear often judges better than the mind. (Wieser, 1884, p. 6, my translation) If one accepted the claim that necessarily true knowledge is 'deeply rooted' in the sound of the natural language of a people (Wieser, 1884, p. 7), then a translation into a formal language might pose an insurmountable problem. The essential features of the sound of the language might get irrevocably lost. Note however that according to this position, a translation between German and English is prima facie equally problematic as a translation between German and a formal language. By studying the German Sprachgeist as an emanation from the German Volksgeist one learns only about the laws governing the German economy. The laws of the Anglo-Saxon economy might be quite different.
Adopting Wieser's essentialist notion of language might help to preclude formalization. This 'achievement' comes at a high price though. We ultimately end up with an oddly relativistic economics and deprived of superior modes of checking proofs and arguments. We might even fuel nationalistic leanings which Wieser indeed sympathized with in his later years.

The prospects of partially formalized Austrian economics
Those readers not convinced by the Sprachgeist argument hopefully accept that, from an Austrian perspective, there is no principled justification to reject formalization altogether and that, historically speaking, the School's main representatives did not actually do so. Many contemporary Austrian economists might nevertheless consider the extent of mathematics in their journal articles and textbooks pragmatically adequate. To be clear, hardly anything in this paper suggests otherwise.
Having dispelled wholesale rejections of formal methods in general and scruples of formalizations as translations in particular, one minor specific proposal pertains to parts of the praxeological branch of Austrian economics. Bearing in mind the many pitfalls of formalization, the concrete content of the axiom 'Man acts.' as well as some more contested verbal chains of praxeological deduction would arguably benefit from explication and proof checks in a formal language. If however, there is in fact no ambition to detect gaps or hidden assumptions in purported deductive proofs or if non-praxeologists among Austrian economists deny the applicability of modern logical analysis to narratives and ethnographic case studies, then perhaps the rejection of formalization has merely been a handy immunizing strategy for preconceived conclusions.
Austrian economics, which does not depend on an untenable extreme apriorism (see Linsbichler, 2017Linsbichler, , 2021a and cautiously permits formal methods will hopefully substantiate how fruitful exchange and comparative evaluations between different schools of thought are possible (see also Backhouse, 2000;Holcombe, 2014;Hudik, 2015;Linsbichler, 2017). Unless one adopts a Sprachgeist argument, the discipline of economics may not be confronted with a detrimental plurality of mutually untranslatable scientific languages and incommensurable, ideologically biased theories. Non-polemical communication across schools of thought may ultimately even promote public trust in economics as a scientific endeavor.
Fortunately, recent scholarly research in Austrian economics has been increasingly following these recommendations instead of popular, simplistic methodological slogans for several years. Many scholars in the vicinity of the Austrian School do not shy away from dosed applications of mathematical nomenclature (see e.g. Koppl, 2017;Lewin & Cachanosky, 2019, signpost possible future uses of formal methods such as multi agent modeling in a Mengerian spirit (Gloria, 2021) and modal logic in formalizations of counterfactual reasoning involving Misesian imaginary constructions (Linsbichler & Cunha, 2023), and last not least actually conduct formalizations of praxeological deductions (Oliva Córdoba, 2017). In light of these and similar developments, the main point of this paper is quite modest. The Austrian methodologists could defuse bad conscience or uneasiness which practicing Austrian economists might have for frequently using (adequate) formal methods. Contradicting some popular prejudices, the reality of scholarly Austrian economics should merely be put on explicit record: the research program of Austrian economics does not and should not impose a wholesale rejection of formalization.

Notes
1. Neither all Austrian economists nor all Austrian critics of formalization favor praxeology. Many Austrians rather emphasize the role of narrative articulations of entrepreneurial action and perhaps implicitly doubt the applicability of logical analysis to narratives. Yet, all scientists (attempt to) explain, predict, argue, or criticize. Since explanation, prediction, argument, and criticism rest on logical rules of inference, these practices are in principle amenable to scrutiny by means of modern, formal versions of logic. Prychitko (1993), for instance, criticizes fellow Austrian economists not only for unrealistic assumptions but also for alleged gaps in the proofs of their conclusions in welfare economics. Despite Prychitko's reservations against formalism, he effectively engages in logical analysis. In case a disagreement persists, the gold standard for checking the correctness of deductive proofs are syntactic rules of inference. 2. Of course, the rigor of the full argument depends not only on the correct application of the inference rules within the formal language but also on the adequacy of the two translations. As for any translation, the assessment of the adequacy of translations between natural languages and formal languages is not always straightforward and unproblematic. An in-depth discussion of problems of the philosophy of formalization as translation extends far beyond the scope of this article though (see e.g. Brun, 2003 andDennis, 1982). 3. Having said that, Morgenstern noted in his diary about Menger's 'brilliant presentation' of the paper which 'demonstrated the necessity for exact thinking in economics' that Haberler did not really understand 'these exact matters' and that 'Mises uttered pure nonsense' (my translation from Gehrke, 2019). Still, Mises never showed any tendency to pussyfoot or spare somebody from polemic criticism and yet wrote a kind and supportive letter about Menger's mathematical and formal paper. 4. Formalization creates a potential for, not a guarantee of precision and clarity. Karl Menger (1972Menger ( /1973, who as a mathematician developed the first clear and applicable definitions of 'curve' and 'dimensions', stresses the potential for precision and clarity but also mentions a counterexample in which the natural language formulation is more precise than the standard mathematical formulation. A related worry is raised by Morgenstern and von Neumann: 'There is no point in using exact methods where there is no clarity in the concepts and issues to which they are to be applied. ' (1944/1953, p. 4) In this vein, Mayer (1993) accuses many papers in mainstream economics of creating an impression of clarity and rigor by focusing on the technical mathematical part, while relegating the ambiguous relation between the mathematical symbols and relevant 'real world phenomena' to a few passing remarks in the introduction or the conclusion. 5. There might be one exception to the assessment of preciseness as a benefit. Rothbard (1976 curiously maintains that since individual human reasoning and behavior is imprecise it should ideally be described by likewise imprecise natural language. In opposition to Rothbard's 'historicist' approach, one might want to describe, explain, or predict imprecise reasoning and behavior as precisely as possible. 6. For instance, the mathematization of mainstream economics is cited as one of several obstacles to interaction between cultural studies and economics and for the two disciplines sometimes even being 'incapable of listening to each other' (Lavoie & Chamlee-Wright, 2000, pp. 3-5). 7. Both Kelvin ('When you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind. ') and Viner ('Yes, and when you can express it in numbers, your knowledge is of a meagre and unsatisfactory kind.') have a point (quoted from Higgs, 1987, p. 20, who argues for both quantitative and qualitative evaluations of the size of government). 8. I am grateful to an anonymous reviewer for urging me to mention this example. 9. To some extent, an important role for culture and especially for meaning interpretations ('Verstehen') by acting individuals as well as by the social scientist studying those individuals have always been inherent to the approach of the Austrian School and many of its fellow-travelers. Weber serves as a methodological inspiration (see Lachmann, 1971;Storr, 2013). Wieser embeds the acting individuals of his theory in a sociocultural frame which, unfortunately, is treated as (almost) independent of the acting individuals and which Wieser explains historically (see Wieser, 1910Wieser, , 1914Wieser, /1927). Mises develops a theory of human action instead of merely human choice between given options, i.e. for Mises human action encompasses the interpretative and subjective identification of the very framework of choice (see e.g. Mises, 1930Mises, /2003. According to Hayek, (many of) the facts of the social sciences are what people believe and think and consideration of processes of cultural evolution are crucial for political economy (see e.g. Hayek, 1982Hayek, , 1988Storr, 2010). Some 'hermeneutical' capital theorists in the succession of Lachmann advance subjectivism so far that physical characteristics of capital goods become economically irrelevant (see e.g. Dekker & Kuchar, 2019). Finally, and perhaps not yet sufficiently incorporated, Kaufmann (1936) elaborates on the necessity of specifying a relevant 'schema of interpretation' for understanding meaning assignments. In the study of understanding ('Verstehen'), this constitutes an innovative step beyond Weber and other predecessors, who target one universal schema of interpretation. Kaufmann's conceptual improvement is potentially essential to an integration of economics and hermeneutic cultural studies because it allows for a consistent combination of universal economic laws with different local, context-dependent schemata of interpretation. 10. The hermeneutical branch of Austrian economics is not uncontested within the School (see e.g. Hoppe, 2006, pp. 260-270). Storr (2004) and Leeson (2009) exemplify two accounts of the economics of piracy with a completely different balance of cultural studies, institutional analysis, and pure economics. 11. This modest reading of Boettke (1996) is also corroborated by his suggestion of an 'understandability criterion' for the use of formal methods. An 'understandability criterion' can serve as a judicious reminder of Morgenstern's and von Neumann's warning that precision within the formal language often obscures the ambiguous relation of the terms of the formal language to the supposed 'real world objects' (see footnote 4). Even so, the relation of natural language terms to the putative 'real world objects' is often highly ambiguous as well.
Obstacles in an attempt to formalize sometimes just reveal the preexisting but unrecognized blur, as anyone who has done coding has experienced: making a computer 'understand' your idea sometimes helps you realize that your idea was hitherto unclear and has to be rendered more specific or discarded. 12. Kaufmann (1931) highlights that the impossibility of measurement in an area of research at most restricts the applicability of some branches of mathematics. If formal methods outside mathematics, especially in logic, are taken into account, Kaufmann's partial defense of formalization is even stronger. 13. Mathematical formulas do not guarantee precision of expressions or exact reasoning. Karl Menger (1961) shows that even pure and applied mathematics sometimes suffer from (curable) semantic ambiguity and Redei (2020) identifies instances of lacking logical rigor in mathematical physics. Besides pragmatic and epistemological reasons, Redei also attributes these shortcomings to problematic psychological reasons: conceptual precision […] exposes the fundamental limits of a physical theory at a given time. Since at that time it might not be possible to go beyond those limits […] This can be frustrating psychologically: […] This is unpleasant, can be experienced even as an existential threat and it is understandable that physicists do not wish to experience it (pp. 421-422).
14. One might try to counter these apprehensions of heterodox economists by studies which indicate an empirical turn in economics. Hamermesh (2013) and Angrist et al. (2017) indeed verify an increasing proportion of empirical work in economic journals. One might conclude that the discipline of economics takes care of itself and does not approach the status of a glass bead game detached from 'reality'. Nonetheless, all-clear signals are premature from an Austrian perspective. Speaking less about idealized model worlds but extensively employing socalled empirical data instead does not guarantee relevance for 'real world problems'. The trend towards empiricaloften quantitativemethods comes with its own cloven hoofs including incentives for data mining and consequent bland papers as well as academic curricula shifting from comprehension-oriented history and methodology of economics towards technical training in quantitative methods. From an Austrian perspective, neither formal economics proving theorems about idealized models nor empirical economics employing statistical methods on allegedly objective data contribute much to a proper understanding of market processes. While the formalism of mathematical economics and the statistical methods of empirical analysis raise separate methodological worries, these two perceived contemporary trends of mainstream economics put the Austrian School between a rock and a hard place. Neither of them sufficiently accounts for crucial factors such as institutions and subjective, interpretative knowledge of individuals. 15. In hindsight (and contrary to separate restrictions posed by Mises's epistemology), one could read this as a plea for the development of econometric methods capable of addressing more complex pricing situations. Mises and many other critics actually do not argue against translations into a formal language but against the content of certain unrealistic statements, regardless of whether they are formulated in English or predicate logic. 16. Notwithstanding their ubiquitous pleas for realisticness, Austrian economists heavily rely on 'imaginary constructions to which nothing corresponds in reality [… as …] an indispensable tool of thinking' (Mises, 1949(Mises, / 1998. 17. 'Inadmissible' is my translation. The German 'unstatthaft' even slightly insinuates an undertone of moral condemnation. 18. Traditionally, Occam's Razor refers to ontological entities and not to steps or products of scientific practice as in Rothbard's appropriation. 19. Carl Menger (1888, 1889 explicitly allows mathematics as a method of presentation. What he denied was any special faculty by which mathematical methods as a means of research could directly grasp causal relationships underlying the observable phenomena. This position seems very similar to Mises's but different from 'some later Austrians' who deny even the role as a method of presentation, as Karl Menger comments (1972. For a more detailed discussion of Carl Menger's position regarding formalization, see Linsbichler (2023). 20. Wieser is an unlikely candidate because many praxeologists who vehemently criticize formalization distance themselves from Wieser due to his early acquaintance with the German Historical School, his not strictly libertarian political positions, and his perceived tendency towards equilibrium analysis (see e.g. Hoppe & Salerno, 1999). Wieser and Rothbard share a strongly essentialist epistemology though (Linsbichler, 2021c). 21. Wieser later attenuated his position. While he continued trying to uncover the essence of value, he abandoned the references to Sprachgeist and used mathematical language when writing down systems of equations.