AND THE PRAXEOLOGICAL
FOUNDATION OF EPISTEMOLOGY
This will suffice here as an explanation of Mises's answer regarding the quest for the foundations of economics. I shall now turn to my second goal: the explanation of why and how praxeology also provides the foundation for epistemology. Mises had been aware of this and he was convinced of the great importance of this insight for rationalist philosophy. Yet Mises did not treat the matter in a systematic fashion. There are no more than a few brief remarks concerning this problem, interspersed throughout his massive body of writing.  Thus, in the following I must try to break new ground.
I shall begin my explanation by introducing a second a priori axiom and clarifying its relation to the axiom of action. Such an understanding is the key to solving our problem. The second axiom is the so-called "a priori of argumentation," which states that humans are capable of argumentation and hence know the meaning of truth and validity.  As in the case of the action axiom, this knowledge is not derived from observation: there is only verbal behavior to be observed and prior reflective cognition is required in order to interpret such behavior as meaningful arguments. And the validity of the axiom, like that of the action axiom, is indisputable. It is impossible to deny that one can argue, as the very denial would itself be an argument. In fact, one could not even silently say to oneself "I cannot argue" without thereby contradicting oneself. One cannot argue that one cannot argue. Nor can one dispute knowing what it means to make a truth or validity claim without implicitly claiming the negation of this proposition to be true.
It is not difficult to detect that both a priori axioms—of action and argumentation—are intimately related. On the one hand, actions are more fundamental than argumentations with whose existence the idea of validity emerges, as argumentation is only a subclass of action. On the other hand, to recognize what has just been recognized regarding action and argumentation and their relation to each other requires argumentation, and so, in this sense, argumentation must be considered more fundamental than action: without argumentation nothing could be said to be known about action. But then, as it is in argumentation that the insight is revealed that—while it might not be known to be so prior to any argumentation—in fact the possibility of argumentation presupposes action in that validity claims can only be explicitly discussed in the course of an argumentation if the individuals doing so already know what it means to act and to have knowledge implied in action—both the meaning of action in general and argumentation in particular must be thought of as logically necessary interwoven strands of a priori knowledge.
What this insight into the interrelation between the a priori of action and the a priori of argumentation suggests is the following: Traditionally, the task of epistemology has been conceived of as that of formulating what can be known to be true a priori and also what can be known a priori not to be the subject of a priori knowledge. Recognizing, as we have just done, that knowledge claims are raised and decided upon in the course of argumentation and that this is undeniably so, one can now reconstruct the task of epistemology more precisely as that of formulating those propositions which are argumentatively indisputable in that their truth is already implied in the very fact of making one's argument and so cannot be denied argumentatively; and to delineate the range of such a priori knowledge from the realm of propositions whose validity cannot be established in this way but require additional, contingent information for their validation, or that cannot be validated at all and so are mere metaphysical statements in the pejorative sense of the term metaphysical.
Yet what is implied in the very fact of arguing? It is to this question that our insight into the inextricable interconnection between the a priori of argumentation and that of action provides an answer: On a very general level, it cannot be denied argumentatively that argumentation presupposes action and that arguments, and the knowledge embodied in them, are those of actors. And more specifically, it cannot then be denied that knowledge itself is a category of action; that the structure of knowledge must be constrained by the peculiar function which knowledge fulfills within the framework of action categories; and that the existence of such structural constraints can never be disproved by any knowledge whatsoever.
It is in this sense that the insights contained in praxeology must be regarded as providing the foundations of epistemology. Knowledge is a category quite distinct from those that I have explained earlier—from ends and means. The ends which we strive to attain through our actions, and the means which we employ in order to do so, are both scarce values. The values attached to our goals are subject to consumption and are exterminated and destroyed in consumption and thus must forever be produced anew. And the means employed must be economized, too. Not so, however, with respect to knowledge—regardless of whether one considers it a means or an end in itself. Of course, the acquisition of knowledge requires scarce means—at least one's body and time. Yet once knowledge is acquired, it is no longer scarce. It can neither be consumed, nor are the services that it can render as a means subject to depletion. Once there, it is an inexhaustible resource and incorporates an everlasting value provided that it is not simply forgotten.  Yet knowledge is not a free good in the same sense that air, under normal circumstances, is a free good. Instead, it is a category of action. It is not only a mental ingredient of each and every action, quite unlike air, but more importantly, knowledge, and not air, is subject to validation, which is to say that it must prove to fulfill a positive function for an actor within the invariant constraints of the categorical framework of actions. It is the task of epistemology to clarify what these constraints are and what one can thus know about the structure of knowledge as such.
While such recognition of the praxeological constraints on the structure of knowledge might not immediately strike one as in itself of great significance, it does have some highly important implications. For one thing, in light of this insight one recurring difficulty of rationalist philosophy finds its answer. It has been a common quarrel with rationalism in the Leibniz-Kant tradition that it seemed to imply some sort of idealism. Realizing that a priori true propositions could not possibly be derived from observations, rationalism answered the question how a priori knowledge could then be possible by adopting the model of an active mind, as opposed to the empiricist model of a passive, mirror-like mind in the tradition of Locke and Hume. According to rationalist philosophy, a priori true propositions had their foundation in the operation of principles of thinking which one could not possibly conceive of as operating otherwise; they were grounded in categories of an active mind. Now, as empiricists were only too eager to point out, the obvious critique of such a position is, that if this were indeed the case, it could not be explained why such mental categories should fit reality. Rather, one would be forced to accept the absurd idealistic assumption that reality would have to be conceived of as a creation of the mind, in order to claim that a priori knowledge could incorporate any information about the structure of reality. And clearly, such an assertion seemed to be justified when faced with programmatic statements of rationalist philosophers such as the following by Kant: "So far it has been assumed that our knowledge had to conform to reality," instead it should be assumed "that observational reality should conform to our mind." 
Recognizing knowledge as being structurally constrained by its role in the framework of action categories provides the solution to such a complaint. For as soon as this is realized, all idealistic suggestions of rationalist philosophy disappear, and an epistemology claiming that a priori true propositions exist becomes a realistic epistemology instead. Understood as constrained by action categories, the seemingly unbridgeable gulf between the mental on the one hand and the real, outside physical world on the other is bridged. So constrained, a priori knowledge must be as much a mental thing as a reflection of the structure of reality, since it is only through actions that the mind comes into contact with reality, so to speak. Acting is a cognitively guided adjustment of a physical body in physical reality. And thus, there can be no doubt that a priori knowledge, conceived of as an insight into the structural constraints imposed on knowledge qua knowledge of actors, must indeed correspond to the nature of things. The realistic character of such knowledge would manifest itself not only in the fact that one could not think it to be otherwise, but in the fact that one could not undo its truth.
Yet there are more specific implications involved in recognizing the praxeological foundations of epistemology—apart from the general one that in substituting the model of the mind of an actor acting by means of a physical body for the traditional rationalist model of an active mind a priori knowledge immediately becomes realistic knowledge (so realistic indeed that it can be understood as being literally not undoable). More specifically, in light of this insight decisive support is given to those deplorably few rationalist philosophers who—against the empiricist Zeitgeist—stubbornly maintain on various philosophical fronts that a priori true propositions about the real world are possible.  Moreover, in light of the recognition of praxeological constraints on the structure of knowledge these various rationalist endeavors become systematically integrated into one, unified body of rationalist philosophy.
In explicitly understanding knowledge as displayed in argumentation as a peculiar category of action, it becomes clear immediately why the perennial rationalist claim that the laws of logic—beginning here with the most fundamental ones, i.e., of propositional logic and of Junctors ("and," "or," "if-then," "not") and Quantors ("there is," "all," "some")—are a priori true propositions about reality and not mere verbal stipulations regarding the transformation rules of arbitrarily chosen signs, as empiricist-formalists would have it, is indeed correct. They are as much laws of thinking as of reality, because they are laws that have their ultimate foundation in action and could not be undone by any actor. In each and every action, an actor identifies some specific situation and categorizes it one way rather than another in order to be able to make a choice. It is this which ultimately explains the structure of even the most elementary propositions (like "Socrates is a man") consisting of a proper name or some identifying expression for the naming or identifying of something, and a predicate to assert or deny some specific property of the named or identified object; and which explains the cornerstones of logic: the laws of identity and contradiction. And it is this universal feature of action and choosing which also explains our understanding of the categories "there is," "all" and, by implication, "some," as well as "and," "or," "if-then" and "not."  One can say, of course, that something can be "a" and "non-a" at the same time, or that "and" means this rather than something else. But one cannot undo the law of contradiction; and one cannot undo the real definition of "and." For simply by virtue of acting with a physical body in physical space we invariably affirm the law of contradiction and invariably display our true constructive knowledge of the meaning of "and" and "or."
Similarly, the ultimate reason for arithmetic's being an a priori and yet empirical discipline, as rationalists have always understood it, now also becomes discernible. The prevailing empiricist-formalist orthodoxy conceives of arithmetic as the manipulation of arbitrarily defined signs according to arbitrarily stipulated transformation rules, and thus as entirely void of any empirical meaning. For this view, which evidently makes arithmetic nothing but play, however skillful it might be, the successful applicability of arithmetic in physics is an intellectual embarrassment. Indeed, empiricist-formalists would have to explain away this fact as simply being a miraculous event. That it is no miracle, however, becomes apparent once the praxeological or—to use here the terminology of the most notable rationalist philosopher-mathematician Paul Lorenzen and his school—the operative or constructivist character of arithmetic is understood. Arithmetic and its character as an a priori-synthetic intellectual discipline is rooted in our understanding of repetition, the repetition of action. More precisely, it rests on our understanding the meaning of "do this—and do this again, starting from the present result." And arithmetic then deals with real things: with constructed or constructively identified units of something. It demonstrates what relations are to hold between such units because of the fact that they are constructed according to the rule of repetition. As Paul Lorenzen has demonstrated in detail, not all of what presently poses as mathematics can be constructively founded—and those parts, then, should of course be recognized for what they are: epistemologically worthless symbolic games. But all of the mathematical tools that are actually employed in physics, i.e., the tools of classical analysis, can be constructively derived. They are not empirically void symbolisms, but true propositions about reality. They apply to everything insofar as it consists of one or more distinct units, and insofar as these units are constructed or identified as units by a procedure of "do it again, construct or identify another unit by repeating the previous operation."  Again, one can say, of course, that 2 plus 2 is sometimes 4 but sometimes 2 or 5 units, and in observational reality, for lions plus lambs or for rabbits, this may even be true,  but in the reality of action, in identifying or constructing those units in repetitive operations, the truth that 2 plus 2 is never anything but 4 could not possibly be undone.
Further, the old rationalist claims that geometry, that is, Euclidean geometry is a priori and yet incorporates empirical knowledge about space becomes supported, too, in view of our insight into the praxeological constraints on knowledge. Since the discovery of non-Euclidean geometries and in particular since Einstein's relativistic theory of gravitation, the prevailing position regarding geometry is once again empiricist and formalist. It conceives of geometry as either being part of empirical, aposteriori physics, or as being empirically meaningless formalisms. Yet that geometry is either mere play, or forever subject to empirical testing seems to be irreconcilable with the fact that Euclidean geometry is the foundation of engineering and construction, and that nobody there ever thinks of such propositions as only hypothetically true.  Recognizing knowledge as praxeologically constrained explains why the empiricist-formalist view is incorrect and why the empirical success of Euclidean geometry is no mere accident. Spatial knowledge is also included in the meaning of action. Action is the employment of a physical body in space. Without acting there could be no knowledge of spatial relations, and no measurement. Measuring is relating something to a standard. Without standards, there is no measurement; and there is no measurement, then, which could ever falsify the standard. Evidently, the ultimate standard must be provided by the norms underlying the construction of bodily movements in space and the construction of measurement instruments by means of one's body and in accordance with the principles of spatial constructions embodied in it. Euclidean geometry, as again Paul Lorenzen in particular has explained, is no more and no less than the reconstruction of the ideal norms underlying our construction of such homogeneous basic forms as points, lines, planes and distances, which are in a more or less perfect but always perfectible way incorporated or realized in even our most primitive instruments of spatial measurements such as a measuring rod. Naturally, these norms and normative implications cannot be falsified by the result of any empirical measurement. On the contrary, their cognitive validity is substantiated by the fact that it is they which make physical measurements in space possible. Any actual measurement must already presuppose the validity of the norms leading to the construction of one's measurement standards. It is in this sense that geometry is an a priori science; and that it must simultaneously be regarded as an empirically meaningful discipline, because it is not only the very precondition for any empirical spatial description, it is also the precondition for any active orientation in space. 
In view of the recognition of the praxeological character of knowledge, these insights regarding the nature of logic, arithmetic and geometry become integrated and embedded into a system of epistemological dualism.  The ultimate justification for this dualist position, i.e., the claim that there are two realms of intellectual inquiry that can be understood a priori as requiring categorically distinct methods of treatment and analysis, also lies in the praxeological nature of knowledge. It explains why we must differentiate between a realm of objects which is categorized causally and a realm that is categorized teleologically instead.
I have already briefly indicated during my discussion of praxeology that causality is a category of action. The idea of causality that there are constant, time-invariantly operating causes which allow one to project past observations regarding the relation of events into the future is something (as empiricism since Hume has noticed) which has no observational basis whatsoever. One cannot observe the connecting link between observations. Even if one could, such an observation would not prove it to be a time-invariant connection. Instead, the principle of causality must be understood as implied in our understanding of action as an interference with the observational world, made with the intent of diverting the "natural" course of events in order to produce a different, prefered state of affairs, i.e., of making things happen that otherwise would not happen, and thus presupposes the notion of events which are related to each other through time-invariantly operating causes. An actor might err with respect to his particular assumptions about which earlier interference produced which later result. But successful or not, any action, changed or unchanged in light of its previous success or failure, presupposes that there are constantly connected events as such, even if no particular cause for any particular event can ever be preknown to any actor. Without such an assumption it would be impossible to ever categorize two or more observational experiences as falsifying or confirming each other rather than interpreting them as logically incommensurable events. Only because the existence of time-invariantly operating causes as such is already assumed can one ever encounter particular instances of confirming or disconfirming observational evidence, or can there ever be an actor who can learn anything from past experience by classifying his actions as successful and confirming some previous knowledge, or unsuccessful and disconfirming it. It is simply by virtue of acting and distinguishing between successes and failures that the a priori validity of the principle of causality is established; even if one tried, one could not successfully refute its validity. 
In so understanding causality as a necessary presupposition of action, it is also immediately implied that its range of applicability must then be delineated a priori from that of the category of teleology. Indeed, both categories are strictly exclusive and complementary. Action presupposes a causally structured observational reality, but the reality of action which we can understand as requiring such structure, is not itself causally structured. Instead, it is a reality that must be categorized teleologically, as purpose-directed, meaningful behavior. In fact, one can neither deny nor undo the view that there are two categorically different realms of phenomena, since such attempts would have to presuppose causally related events qua actions that take place within observational reality, as well as the existence of intentionally rather than causally related phenomena in order to interpret such observational events as meaning to deny something. Neither a causal, nor a teleological monism could be justified without running into an open contradiction: physically stating either position, and claiming to say something meaningful in so doing, the case is in fact made for an indisputable complementarity of both, a realm of causal and teleological phenomena. 
Everything which is not an action must necessarily be categorized causally. There is nothing to be known a priori about this range of phenomena except that it is structured causally—and that it is structured according to the categories of propositional logic, arithmetic and geometry.  Everything else there is to know about this range of phenomena must be derived from contingent observations and thus represents aposteriori knowledge. In particular, all knowledge about two or more specific observational events being causally related or not is aposteriori knowledge. Obviously, the range of phenomena described in this way coincides (more or less) with what is usually considered to be the field of the empirical natural sciences.
In contrast, everything that is an action must be categorized teleologically. This realm of phenomena is constrained by the laws of logic and arithmetic, too. But it is not constrained by the laws of geometry as incorporated in our instruments of measuring spatially extending objects, because actions do not exist apart from subjective interpretations of observable things; and so they must be identified by reflective understanding rather than spatial measurements. Nor are actions causally connected events, but events that are connected meaningfully within a categorical framework of means and ends.
One can not know a priori what the specific values, choices and costs of some actor are or will be. This would fall entirely into the province of empirical, aposteriori knowledge. In fact, which particular action an actor is going to undertake would depend on his knowledge regarding the observational reality and/or the reality of other actors' actions. And it would be manifestly impossible to conceive of such states of knowledge as predictable on the basis of time-invariantly operating causes. A knowing actor cannot predict his future knowledge before he has actually acquired it, and he demonstrates, simply by virtue of distinguishing between successful and unsuccessful predictions, that he must conceive of himself as capable of learning from unknown experiences in as yet unknown ways. Thus, knowledge regarding the particular course of actions is only aposteriori. And since such knowledge would have to include the actor's own knowledge—as a necessary ingredient of every action whose every change can have an influence on a particular action being chosen—teleological knowledge must also necessarily be reconstructive, or historical knowledge. It would only provide ex-post explanations which would have no systematic bearing on the prediction of future actions, because, in principle, future states of knowledge could never be predicted on the basis of constantly operating empirical causes. Obviously, such a delineation of a branch of aposteriori and reconstructive science of action fits the usual description of such disciplines as history and sociology. 
What is known to be true a priori regarding the field of action, and what would then have to constrain any historical or sociological explanation is this: For one thing, any such explanation, which essentially would have to reconstruct an actor's knowledge, would invariably have to be a reconstruction in terms of knowledge of ends and means, of choices and costs, of profits and losses and so on. And secondly, since these are evidently the categories of praxeology as conceived of by Mises, any such explanation must also be constrained by the laws of praxeology. And since these laws are, as I have already explained, a priori laws, they must also operate as logical constraints on any future course of action. They are valid independent of any specific state of knowledge that an actor might have acquired, simply by virtue of the fact that whatever this state might be, it must be described in terms of action categories. And as referring to actions as such, the laws of praxeology must then be coextensive with all the predictive knowledge there can be in the field of the science of action. In fact, ignoring for the moment that the status of geometry as an a priori science was ultimately grounded in our understanding of action and in so far praxeology would have to be regarded as the more fundamental cognitive discipline, the peculiar role of praxeology proper within the entire system of epistemology can be understood as somewhat analogous to that of geometry. Praxeology is for the field of action what Euclidean geometry is for the field of observations (non-actions). As the geometry incorporated in our measuring instruments constrains the spatial structure of observational reality, so praxeology constrains the range of things that can possibly be experienced in the field of actions. 
 Mises writes: "Knowledge is a tool of action. Its function is to advise man how to proceed in his endeavor to remove uneasiness.... The category of action is the fundamental category of human knowledge. It implies all the categories of logic and the category of regularity and causality. It implies the category of time and that of value.... In acting, the mind of the individual sees itself as different from its environment, the external world, and tries to study this environment in order to influence the course of events happening in it" (The Ultimate Foundation of Economic Science, pp. 35-36). Or: "Both, apriori thinking and reasoning on the one hand and human action on the other, are manifestations of the mind. . . . Reason and action are congeneric and homogeneous, two aspects of the same phenomenon" (ibid., p.42). Yet he leaves the matter more or less at this and concludes that "it is not the scope of praxeology to investigate the relation of thinking and action" Human Action , p. 25).
 On the a priori of argumentation see also K. 0. Apel, Transformation der Philosophie, vol. 2.
 Immanuel Kant, Kritik der reinen vernunft, p. 25. Whether or not such an interpretation of Kant's epistemology is indeed correct is, of course, a very different matter. Clarifying this problem is, however, of no concern here. For an activist or constructivist interpretation of Kantian philosophy see E. Kambartel, Erfahrung und Struktur, chapter 3; also Hoppe, Handeln und Erkennen (Bern: Lang, 1976).
 In addition to the works mentioned in note 46 see Brand Blanshard, The Nature of Thought (London: Allen and Unwin, 1921); M. Cohen, Reason and Nature (New York: Harcourt, Brace, 1931); idem, Preface to Logic (New York: Holt, 1944); A. Pap, Semantics and Necessary Truth (New Haven: Yale University Press, 1958); S. Kripke, "Naming and Necessity," in D. Davidson and G. Harman, eds., Semantics of Natural Language (New York: Reidel, 1972); H. Dingler, Die Ergreifung des Wirklichen (Frankfurt/M.: Suhrkamp, 1969); idem, Aufbau der exakten Fundamentalwissenschaft (Munich: Eidos, 1964); W Kamlah and P. Lorenzen, Logische deutik Propädeutik Mannheim: (Mannheim: Bibliographisches Institut, 1968); P. Lorenzen, Methodisches Denken (Frankfurt/M.: Suhrkamp, 1968); idem, Normative Logic and Ethics (Mannheim: Bibliographisches Institut, 1969); K. 0. Apel, Transformation der Philosophie.
0n rationalist interpretations of logic see Blanshard, Reason and
Analysis, chapters 6, 10; P. Lorenzen, Einführung in die
operative Logik und Mathematik (Frankfurt/M.: Akademische
Verlagsgesellschaft, 1970); K. Lorenz, Elements der Sprachkritik
(Frankfurt/M.: Suhrkamp, 1970); idem, "Die dialogische Rechtfertigung
der effektiven Logik," in: F. Kambartel and J. Mittelstrass, eds., Zum
normativen Fundament der Wissenschaft (Frankfurt/M.: Athenäum,
On the propositional character of language and experience, in particular, see W. Kamlah and P. Lorenzen, Logische Propädeutik, chapter 1; P. Lorenzen, Normative Logic and Ethics, chapter 1. Lorenzen writes: "I call a usage a convention if I know of another usage which I could accept instead.... However, I do not know of another behavior which could replace the use of elementary sentences. If I did not accept proper names and predicators, I would not know how to speak at all. ... Each proper name is a convention ... but to use proper names at all is not a convention: it is a unique pattern of linguistic behavior. Therefore, I am going to call it 'logical'. The same is true with predicators. Each predicator is a convention. This is shown by the existence of more than one natural language. But all languages use predicators" (ibid., p. 16). See also J. Mittelstrass, "Die Wiederkehr des Gleichen," Ratio (1966).
On the law of identity and contradiction, in particular, see B. Blanshard, Reason and Analysis, pp. 276ff, 423ff.
On a critical evaluation of 3- or more-valued logics as either meaningless symbolic formalisms or as logically presupposing an understanding of the traditional two-valued logic see W. Stegmüler, Hauptströmungen der Gegenwartsphilosophie vol. 2 (Stuttgart: Kröner, 1975), pp. 182-91; B. Blanshard, Reason and Analysis, pp. 269-75. Regarding, for instance, the many-valued or open-textured logic, proposed by F Waismann, Blanshard notes: "We can only agree with Dr. Waismann—and with Hegel—that the black-and-white distinctions of formal logic are quite inadequate to living thought. But why should one say, as Dr.Waismann does, that in adopting a more differentiated logic one is adopting an alternative system which is incompatible with black-and-white logic? What he has actually done is to recognize a number of gradations within the older meaning of the word 'not'. We do not doubt that such gradations are there, and indeed as many more as he cares to distinguish. But a refinement of the older logic is not an abandonment of it. It is still true that the colour I saw yesterday was either a determinate shade of yellow or not, even though the 'not' may cover a multitude of approximations, and even though I shall never know which was the shade I saw" (ibid., pp. 273-74).
 0n a rationalist interpretation of arithmetic see Blanshard, Reason and Analysis, pp. 427-31; on the constructivist foundation of arithmetic, in particular, see Lorenzen, Einführung in die operative Logik and Mathematik; idem, Methodisches Denken, chapters 6, 7; idem, Normative Logic and Ethics, chapter 4; on the constructivist foundation of classical analysis see P. Lorenzen, Differential und Integral. Eine konstruktive Einführung in die klassische Analysis (Frankfurt/M.: Akademische Verlagsgesellschaft, 1965); for a brilliant general critique of mathematical formalism see Kambartel, Erfahrung und Struktur, chapter 6, esp. pp. 236-42; on the irrelevance of the famous Gödel-theorem for a constructively founded arithmetic see P. Lorenzen, Metamathematik (Mannheim: Bibliographisches Institut, 1962); also Ch. Thiel, "Das Begründungsproblem der Mathematik und die Philosophie," in F. Kambartel and J. Mittelstrass, eds., Zum normativen Fundament der Wissenschaft, esp. pp. 99-101. K. Gödel's proof—which, as a proof, incidentally supports rather than undermines the rationalist claim of the possibility of a priori knowledge—only demonstrates that the early formalist Hilbert program cannot be successfully carried through, because in order to demonstrate the consistency of certain axiomatic theories one must have a metatheory with even stronger means than those formalized in the object-theory itself. Interestingly enough, the difficulties of the formalist program had led the old Hilbert already several years before Gödel's proof of 1931 to recognize the necessity of reintroducing a substantive interpretation of mathematics à la Kant, which would give its axioms a foundation and justification that was entirely independent of any formal consistency proofs. See Kambartel, Erfahrung und Struktur, pp. 185-87.
 Examples of this kind are used by Karl Popper in order to "refute" the rationalist idea of rules of arithmetic being laws of reality. See Karl Popper, Conjectures and Refutation (London: Routledge and Kegan Paul, 1969), P. 211.
 See on this also Mises, The Ultimate Foundation of Economic Science, pp. 12-14.
 On the aprioristic character of Euclidean geometry see Lorenzen, Methodisches Denhen, chapters 8 and 9; idem, Normative Logic and Ethics, chapter 5; H. Dingler, Die Grundlagen der Geometrie (Stuttgart: Enke, 1933); on Euclidean geometry as a necessary presupposition of objective, i.e., intersubjectively communicable, measurements and in particular of any empirical verification of non-Euclidean geometries (after all, the lenses of the telescopes which one uses to confirm Einstein's theory regarding the non-Euclidean structure of physical space must themselves be constructed according to Euclidean principles) see Karnbartel, Erfahrung und Struktur, pp. 132-33; P. Janich, Die Protophysik der Zeit (Mannheim: Bibliographisches Institut, 1969), pp. 45-50; idem, "Eindeutigkeit, Konsistenz und methodische Ordnung," in F. Karnbartel and J. Mittelstrass, eds., Zum normativen Fundament der Wissenschaft.
Following the lead of Hugo Dingler, Paul Lorenzen and other members of the so-called Erlangen school have worked out a system of protophysics , which contains all aprioristic presuppositions of empiriical physics, including, apart from geometry, also chronometry and hytometry (i.e., classical mechanics without gravitation, or "rational" mechanics). "Geometry, chronometry and hytometry are a-priori theories which make empirical measurements of space, time and materia 'possible'.They have to be established before physics in the modern sense of fields of forces, can begin. Therefore, I should like to call these disciplines by a common name: protophysics." Lorenzen, Normative Logic and Ethics, p. 60.
 On the aprioristic character of the category of causality see Mises, Human Action , chapter 1; Hoppe, Kritik der kausalwissenschaftlichen Sozialforschung idem, "Is Research Based on Causal Scientic Principles Possible in the Social Sciences?"; on the causality principle as a necessary presupposition in particular also of the indeterminacy principle of quantum physics and the fundamental misconception involved in interpreting the Heisenberg-principle as invalidating the causality principle see Kambartel, Erfahrung und Struktur, pp. 138-40; also Hoppe, "In Defense of Extreme Rationalism," [in .PDF] Review of Austrian Economics 3 (1988) footnote 36. In fact, it is precisely the indisputable praxeological fact that separate measurement acts can only be performed sequentially which explains the very possibility of irreducibly probabilistic—rather than deterministic—predictions as they are characteristic of quantum physics; and yet, in order to perform any experiments in the field of quantum mechanics, and in particular to repeat two or more experiments and state this to be the case, the validity of the causality principle must evidently already be presupposed.
 On the necessary complementarity of the categories of causality and teleology see Mises, Human Action , P. 25; idem, The Ultimate Foundation of Economic Science, pp. 6-8; Hoppe, Kritik der kausalwissenschaftlichen Sozialforschung idem, "Is Research Based on Causal Scientific Principi Social Sciences?"; also G. v. Wright, Norm and Action (London: Routledge and Kegan Paul, 1963); idem, Explanation and Understanding (Ithaca, N.Y.: Cornell University Press, 1971); K. 0. Apel, Die Erklären: Verstehen Kontroverse in transzendental-pragmatischcr Sicht;(Frankfurt/M.: Suhrkamp, 1979).
 More precisely still: it is structured according to the categories of logic, arithmetic, and protophysics (including geometry). See note 62 above.
 0n the logic of history and sociology as reconstructive disciplines see in addition to the works of Mises mentioned at the outset of this chapter Hoppe, Kritik der kausalwissenschaftlichen Sozialforschung, chapter 2.
 On the categorical distinctiveness Of Praxeological theory and history and sociology and the logical constraints that praxcology imposes on historical and sociological research as well as on social and economic predictions see Mises, Human Action , pp. 51-59,117-18; Hoppe, "In Defense of Extreme Rationalism," [in .PDF] Review of Austrian Economics 3 (1988).