K O D I K A S / C O D E 44 (2021) · No. 1 - 3 Gunter Narr Verlag Tübingen Karl Bühler ’ s Axiomatics and the Axiom. Karl Bühler ’ s Axiomatik und das Axiomensystem (1984) Abstract: Eschbach examines Bühler ’ s notion of axiom in-depth, discussing it against the background of numerous other notions of axiom and relating it to the use of this notion by some other authors (Haig, Peirce, Gomperz, Gätschenberger). In his essay about Karl Bühler ’ s axiomatics and the axiom system of sign theory Eschbach adds to the equation of logic and semiotics another link, so that the equation now reads: logic = semiotics = general theory of representation. With this equation it is indicated, on the one hand, that the “ deepening of the foundations ” of linguistics must result in a general theory of representation or sematology, or, viewed actually the other way around, that the representational function of language, as the subtitle of Bühler ’ s main work on language reads, is a form of manifesting sematology. The research program of sematology is following Eschbach ’ s comments openly apparent, for if language is to be understood - as Bühler says - as an intersubjective representational device, i. e., as an organum for one to communicate something to another about things. It further follows that sematology, within the framework of this organon model, has to ask about the general principles of sign traffic, with logic at its disposal as an instrument. “ It, therefore, belongs to the understanding of every philosopher to know the unproved presuppositions from which he proceeds, and the aims, usually more guessed at than recognized, toward which his thoughts strive. ” (Bühler 1904: 58). “ Only a philosophy that is clearly aware of its axiomatic foundations, only an ‘ axiomatic philosophy ’ that is, is truly ‘ critical ’ and not dogmatic. ” (Austeda 1962: 5). Introduction All people who experienced Karl Bühler at lectures or talks unanimously report his great rhetorical talent (cf., e. g., Kardos 1983), with which he could captivate and inspire his listeners. Numerous elements of his oratory style can be found in his written texts, which can be explained not least by the fact that the published texts are often based on lectures. Bühler ’ s typical language style of face-to-face communication, involving the reader/ listener, as found especially in Theory of Language, very often had the undesirable side effect that the utterances were not taken word for word, which then understandably led to serious abbreviations and misunderstandings. Such abbreviations and misunderstandings not infrequently favored a reception that took up specific catchy formulations, such as that of the so-called organon model, and used them detached from their systematic context (cf. Fónagy 1983). It should be evident that such a reception is unsuitable to do justice to Bühler ’ s far-reaching designs. Another critical circumstance that may have contributed significantly to the fact that Bühler did not find the understanding that his work deserved is to be found in the fact that his entire approach was developed in a scientific climate that was alien or indifferent to his fundamental critical interests. Bühler himself, however, contributed significantly to the fact that his name was always associated with fierce and sometimes highly polemical attacks on the prevailing scientific paradigm, as evidenced, for example, by the Wundt-Bühler controversy that Bühler triggered with his habilitation thesis, or - a fortiori - the Crisis of Psychology, in which Bühler presented a cutting critique of association psychology, behaviorism, and psychoanalysis, not to mention the countless smaller disputes that Bühler conducted, as it were, in passing in notes or reviews. Karl Bühler could work and publish relatively undisturbed in Vienna until the early summer of 1938. If one were to measure his impact by the number of his doctoral students who came to his institute from all over the world, his success would certainly have to be highly rated. However, suppose one asks to what extent his entire, highly complex approach was taken up and further developed. In that case, a completely different picture emerges, since only a few publications address this difficult task. That this situation worsened considerably for Bühler after 1938 cannot be surprising insofar as he, rooted entirely in the European tradition of thought and teaching, came to a country strongly influenced by the behaviorist approach. In addition, Bühler was already sixty years old when he arrived in the U. S., his command of the English language was mediocre despite several stays in America, and the few university positions available were already occupied elsewhere. In addition, despite intensive efforts, it has not been possible to organize translations of his most important works into English; for example, there is still no translation of the Theory of Language - together with E. F. K. Koerner I am currently trying to remedy this deficiency - and the Axiomatics of Linguistics was only translated into American in 1982 by Robert E. Innis. This situation did not change after the end of the Second World War. Neither in psychology nor in the philosophy of language/ linguistics was there a link to Bühler; the synchronic approach of descriptive-structural grammar was not compatible with Bühler ’ s basic-critical thinking, and when Chomsky ’ s Syntactic Structures ushered in the era of generative transformational grammar in 1957, there was no longer any severe thought of basic-critical work for many years to come. Even though Bühler ’ s work was not intensively received in the German-speaking world or anywhere else after 1945, it should not be ignored that at least the Theory of Language, the Theory of Expression, the Krise der Psychologie, and the Axiomatics of Linguistics are easily accessible today in new editions. Axiomatics of Linguistics first appeared in 1933 in Kant- Studien and was reissued in 1969 with an introduction and commentary by Elisabeth Ströker. The claim has been made repeatedly that the axiomatics is nothing more than the socalled “ principles ” chapter from Bühler ’ s Theory of Language, which he merely left to the Kant Studies for pre printing. This view is false and misleading in at least two respects since it firstly assumes - unspokenly - that Bühler once developed his axiomatics, namely in Kant Karl Bühler ’ s Axiomatics and the Axiom (1984) 53 Studies, and later merely integrated it as chapter I into his Theory of Language. That this is by no means the case, however, becomes clear from the fact that not only do the texts differ considerably, but also the axioms are treated in a different order and weighting, which will be discussed in detail later. At this point, we shall only refer to the preface to the first edition of the Theory of Language, where Bühler noted: For the book I have rewritten them [the four guiding principles about language], rearranged them, and formulated them more prospectively, i. e., in anticipation of the chapters that will follow; moreover, the dichotomy ‘ speech action and speech formation ’ has been expanded into the richer four-field scheme of Guiding Principle C (Bühler 1934: X). The view is wrong and misleading in a second respect, as there are axiomatic considerations of Bühler before the publication of Kant Studies and after the publication of the Theory of Language. Hence, it seems advisable to assess Bühler ’ s axiomatics against the background of all his statements in this respect. Moreover, in the “ Erläuterung des Themas ” (Explanation of the Topic), which Elisabeth Ströker surprisingly did not include in the new edition, Bühler gave some essential hints which can help us very well here. Bühler ’ s primary concern in the “ Explanation of the Subject ” is a defense against exaggerated expectations that could be directed at his design of axiomatics, primarily rejecting the assumption that axiomatics can draw its dignity from the proof of its apriority. Instead, he characterizes his approach in the following way: We propose a way of dealing with axioms which may be called, in my opinion, a purely phenomenological explication or an epistemologically (and ontologically) neutral fixation of principles. They are principles to be obtained from the stock of successful linguistic research by reduction. D. Hilbert calls this procedure axiomatic thinking and demands it precisely in our sense for all sciences (Bühler 1933a: 22). Against the background of this declaration of intent, it makes sense when Bühler describes his axiomatics as several propositions “ which claim either to be regarded as axioms of linguistic research themselves or at least to serve as a starting point for progressive theoretical efforts to establish a closed system of such axioms ” (ibid.: 23). Another essential hint, found in the “ explanation of the subject ” , refers to the question of how the axiomatist arrives at the first propositions, which Bühler describes in the same section as “ constitutive, area-determining theses ” and as “ thoroughgoing ideas of induction ” (ibid.). To answer this question, Bühler refers to the preface to the second edition of Kant ’ s Critique of Pure Reason, where it is stated that all our knowledge begins with experience, without therefore being allowed to claim that it springs from experience. This reference to the critique of reason is reflected in the following work program for axiomatics: The highest terms and axioms must first be picked up and formulated from the linguistic sciences. We offer what we can, without claiming completeness. We explain terms and axioms in each other, as one finds them connected in the research enterprise and the result of linguistics. And yet, a sure foreshadowing of the structure, which is to be examined later, may already determine our list (ibid.: 24). As will be shown, the reference to the critique of reason is not a mere allusion or a rhetorical effort to gain authority: it will turn out that Bühler ’ s ‘ axiom concept ’ is to be understood precisely from the interrelation of experience and reason addressed by Kant. 54 Karl Bühler ’ s Axiomatics and the Axiom (1984) In contrast to previous years and decades, there has been an increasing tendency in the recent past to focus on historical-systematic research. This turn of tendency, which is favored by the fading of the euphoria of the transformation grammarians as well as by the growing insight into the urgent necessity of basic research, has also led to a sense of the fact that in the twenties and thirties of our century - not only in the German-speaking area - a multitude of highly significant works was produced, which were largely excluded from the discussion. However, they could orient us in their farsightedness, their profundity, and their modernity also and especially today. Just as the present volume will help to give a new voice to a study that is now fifty years old and carry it forward, several essays that reflect Karl Bühler ’ s work have recently been written. Two undertakings are particularly noteworthy in this context: A collection of twenty-five essays dealing with Bühler ’ s complete works will appear in 1983 under the title Bühler-Studien. In addition to the already published works, the complete edition will include Bühler ’ s extensive unpublished estate and a selection from his scholarly correspondence. A volume of materials accompanying the edition will contain, in addition to a biography of Karl Bühler and a bibliography of primary and secondary literature, an attempt to show the unity and rich filler of Bühler ’ s work, or in other words, an attempt to understand the multiplicity of Bühler ’ s works as the realization of a large research program. The fact that the view that Bühler ’ s work is under a unified research programmatic is not an idea brought to the work from the outside, but was repeatedly emphasized and explained by Bühler himself, will occupy us for a while since this question is also relevant for understanding the problem at hand. Bühler closes the second paragraph of the principles chapter of his Theory of Language, in which he treats axiom A about the organon model of language, with the remark: “ It [the thesis of the three language functions] will be verified as a whole when all three books about language required by the organon model have been written ” (Bühler 1934: 33). That this remark can by no means be a rather accidentally interspersed incidental fact can already be seen from the fact that Bühler closes the second paragraph with this statement. In addition, in the preface to the Theory of Language, Bühler retraces the path he has taken since 1907 to realize his research program, even if he does not even list all the important stations along the way in this tour d ’ horizon. Even more clearly than in the Theory of Language, there is repeated talk in the Krise der Psychologie about the uniformity of the research program. There it says: As to the history of these reflections, let us note that they go back more than two decades. I did not set out to reform psychology, but to find the axioms of language theory. A nearly completed book “ Theory of Language ” will give an exact account of it. It means anticipating the main results if I try to show here in abstract proof that one can understand the phenomenon of language scientifically only under the three aspects (Bühler 1927: 29). Bühler offers an even clearer description of his research program in the summary seventh paragraph of the second chapter of Crisis, where he emphasizes that the insights achieved are not the result of an ad hoc investigation, but the outcome of two decades of purely factual research on language (cf. ibid.: 57 ff.). Now, it could certainly be argued with some justification that Bühler had occasionally emphasized the unity of his research program, but that the third book on language had Karl Bühler ’ s Axiomatics and the Axiom (1984) 55 never been written; moreover, it was a research program declared post festum so that only very little weight could be attached to statements in this regard. The first objection can be refuted concerning many publications after 1938 and because of the manuscripts in Bühler ’ s estate. As far as the second objection is concerned, on the one hand, I would like to refer to a series of letters in which Bühler told some friends and colleagues about his research projects at different times; on the other hand, to explain my thesis of the uniformity of Bühler ’ s research program, I would like to quote at length from a letter that Karl Bühler wrote to his former Viennese collaborator Paul Lazarsfeld on August 24, 1953: ( … ) Now to the news: These are two articles about navigation (= guided location), which attack the control where it can be isolated best. I am sending you the first already printed article again and enclosing the second, which will be printed in September at Revesz in the manuscript. If you do not want to digest everything in it, please read the manuscript I., II., and III. chapter and then in the V. a constructive criticism by I. Loeb. My special question to you: Does what is said in V seem physically correct to you? And at the very end of V is hinted at what I am ultimately getting at. The syntaxes in animal control prepare for the syntactic control of human speech. The theory of language is in between and has prepared the analogy. There is the pointing field of language and the symbol field, the coordinate system. The ‘ arrow-moment in the landmark control ’ is what the pointing words do in the syntactic control of speech. The symbol field, of course, is demonstrable only in humans and is attached to the two great classes of syntactic devices which occur in all human languages. Think of the succession factor in English (even more so in Chinese) where parents love children and children love parents two quite different facts meet while Latin filius amat patrem und patrem amat filius meets the same. Or, since you are an excellent Latin speaker, think of Horace, where the second stanza of Integer vitae reads: Namque me Silva lupus in Sabina Nam meam canto Lalagen et ultra Terminum fines vagor expeditus Fugit inermen. And find out how the words come together to form a definitive sense of control. Conclusion: The evolution developed control means already in the controlled local movements of the insects. And comparable to it is present in the syntactic controls. As is known, there is also a logical syntax (Carnap). The whole thing with the ‘ overview from the insects (or amoebae) to the human being ’ is now forming a guide through comparative cybernetics. This idea, which I am obsessed with at the moment, meets the basic idea in Sherrington ’ s ‘ Man on his Nature ’ VII, p. 204 - 214 or so. First, I need only the controlled local movements, where the directional controls are directly observable. And secondly, I don ’ t need an aspect change for it. For I speak of mechanisms which in principle can be reproduced in ‘ guided missiles ’ and not yet like Sherrington on p. 213 of ‘ recognizable mind. ’ Do you like it? Please, tell me something about it, I need encouragement. And it needs two more articles like the enclosed to make what is said palpable to a readership. 56 Karl Bühler ’ s Axiomatics and the Axiom (1984) Good luck and progress in your own great company Yours sincerely Karl Bühler, Ph. D. So, suppose we have to start from the assumption that Karl Bühler strove for the realization of a unified research program throughout his life. In that case, we will have to look for an answer, at least to some extent, to the question of what ultimately motivated him to approach the axiom problem again and again and from the most diverse perspectives since his medical doctoral thesis, which I understand as an axiomatics of Helmholtz ’ s color theory. From what has been said so far it should have become clear that a simple and quick answer to this difficult question is impossible so we can only think of a comprehensive answer after discussing a number of constituent moments. Nevertheless, we can already state at this point that Bühler ’ s design of axiomatics could be linked to various strands of tradition, which will be discussed in the following discussion. However, it should already be recalled here that the doyen of German psychology, Wilhelm Wundt, wrote Die physikalischen Axiome und ihre Beziehung zum Kausalprinzip (The Physical Axioms and their Relationship to the Causal Principle), which appeared in its second edition in 1910 under the title Die Prinzipien der Mechanischen Naturlehre (The Principles of the Mechanical Theory of Nature.). Reference should also be made to the work of Bühler ’ s Freiburg teacher Johannes v. Kries - especially to General Sensory Physiology (V. Kries Allgemeine Sinnesphysiologie 1923) - from which Bühler drew not only with regard to the axiom problem (cf. Eschbach 1984b). Finally, before starting the discussion, it should be unmistakably pointed out that Bühler pursued his axiomatic studies in a foundation-critical interest, which he characterized in the Theory of Expression as follows: However, in order that the new experimentation and evaluation does not become a blind wandering and a journey without a compass into the shoreless, one must work with adequate energy on the axiomatics of the theory of expression. It seems appropriate and advisable to combine the research on principles with a renewed review of the history of the theory of expression (Bühler 1968: 1 f.). In the opposite sense, we can at the same time also note what Bühler did not aim at with his axiomatic work: He was neither interested in a formalization nor a mathematization of psychology or linguistics (for a contrary opinion cf. Lieb 1980: 301) since it was absolutely clear to him that a two-class system of the type of language eludes such an attempt. In an extremely important passage, which may well be read as an anticipatory critique of transformational grammatical and/ or information-theoretical efforts, Bühler states: A single-class system of global symbols of the type of ship signals is scientifically exhaustively determined if, first, the structure of the signals is specified and, second, for each signal the typical situation of use and in it the communication purpose which it has to fulfill is described. This is done in the case of artificially arranged flag signals by the code, a book with two chapters. [ … ] The scientific determination of a system of the type of language requires something different from a book on the type of code. One can only partially parallel phonology in the strictest sense of the word with the first chapter of the code. The lexicon, on the other hand, and grammar, which reflect the two classes of settings and entities in the realm of language, are, first, distinct among themselves and, second, distinct in essence from the code (Bühler 1933a: 69). Karl Bühler ’ s Axiomatics and the Axiom (1984) 57 Historical facts about the axiomatic method If one subjects the extensive literature on the concept of “ axioms ” and the ideas of the axiomatic method derived from it to a critical examination, one will very soon come to the irritating conclusion that two fundamentally different and mutually exclusive meanings are attributed to the concept. This area, which has often been collected by historians of science, philosophers, and mathematicians in a questionable etymologizing way, could easily be pushed aside in the present context as a problem concerning the philologist if the said duplication of the term ‘ axiom ’ did not at the same time provide the foil of two mutually exclusive strategies in dealing with the axiomatic method, which until today run side by side competitively (cf. Schüling 1969). In the following considerations, it shall not be a question of emphasizing one or the other reading of the concept of “ axioms ” as the only authentic and legitimate one, which very soon proved to be a futile undertaking since both traditions have existed factually for more than two millennia; instead, it shall be clarified in outlines, under which epistemological interests and in which scientific-systematic contexts the two traditions were built up. The contradiction between the two traditions becomes quickly obvious if one holds some dictionary entries for the keyword ‘ axiom ’ side by side. Kondakov ’ s Dictionary of Logic says: “ Axiom, meaning possessing, deserving attention, accepted, indisputable: true judgment, etc. true proposition, which is accepted as initial thesis in deductive construction of a theory, within a closed theory without proof and is taken as a basis for the proofs of all other theses of this theory ” (Kondakow 1978: 65). The Philosophical Dictionary writes: “ Axiom (validity, demand), principle: a proposition that cannot be proved, but also does not need to be proved, since it is immediately obvious as correct and therefore serves as a ‘ principle ’ for other propositions (deduction), or can also be agreed upon as such (conventionalism) ” (Schmidt 1974: 51). On the other hand, the Historical Dictionary of Philosophy states: “ Originally, the axiom was not a proposition which, neither capable of proof nor in need of proof, was generally accepted by everyone and admitted as correct, but on the contrary: Just that proposition was called axiom which only one dialogue partner wanted to base the discussion on as a correct assertion, while the other partner agreed with this endeavor only conditionally or not at all ” (Ritter, Vol. 1/ 1971: 738 f.). In the Dictionary of Philosophical Terms, one reads: “ Axiom, demand ” , in logic and mathematics since Aristotle and Euclid a principle whose truth is immediately obvious, which neither needs nor is capable of a reason of proof and is considered as a basis of proof for further propositions ” (Hoffmeister 1955: 101). Krug ’ s Allgemeines Handwörterbuch der philosophischen Wissenschaften differentiates as follows: Axiom (to appreciate, to judge, to hold true) means in a broader sense any judgment that one assumes to be true, but in a narrower sense an immediately certain judgment, which is therefore indemonstrable, i. e., neither capable of nor in need of proof ” (Krug 1969: 277). Finally, in the Encyclopedia Philosophy and Philosophy of Science, the following entry is found: “ Axiom, in the ancient technique of discussion and so also in Aristotelian topics a term for those propositions (axiomata) whose acceptance was demanded by one of the dialogue partners at the beginning of a dispute. [ … ] The term ‘ axioma ’ also denotes, at the latest in Aristotle, a proposition whose credibility [ … ] is generally admitted, because it is not capable of justification by reference to other 58 Karl Bühler ’ s Axiomatics and the Axiom (1984) propositions. Still, because of its evidence, it is also not in need of it ” (Mittelstraß 1980: 239 f.). Despite certain leitmotifs in common, these definitions show such serious differences that it is hard to imagine that the definiendum has not changed under the table. In order to expose the roots of this obvious contradiction, it is not sufficient to return to the term “ axiom ” by Greek mathematicians and logicians, for we have heard that Euclid and Aristotle have been called upon to be key witnesses of different conceptual fillings. We get a first clarifying hint from Árpád Szabó, who repeatedly dealt with the question of the meaning of the term ‘ axioma ’ . In Szabó ’ s opinion, all known ancient attempts to define the mathematical concept of ‘ axioms ’ can be traced back to Aristotelian influences (cf. Szabó 1960: 91). However, the concept of ‘ axioms ’ as a mathematical term was already in use in Euclidean and even pre- Euclidean times. If one asks for the origin of the mathematical term ‘ axiom ’ , one will notice that it borrows from dialectics, which is not surprising since a large part of the mathematical terms originates from dialectics. Thus, in order to take our conceptual explanation a step further, we need to examine how the ‘ axiom ’ concept was determined in dialectics. For this reason, Szabó recalls the situation of a dialectical argument between two interlocutors: The task of one partner in an argument is to get the other to admit a proposition he chose. For this purpose, he must find such premises which the partner considers correct and therefore will admit, and from which the final sentence that the partner does not consider correct and does not want to admit can be derived with logical necessity. Therefore, one participant in the conversation asks the other to base the argument on some initial proposition without proof as a correct assertion (Szabó 1960: 94). From this characterization of the opening situation of a dialectical argument, we may at least infer that the initial proposition, which is asked to be taken over, must be certain only for the first dialogue partner, whereas it remains completely open whether he will receive an agreement to this proposition from his opponent or not. Accordingly, the meaning of the term ‘ axiom ’ in dialectical terminology would be ‘ assertion ’ , ‘ assumption, ’ or ‘ request ’ . Request “ demand ” or “ opinion ” (cf. ibid.: 97). With this result, however, we have only half the truth, because even if it is to be regarded as clarified that Euclid used the term ‘ axiom ’ in the dialectical understanding, it must be considered at the same time that already in the Stoic use the old sense of the word has been forgotten and the axioms figure as self-evident truths. In Szabó ’ s opinion, this concept change is due to the fact that the essential implications of the Euclidean use of the term were very soon no longer understood. It said: Thus axioma became a truth that is ‘ naturally considered to be right. ’ [ … ] But even in the new meaning the word axioma still seemed uncomfortable in the Euclid text; therefore, instead of the old designation one soon preferred to write: koinai ennoia ‘ ideas common to all men ’ . In this way, the dialectical origin not only of the expression but also of the genre itself was almost completely concealed (ibid.: 105). Although Szabó ’ s considerations found approval by some historians of science, it seems to me that not all the arguments necessary to arrive at a satisfactory definition of the concept of ‘ axioms ’ have been presented, which is why I would like to join Hintikka ’ s critique of Szabó ’ s remarks, which boils down to the following position: “ The syllogistically rather Karl Bühler ’ s Axiomatics and the Axiom (1984) 59 than mathematically motivated character of an axiomatic theory according to Aristotle probably explains Szabó ’ s low opinion of Aristotle ’ s significance ” (Hintikka 1981: 138). Based on the assumption that Aristotle builds his entire view of an axiomatically organized science on the syllogistic model, Hintikka argues for distinguishing four types of basic presuppositions in Aristotle: 1. Axioms (in Aristotle ’ s narrow sense) common to all sciences 2. Atomic premises connecting two adjacent terms figuring in a minimal syllogistic premise 3. The widest premise of the science in question 4. Nominal definitions (ibid., cf. Wiener 1968: 166). Now Aristotle emphasizes in two places (An. Post. 11,3 90b 24-28) that the starting points of proof are definitions (cf. Scholz 1961: 29 f.): From the unmediated principles of a conclusion, I call these which one cannot prove, and not everyone already needs to have in mind who wants to learn something. [ … ] Of the theses, those which assume one of the two parts of the statement [ … ] are hypotheses, those which do not are definitions. For the definition is indeed a thesis (setting) [ … ], but not a hypothesis (An. Post., 72a 15- 30). Hintikka states that in Aristotle there is a twofold determination of the term ‘ definition ’ , the first one meaning the nominal definition mentioned in point (4), while according to the more comprehensive understanding the basic presuppositions (2)-(3) are meant. Hintikka ’ s thesis is now that the Aristotelian discussion of the different kinds of definitions would ultimately amount to a discussion of the different constituents of axiomatic theories (cf. Hintikka 1981: 139 f.). A problem arises, in Hintikka ’ s opinion, if the status of the basic presupposition (3) as the only unprovable existential assumption of a scientific theory ipso facto meant at the same time that it was the only unprovable predictive assumption of science. However, according to Hintikka, this kind of unprovability cannot be an apodeictic inability, but only a special form of deixis, which is why Hintikka asks: Is there in Aristotle some non syllogistic sense of proving or ‘ showing ’ in which the widest (and possibly also the narrowest) premise of each science, and only they, cannot be proved by the normal means that science operates with? (ibid.: 141). Hintikka sees a solution to this problem in An. Pr. II, 23, where Aristotle calls such a procedure apagoge, and which Hintikka characterizes as follows: Since it involves inverting one of the two premises of a syllogism, it involves terms that are prima facie wider or narrower than the extremes of the three syllogistic terms in question. Accordingly, it cannot be used to justify the widest premises (3) of an axiomatic science. They are therefore unprovable in a double sense for Aristotle. They are the only premises of an axiomatic science that carry irreducible existential assumptions, and they must (possibly together with the narrowest premises) be justified by direct intuition (noûs) rather than by the systematic procedure of epagoge or ‘ induction ’ through which atomic premises (2) are established (Hintikka 1981: 140). Although I can agree with Hintikka insofar as he identifies with apagogé the procedure which constitutes the particular form of deixis directed to the constitution of the basic assumption (3) and, if necessary, also of the basic assumption (1), I do not agree with him at all on the question of the non-syllogistic character of this form of deixis. In order to 60 Karl Bühler ’ s Axiomatics and the Axiom (1984) substance this objection, which is of essential importance for the determination of the status of axioms, I will in the following refer at length to the only logician known to me who has not only developed a completely novel view on this question but who, moreover, with his proposed solution provides the basis for a satisfactory clarification of the axiom problem. In the Lectures on Pragmatism Charles S. Peirce writes: In order to answer that question it is necessary to recognize three radically different kinds of arguments I signalized in 1867 and which had been recognized by the logicians of the eighteenth century, although those logicians quite pardonably failed to recognize the inferential character of one of them. Indeed, I suppose that the three were given by Aristotle in Prior Analytics. However, the unfortunate illegibility of a single word in his MS. and its replacement by a wrong word by his first editor, the stupid Apellicon, has completely altered the sense of the chapter on Abduction. At any rate, even if my conjecture is wrong, and the text must stand as it is. Still, Aristotle, in that chapter on Abduction, was even in that case groping for that mode of inference which I call by the otherwise quite useless name of Abduction. This word is only employed in logic to translate the apagoge of that chapter (C. P. 5.144). Peirce claims to have solved Kant ’ s knowledge problem more radically than the latter. Peirce clearly expresses the uncertainty of the objects of experience, which can only be extrapolated from Kant ’ s remarks, by saying that our percepts are conjectures. If Kant performs on the occasion of experience by applying the categories to Data, by which application the Data are ordered to objects of experience, he cannot - as he explains - make any statement about things in themselves. Thus, the objects of experience have a certain uncertainty, namely insofar as they do not show things in themselves. The emphasis on this uncertainty is the core of Peirce ’ s critique of knowledge. What Kant calls the object of experience, Peirce calls percept. One must be clear that the percept according to Peirce is the result of a mental operation that has a synthesis character; however, the percept does not reveal at first that it owes itself to a synthesis performance. To show the mediatedness of the percept, the remarks made in Peirce ’ s Lectures on Pragmatism are suitable. That a percept is mediated in itself is expressed by Peirce in his dictum that the beginning of cognition is a process of beginning. We find in Peirce the two names ‘ abduction ’ and ‘ perceptual judgment ’ for a mental operation. Since there are two names, it would be obvious to expect two mental operations. Abduction is a controllable and conscious process, perceptual judgment is a noncontrollable and non-conscious process- According to Peirce, both are the same mental process, which follows from the fact that Peirce shows that perceptual judgment is a borderline case and ultimately of the same character as abduction: “ Perceptual judgments are to be regarded as an extreme case of abductive inferences ” (C. P. 5.181). The only symptom by which the two can be distinguished is that we cannot imagine what it would mean to deny the perceptual judgment (cf. C. P. 5.186), i. e., Peirce ’ s so-called “ test of inconceivability ” (C. P. 5.187). However, it cannot be decided with ultimate certainty whether there is a perceptual judgment or an abduction; this corresponds to Peirce ’ s statement, “ that we never can be absolutely sure that judgment is perceptual and not abductive ” (C. P. 5.187). Thus, the possible uncertainty of whether it is one or two mental operations can be removed to the extent that we are justified and obliged to speak of a process. Perceptual judgments are “ operations of the mind which are logically exactly Karl Bühler ’ s Axiomatics and the Axiom (1984) 61 analogous to inferences excepting that they are unconscious and therefore uncontrollable and therefore not subject to criticism ” (C. P. 5.108). To clarify Peirce ’ s statements about perceptual judgment, I would like to cite a longer passage: The perceptive judgment is the result of a process, although of a process not sufficiently conscious to be controlled, or, to state it more truely, not controllable and therefore not fully conscious. If we were to subject this subconscious process to logical analysis, we should find that it terminated in what that analysis would represent as an abductive inference, resting on the result of a similar process which a similar logical analysis would represent to be terminated by a similar abductive inference and so on ad infinitum (C. P. 5.181). Peirce ’ s characteristic claim, then, is that percepts are the results of a process that, if controllable, would turn out to be of the character of the operation of abduction. Thus it is said that there are no immediate percepts. The conscious and controllable process of abductive judgment is invoked by Peirce to clarify the unconscious and uncontrollable process of perceptual judgment. The result of abduction is a hypothesis of the form: A surprising fact is observed; But If A were true, C would be a matter of course, Hence, there is a reason to suspect that A is true (C. P. 5.189). The hypothesis obtained by abduction corresponds to the percept obtained by perceptual judgment. “ The abductive suggestion comes to us like a flash. [ … ] The different elements of the hypothesis were in our minds before ” (C. P., 5.181). This flashiness of the hypothesis and its logical unfolding into an abductive judgment corresponds to the flashiness of the percept, which can be analyzed in its development into the mental operation called perceptual judgment by Peirce. The percept, which is the result of the perceptual judgment, is “ of course [ … ] not itself a judgment, nor can a judgment in any degree resemble to a percept ” (C. P. 5.54). Peirce emphasizes this fact in order to make it unmistakably clear that the percept is the result of a judicial process that takes the form of a synthesis of elements. To these crucial elements of thinking, with which working the operation of the perceptual judgment has a percept as a result, correspond the elements of the abductive judgment, which reaches as a result a hypothesis. Peirce shows by his assertion that percepts are connecting links between abductions and perceptions (cf. C. P. 5.183) that these perceptions, whose results are always percepts, are judgmental, precisely perceptual judgments; this corresponds to the equation of perceptions and perceptual judgments, which Peirce carries out expressis verbis: “ by direct perception that is in a direct perceptual judgment ” (C. P. 5.58). By this equation of perceptions and perceptual judgments, it is made clear that perceptions never ‘ receive ’ the mentioned elements of the perceptual judgment unprocessed. Elements of perceptual judgments are immediately ordered into percepts in these perceptual judgments, i. e., perceptions. Peirce ’ s percepts are analogous to Kant ’ s appearances, which also originate in a mental operation with the data corresponding to the facts of experience. Peirce says that facts of experience are given in direct perceptual judgments 62 Karl Bühler ’ s Axiomatics and the Axiom (1984) (cf. C. P. 5.54), as he speaks of facts of experience being “ premisses to us ” (C. P. 5.119). These are, in analogy to Kant ’ s data, processed in the perceptions, i. e., perceptual judgments, when they are given. Experiential facts are qua premises logically original, but are taken into consciousness only at the process of processing: We have already heard, the beginning of cognition is a process of beginning. As Kant, expressis verbis, cannot make any statements about things in themselves, Peirce - without expressing it specifically - cannot make any statements about that which is the basis of the percepts besides process, namely about the facts of experience explicitly called the premises. He simply calls it “ what is before his (sc. a person ’ s) senses ” (C. P. 5.115). In summary, against the background of these considerations, we can thus state that the constitution of our basic assumptions or axioms takes place judgmentally, i. e., by way of perceptual judgments, which have been identified as extreme cases of abductive reasoning. However, if axioms are forms of deixis to be characterized apagogically, it makes no sense to demand self-evidence, completeness, etc. from an axiomatic system. We may demand from axioms only that they show us the case. Verification of whether this demand is fulfilled or not, however, can no longer be conducted deictically, but only apodeictically. That this finding can not only be based on the work of C. S. Peirce but is also fully consistent with the position advocated by Bühler, is clear from the following passages: Perhaps it will serve further elucidation if we focus on the other, the sign function of the sense data in perception. We say signs, because of the content of the perceptual judgment, because the state of affairs, which we think to grasp in perception, always exceeds the area of sensory data (Bühler 1978: 78). A little later it says: We adult humans have our well-ordered world of perception. Into it, into this comprehensive system of determinations, the messages of the senses enter themselves. The sensed equips the things and events of our perceptual world with properties by virtue of the intentional relation; we see the “ red ” as a property of the apple and feel the “ warm ” as a property of the touched stove. This is the basis. But beyond that, the same sense of data functions as signs for this and that, what is to be said further about the things, what is expected further from them. That is the sign function of the sense data in our observations. So it is with us humans (ibid.: 78 f.). Models of Bühler ’ s Axiomatics In the interest of a comprehensive understanding of Karl Bühler ’ s axiomatic approach, it is appropriate to ask about the models on which he oriented himself. From the second edition of Axiomatik, edited by Elisabeth Ströker, an answer to this question can only be extrapolated, since she did not include the long first note on pages 22 f. in her new edition. Since this note, which recurs verbatim in the Theory of Language (Bühler 1934: 20), must significantly influence further understanding, I will reproduce it in full: D. Hilbert, Axiomatic Reasoning. Mathematische Annalen 78 (1918). Let ’ s take a closer look at a certain theory. We always recognize that constructing the framework of concepts is based on a few excellent propositions of the field of knowledge and that these alone are sufficient to build up the whole framework from them according to logical principles ” (406). Karl Bühler ’ s Axiomatics and the Axiom (1984) 63 One of the historically most interesting arguments about the problems towards which “ axiomatic thinking ” in the sense of Hilbert leads, are the few polemical remarks against W. Whewell in the induction theory of J. St. Mill. The “ Philosophy of Discovery ” of Whewell (the preface is from 1856, and the edition before me is from 1860) is inspired by Kant, so the dispute is between Mill and Kant. We can say: that what neither of them denies, that what Mill recognizes again and again as the correct core of Whewell ’ s conception, exactly is the research area of the axiomatics of empirical science. Note in Mill especially remarks like the following: “ The difficulty for the latter (it is the judge who has to make a judgment of fact) is not that he has to make an induction, but that (lay he has to choose it. ” In the axiomatics of the individual sciences, it is about first choices, so to speak, of fertile initial ideas. From which source of knowledge they are fed is a question that exceeds the framework of the axiomatics of the individual sciences (Bühler, 1933a: 22 f. note; emphasis mine - A. E.). To my knowledge, the only author who has not only taken these Bühlerian hints in due earnest but also made inquiries as to what it is that is not disputed either by Whewell or by Mill is Rudolf Kamp in his excellent and knowledgeable study Axiomatic Theory of Language (Kamp 1977), to which I will repeatedly refer in the following. For systematic reasons it further seems appropriate not to consider the models of Bühler ’ s axiomatics according to the order of their dates of origin, but - like Bühler himself - to start with Hilbert ’ s approach. David Hilbert ’ s Munich lecture, published in 1918 under the title “ Axiomatic Thinking ” (Reprint: Hilbert 1964), reflects in an extremely general and complex form the central moments of Hilbert ’ s axiomatics, to which Bühler repeatedly refers in various of his writings. Hilbert ’ s formulations in this essay are such that at first glance a transfer of this approach to contexts other than geometrical or mathematical seems legitimate, and indeed Hilbert states without restriction to any particular discipline: If we compile the facts of a certain more or less comprehensive field of knowledge, we soon notice that these facts are capable of an order. This order takes place each time with the help of a certain framework of concepts in such a way that to the individual object of the field of knowledge corresponds a concept of this framework and to each fact within the field of knowledge a logical relation between the concepts. The framework of concepts is nothing else than the theory of the field of knowledge (Hilbert 1964: 1). These statements, which in their globality leave a wide space for misunderstandings, Hilbert specifies in a summarizing remark to such an extent that there can only be disagreement about the redeemability of Hilbert ’ s program, but no longer about the intended direction: I believe everything that can be the subject of scientific thinking at all, as soon as it is ripe for the formation of a theory, falls into the axiomatic method and thus indirectly into mathematics. By advancing to deeper and deeper layers of axioms in the sense explained above, we also gain deeper and deeper insights into the essence of scientific thinking and become more and more aware of the unity of our knowledge. In the sign of the axiomatic method, mathematics appears to play a leading role in science in general (ibid.: 10 f.). Now, one could get the impression that in Hilbert ’ s approach, two axiomatic conceptions compete with each other, insofar as he articulates on the one hand the intention to justify the basic propositions of a theory, i. e., the axioms, by a “ deepening of the foundations ” (ibid.: 3) on their part, and the other hand “ to guarantee the dependence or independence of the 64 Karl Bühler ’ s Axiomatics and the Axiom (1984) propositions of the theory ” as well as “ the lack of contradiction of all propositions of the theory ” (ibid.: 3). independence of the propositions of the theory ” as well as the “ contradictionlessness of all propositions of the theory ” (ibid.), resp. to show “ that every time within a field of knowledge on the basis of the established axiom system contradictions are impossible at all ” (ibid.: 7). If we disregard some system-immanent implications of Hilbert ’ s approach (cf. Gabriel 1980), which need not concern us in the present context, we may nevertheless state that the “ lowering of the foundations ” and the “ independence and noncontradiction ” of the axioms were not presented alternatively by Hilbert, but necessarily follow each other. If Bühler, in his reference to Hilbert, confines himself only to the first condition but completely disregards the second aspect, such an approach would indeed have to be characterized by Kamp as “ a decisive truncation of Hilbert ’ s conception ” (Kamp 1977: 148). This reproach seems unavoidable insofar as Bühler has at no point distanced himself from Hilbert ’ s approach in a restrictive way, so that the axiomatics of linguistics would also be subject to the criticism to be levied against Hilbert ’ s approach. Kamp, however, believes - for good reasons, it seems to me - that Hilbert ’ s and Bühler ’ s axiomatic conceptions differ significantly. While there is some form of agreement between Hilbert and Bühler with respect to the emphasis on the reflective moment of axiomatics and, to a more limited extent, with respect to the definition of terms, the crucial difference results from the respective assessment of the validity of the axioms. Hilbert, in a letter to Frege, explicitly speaks of “ setting ” an axiom (cf. Gabriel 1980: 12), whereas - as we have already heard - Bühler emphasizes that axioms have to be “ sought. ” That this is not merely a minor difference in the choice of words is evident from the fact that Hilbert writes elsewhere: When it is a question of investigating the foundations of science, one has to establish a system of axioms that contain an exact and complete description of those relations that take place between the elementary concepts of that science (ibid.: 21, note 4; emphasis mine - A. E.), whereas Bühler emphasizes that the axioms have to be “ picked up ” from the linguistics (Bühler 1933a: 24). Kamp summarized this crucial difference as follows: Hilbert ’ s axioms function as a deduction basis and Bühler ’ s axioms as an induction basis. It is exactly in this sense that Bühler repeatedly refers to his axioms as guiding principles (Kamp 1977: 161). However, if Kamp then draws from this contrast between Hilbert and Bühler with regard to the question of the validity of axioms Bühler ’ s position negatively by criticizing ‘ traditional apriorism ’ as well as ‘ modern formalism ’ (cf. ibid.: 162) and positively by the key concept of the “ induction idea, ” which will be the subject of the following discussion, I can only agree with this opinion with respect to the key function of the “ induction ideas, ” because as the investigation of the previous section has shown, at least in Peirce ’ s interpretation of Aristotle, there can be no talk of ‘ apriorism ’ , since from a dialectical perspective, in the context of his investigation of the role of the apagoge, he came to the conclusion that the axioms had only the status of hypotheses. Suppose Hilbert ’ s axiomatic essay is to be used as a model for Bühler ’ s approach. In that case, this could only be done with a negative sign, because Bühler does not include Hilbert ’ s central demands, such as those for independence and freedom from contradiction, in his approach. In contrast, he introduces a condition Karl Bühler ’ s Axiomatics and the Axiom (1984) 65 under the keyword of the ‘ induction idea ’ , which is fundamentally contrary to Hilbert ’ s conception. Bühler calls it an urgent desideratum of linguistic science to “ uncover the logical first steps of induction of the linguistic researcher ” (Bühler 1934: 14), which should make it clear that a theory of language in the sense of axiomatics of linguistics is for Bühler the theory of linguistic induction ideas. In elaborating this idea, Bühler has been guided by the considerations of Whewell and Mill, or, more precisely, by those aspects of the two theoretical designs that seem compatible with each other, although it should not be overlooked that the argument is ultimately between Mill and Kant, since Whewell ’ s Philosophy of Discovery is occasionally nothing more than a literal translation of the Critique of Pure Reason, as Whewell himself points out. According to Whewell, two opposing elements can be distinguished in every act of cognition, which he calls concepts (ideas) and perceptions (perceptions). This fundamental antithetic of the process of cognition appears in manifold forms, such as in the oppositions of theory and fact or necessary and experimental truth, etc. According to Whewell, for cognition to become cognition at all, it must derive its character and nature from the respective first element of the fundamental opposition: The two elements which are essential to our knowledge in the above cases, are necessary to human knowledge in all cases. In all cases, knowledge implies a combination of Thoughts and Things. Without this combination, it would not be Knowledge. Without Thought, there could be no connection; without Things, there could be no reality; Thoughts and Things are so intimately combined in our Knowledge, that we do not look upon them as distinct. One single act of the mind involves them, and their contrast disappears in their union (Whewell 1967, I: 18). From this general epistemological maxim, Whewell derives the conclusion for the philosophy of science of the empirical sciences that we must approach the facts with the right induction idea in order to arrive at the truth. The induction ideas, which Whewell introduces under the name ‘ fundamental ideas ’ (cf. ibid.: 139 ff.), are thus the conditions of the possibility of scientific work: … the necessity and universality of the truths which form a part of our knowledge, are derived from the Fundamental Ideas which those truths involve. These ideas entirely shape and circumscribe our knowledge; they regulate the active operations of our minds, without which our passive sensations do not become knowledge. They govern these operations, according to rules which are not only fixed and permanent but may be expressed in plain and definite terms. These rules, when expressed, may be made the basis of a demonstration by which the necessary relations imparted to our knowledge by our Ideas may be traced to their consequences in the most remote ramifications of scientific truth. These enunciations of the necessary and evident conditions imposed upon our knowledge by the Fundamental Ideas which it involves are termed Axioms (ibid.: 66 f.). Whewell ’ s definition of the concept of axioms can be described as classical, insofar as he characterizes them as evidential conditions; at the same time, however, he points out that the insight into axiomatic truths depends on our prior knowledge, of the degree of clarity of the discipline they establish, and thirdly on the progress of knowledge in the history of science (cf. Kamp 1977: 166). The concept of axioms, however, is also the place where Whewell ’ s and Mill ’ s conceptions differ, for a while Whewell, as we have heard, regards axioms as conditions of experience and knowledge, while Mill conceives them as results of 66 Karl Bühler ’ s Axiomatics and the Axiom (1984) the process of knowledge, arrived at by way of generalizations from observations. This considerable conceptual difference prompts the question of where Bühler saw the common ground undisputed by both. The intersection of Whewell ’ s and Mill ’ s conceptions is, according to Kamp, to be found in the hypothetical character of descriptive-theoretical conceptions (cf. Kamp 1977: 177). Moreover, for Whewell as for Mill, the assumption holds that ideas of induction are in principle bound to linguistic mediation. This insight is expressed particularly clearly in a passage from Mill ’ s System of Deductive and Inductive Logic: If in the simplest observation, or in what counts for it, very much is not observation but something else, then in the simplest description of observation more is always asserted, and must always be, than is contained in the truth itself. [Consequently, it is impossible] to express a result of observation in words without committing an act that possesses what Dr. Whewell considers to be that which characterizes induction. Something is always introduced which was not in the observation; a conception common to the phenomenon with other phenomena with which it is compared. An observation cannot be expressed in the language without asserting more than one observation, without comparing it with other phenomena already observed and thus classifying it (Mill 1968, II: 209). Against this background, it becomes plausible why Bühler concludes the “ explanation of the topic ” with the already mentioned statement that he offers an intertwined discussion of concepts and axiomatics, whereby he separately emphasizes in the last sentence that “ certain premonitions ” had determined his conception of axiomatics (cf. Bühler 1933a: 24). But if every induction, and even more generally, every experimental research is preceded by the linguistically mediated identification of the object as an object, then the theory of induction ideas or axiomatics leads into a constitutional theory, which can manifest itself as an object-constituting as well as a domain-constituting theory. Kamp summarizes this result succinctly by means of an example: Kepler “ recognized “ identified “ constituted “ every single observed orbital point of Mars “ as “ a point of a geometrical figure, in this case, an ellipse. [ … ] Kepler “ conceived “ identified “ constituted “ the field of astronomical phenomena as a whole “ as ” a system of geometrical figures (Kamp 1977: 179 f.) Bühler clearly emphasized in several places that he wanted to follow Rickert ’ s considerations in his axiomatics (cf. Bühler 1933a: 20 f.; 1934: 5) so that a comprehensive understanding of Bühler ’ s approach is hardly possible without reference to Rickert. In his work, Kamp has taken up Bühler ’ s hint that an important model of the axiomatics of linguistics is to be sought in Rickert ’ s concept, and has compiled Rickert ’ s thoughts in the form of six sentences: 1. the theorem of the unmissability of everything real, 2. the theorem of the continuity of everything real, 3. the theorem of the heterogeneity of everything real, 4. the theorem of the irrationality of everything real, 5. the theorem of the rationality of everything real, or the theorem of transformativity of conceptual knowledge, 6. the theorem of the perspectivity of everything real or the theorem of the selectivity of conceptual knowledge (Kamp 1977: 126). Karl Bühler ’ s Axiomatics and the Axiom (1984) 67 Rickert explains the first theorem, which appears in Bühler ’ s pre-axiomatics as “ Mannigfaltigkeitssatz ” (multiplicity theorem), to the effect that the world of objects presents itself in a neither temporally nor locally limited manifold of quantitatively and qualitatively diverse things, without it being possible for the finite human mind to grasp all these phenomena. On the contrary: The more intensively and in more detail we delve into the immense multiplicity, the more multifaceted and multiform it becomes, which leads to the contradictory sound Behind, that an increase of the known is accompanied by an increase of the strange. If it is true that the given can neither be limited temporally nor locally, it follows that there can be no sharp boundaries either, but only flowing transitions. Accordingly, Rickert uses the old formula “ everything flows ” in his continuity theorem. The heterogeneity theorem is supposed to do justice to the fact that in principle there can be no process in the world that would completely correspond to a second one, which manifests itself, for example, in the non-repeatability of perceptual judgments. Kamp regards the irrationality theorem as a summary of the second and third theorems. This theorem is supposed to do justice to the fact that when the given turns out to be fundamentally heterogeneous we can always only recognize it diacritically, and when the given is integrated into a continuum that we cannot sharply segment, reality shows itself to us in a peculiar irrationality, since a heterogeneous continuum as such cannot be conceptualized. The transformativity theorem states that reality must appear irrational only to those who attempt to represent it as a heterogeneous continuum without transforming it. However, if we transform the heterogeneous continuum, offering the possibilities of transforming it into a homogeneous continuum or a heterogeneous discreteness, the possibility of rationally grasping reality opens up, although it must be added that both transformation procedures are simplifications. The perspectivity theorem, which concludes Rickert ’ s axiomatics, posits that in order to avoid arbitrary decisions in the transformation of the heterogeneous continuum, there is a need for an a priori fixed point of view, i. e., a prejudice, which orients all transformation steps. While Bühler follows Rickert ’ s propositions one to five, the perspectivity proposition can only be partially reconciled with his own position, which, in contrast to Rickert ’ s approach, is not deductively determined. However, the difference of opinion concerning the perspectivity theorem is not an irreconcilable contradiction, because what Bühler discusses under the term induction idea shows considerable similarity with Rickert ’ s perspectivity theorem, apart from the not insignificant difference that Rickert ascribes a priori validity to perspective. In contrast, Bühler wants to deduce the induction idea from the successful research business. The fact that Bühler did not only orientate himself on Hilbert ’ s, Whewell ’ s, Mills ’ , and Rickert ’ s preliminary considerations in constructing his axiomatics did not need to be specifically noted. However, it might be particularly worthwhile to determine more precisely the degree of agreement that exists between Bühler and Meinong. Such similarities can be inferred from a note in Krise der Psychologie (cf. Bühler 1978: 61). A 68 Karl Bühler ’ s Axiomatics and the Axiom (1984) detailed analysis of these correspondences, including the letters exchanged by the two scholars, must be reserved for another context. In a brief remark that will conclude this section, I would like to pursue the question of why Bühler did not bother with a word about the axiomatics developed by Weiss (1925) and Bloomfield (1926), whereas Weiss presented an axiomatics of psychology and Bloomfield an axiomatics of linguistics, which Bloch (1948: 3) assesses in a similarly wrong way as Lieb (1980: 299). Bühler has provided an answer to this question in the form of his sharp critique of the one-sidedness of the behaviorist approach, which he puts forward in The Krise der Psychologie (cf. Bühler 1978: 18-29). If one remembers that the “ subjectivist axiom ” in the preface to the second edition of the Krise der Psychologie determined self-observation as the only legitimate starting point of psychology, and if one compares this axiom with the remark: “ That behaviorism, in the course of its short history, behaves more and more rejectively toward everything that in psychological determinations comes from selfobservation, is just as understandable as it can become, and in part has already become, fatal for its basic concepts and axioms ” (ibid.: 22), it is clear why Bühler did not need to deal with the works of Weiss and Bloomfield in more detail. Alternative sematological axiomatics While Bühler could refer to a number of models in the field of general axiomatics, the situation is different in sematological axiomatics. In two cases at most, namely in Gomperz and Gatschenberger, there could be the talk of orientation to these alternative sematological axiomatics. At the same time, the other two drafts under discussion here, that of Haig and Bense, cannot be considered models. Nevertheless, I consider comparing these approaches useful in the present context as Bühler ’ s axiomatic method becomes clearer in its special character. In his 1869 work Symbolism or Mind-Matter-Language, the Scottish philosopher James Haig dealt with problems of axiomatics in two chapters, chapter IV being reserved for logical axioms, while Haig deals with questions of sign-theoretical axiomatics in chapter XIII. Haig ’ s semiotic study, which has been almost completely overlooked, at least by the continental European discussion, which applies to a number of semiotic texts written at the same time (cf., e. g., Smart ’ s Sematologie; Engl. Smart 1978), - the copy of Haig ’ s Symbolism belonging to the Frankfurt University Library had not even been cut open at the end of 1982 - is of great value to us because, analogous to Whewell ’ s and Mill ’ s approaches, it assumes the fundamental linguistic or semiotic mediatedness of the cognitive process: There are not two unities, but three unities - the object, the subject, and the word - or else your mouth is shut about them! There are three, not two, factors in every human cognition, and till the word is created or assumed, your cognition is incomplete, and your reasoning cannot begin (Haig 1869: 193). If, on the one hand, we have to assume as the three foundations of knowledge in every act of cognition the cognizing subject, the object of cognition, and the semiotic mediation between them, on the other hand, we must also take into account that there can be no science until we also assume fundamental categories, general concepts, and axioms (cf. ibid.: 192). Haig determines axioms as self-evident propositions (cf. ibid.: 194), whereby he considers it Karl Bühler ’ s Axiomatics and the Axiom (1984) 69 contradictory to ask about the evidence of axioms at all since the constitutional conditions of axioms already exclude such a question. The explication of this position, which at first sight seems traditional, will prove that Haig has taken an original semiotic conception with regard to the ‘ axioms ’ problem. If doubts about the validity of an axiom arise, then due to the self-evident character of axioms this doubt can only be resolved with reference to language and logic, since axioms as logically general things must be expressed linguistically. While the self-evidence of axioms is always referred back to the individuality of the subject of knowledge so that someone can only settle with himself whether he regards something as self-evident or not, a general consensus on the validity of an axiom can only be brought about linguistically (cf. ibid.: 203). But if we say that basically, every act of cognition depends on mediation by signs - which then of course must also apply to the individual act of cognition, and here there seems to be an inconsistency in Haig - then the semiotically conceived axiom cannot involve more than has been linguistically put into it. On the basis of this consideration it is then only logical when Haig regards a true axiom as a true explanation of the signs concerned: What are called axioms, are all, as I think, truly involved in the proper understanding of the words themselves; and they cannot be called truly axioms if they are not self-evident when the words are fully understood by our internal senses. But it takes time to revolve and settle the true meanings of words in our own minds, and that is a very laborious mental exercise for the conscientious thinker (ibid.: 211). From this explanation, it is evident that the axiomatic method, in Haig ’ s opinion, amounts to a program centered on the progressive clarification of the meaning of our signs, by which it is also said - incidentally - that this program has extensive parallels with Mauthner ’ s Sprachkritik. The procedure Haig proposes for realizing his program, and by which he intends to put the role of signs in the process of cognition to their adequate function, amounts to the comparison and reflection of the logical inferences and relations we derive from axioms. At this important juncture, Haig emphasizes that “ logical inference is always hypothetical in the form ” (ibid.: 217), opening up a perspective that implies extremely farreaching semiotic consequences, without himself dealing at length with the unfolding of those consequences. If it is true that, as Haig says, we can think about human actions only by means of and in terms of signs that produce and cause the actions. If it is true that we can approach both minds and matter only by means of linguistic signs, and if it is true, thirdly, that all inferences, i. e., also the inferences from signs, are hypothetical, then it follows that there can in principle be no such thing as fixed, definable word meanings, but only an indefinably long and difficult process of explaining the meaning. Haig summarizes his considerations on axiomatics as follows: But the conclusion which I wish the reader to admit is simply this: that it is not true or accurate language to speak or reason concerning scientific ideas, but only concerning scientific words; and that the axioms of every science must always be self-evident verbal propositions arising out of and involved in the scientific meanings of the words themselves, when carefully and conscientiously attended compared, and reflected on by the mind in thought. Of course, we might call these judgments or intuitions, or some other internal name no better than an idea, but we have rejected all such words not founded upon number as being inaccurate and beyond the true region of general 70 Karl Bühler ’ s Axiomatics and the Axiom (1984) human cognition. An axiom, therefore, is a necessary and self-evident relation between the scientific words employed in the axiom itself (ibid.: 219). While, to my knowledge, there is not a single place where Bühler refers to Haig ’ s axiomatics, so that the two approaches can only be made fruitful for each other in comparison, Bühler refers at argumentatively very important places of his axiomatics to the second volume of Heinrich Gomperz ’ s Weltanschauungslehre (Worldview teaching), which bears the title Noology and the subtitle Introduction and Semasiology. Already on the first page of the theory of language, he mentions Gomperz in the same breath as Plato, Humboldt, Wundt, Cassirer, Marty, and the Meinong school, to whom Bühler owes the main ideas of his book, as he explains. In the second passage, where Bühler discusses Gomperz, it becomes understandable why Gomperz is cited as a model since Bühler can draw on Gomperz ’ s semasiology in discussing the representational function that is central to his overall conception. The third passage is no less important because in this context Bühler discusses the principle of abstract relevance (cf. Bühler 1933a: 29 f.; 1934: 225). Gomperz develops four main propositions in his semasiology, which 1) concern the inconceivability of the propositional content, the fact of logical intercourse, and the propositional content as a mental fact; 2) Gomperz deals with the representational nature of propositions, the empirical reality of noetic objects, and the relation of meaning, matter, and consciousness; 3) Gomperz distinguishes between real and intelligible parts, discusses the fact as an intelligible part of the propositional basis, and treats the relation of conception and abstraction; 4) Gomperz deals with the members of the relation of designation and meaning, emphasizes the differences in essence between designate and mean, and presents ‘ mean ’ as ‘ represent ’ . In his investigation of the problem of meaning, Gomperz starts from the premise that thought must either possess a linguistic form or be sufficiently structured to assume such a form so that there can be any talk of meaning at all in the logical and noological sense. Thoughts that fulfill this condition are called statements by Gomperz (cf. Gomperz 1908: 54). From the observation that the same propositional content can be expressed by different propositional sounds and different propositional content by the same propositional sounds, Gomperz concludes that propositional content and propositional sounds cannot coincide. But since only the propositional sounds are perceptible, this results in the first main semasiological question, how the propositional content presents itself to consciousness (cf. ibid.: 91). Gomperz can only give an answer to this first question ex negativo, since he can only say that different rules apply to the propositional content than to the propositional sound and the propositional basis (cf. ibid.: 97). According to Gomperz ’ s opinion, the relation of expression prevailing between the content of expression and the propositional sound shows in several respects a similar relation to the relation of inherence existing between the substance and the qualities of a thing. This impression is reinforced by the fact that the statements, i. e., the complexes consisting of statement content and statement sounds, are experienced as unified and persistent when the statement contents remain the same so that one can say that the statements are experienced representationally just as things are. Against this background, Gomperz formulates the second main semasiological question, which investigates “ what we Karl Bühler ’ s Axiomatics and the Axiom (1984) 71 mean by the expressive relation between propositional content and propositional sounds in general, and what we mean by the representationality of propositions in particular ” (ibid.: 98). Gomperz justifies the third semasiological main question in the way that the relation of apprehension to be stated between propositional content and propositional basis has two peculiarities: First, different propositions, which can refer to the same propositional bases as their apprehensions, do not correspond to reality, but only to mentally distinguishable parts. Secondly, it must be noted that the relation of apprehension must also be in a relation of similarity to the relation of inherence since the complexes formed from propositional content and propositional basis appear to us representational, i. e., uniform and persistent. Accordingly, the third question is: Hence, the question arises of what we mean by intelligible parts, what we mean by the apprehension relation between propositional content and propositional basis, and what we mean by the concreteness of the propositional facts (ibid.: 121). The last semasiological main theorem concerns the relation between designation and meaning. In order to clarify this relation, Gomperz assumes, on the one hand, (that the designation relation existing between propositional sounds and the propositional foundation is merely mediated and purely external and is characterized by the fact that the existence of the second can be inferred from the existence of the first relational foundation. On the other hand, Gomperz determines the meaning relation existing between statement and stated fact as a proxy or representation relation. The fourth semasiological main question is then literally: The question, therefore, arises as to what we mean by the meaning relation between statement and fact (ibid.: 132). Gomperz ’ s axiomatics, built up from four main semasiological questions, shows, besides some obvious similarities, considerable differences to Bühler ’ s approach, because Gomperz also axiomatically foregrounds the sign nature of language, the question of elementarization, and the expressive and representational function, but, unlike Bühler, he chooses a purely linguistically oriented starting point, which manifests itself, for example, in the neglect of the appellative function. Significant differences are also found in that Gomperz does not provide for a differentiation equivalent to the linguistic four-field scheme, nor does he distinguish between a pointing field and a symbolic field. Nevertheless, Bühler ’ s axiomatics should be regarded as an elaboration and continuation of the semasiology envisaged by Gomperz, despite the aforementioned deviations. For Richard Gätschenberger ’ s sematological axiomatics, it cannot be claimed with the same certainty as for Heinrich Gomperz that Bühler chose it as a model for his own approach since he does not refer to Gätschenberger at any point that I know of. Even if at present it is not possible to speak of a direct relationship between the models of Gätschenberger and Bühler, there are a number of quite impressive indications suggesting such a direct relationship (cf. Preface to Gätschenberger 1983). Among the most important of these indications are, for example, the unusual terminological coinages - both Bühler and Gätschenberger speak of a ‘ sematological ’ axiomatics; the only author who has a 72 Karl Bühler ’ s Axiomatics and the Axiom (1984) corresponding terminology is Benjamin H. Smart (1978); furthermore, the fact that both Bühler and Gätschenberger, as psychologists, set out to design an axiomatic system, and thirdly, the fact that both Gätschenberger and Bühler were Schillers of Oswald Külpe and Gätschenberger practiced as a physician in Würzburg when the famous thought experiments of Külpe ’ s Würzburg School were carried out with Bühler ’ s substantial participation. Gätschenberger ’ s sematological axiomatics is characterized, on the one hand, by a much higher degree, of generality and variety of application, than was found in Haig ’ s or Gomperz ’ s work, and, on the other hand, by a certain aggressiveness that is reflected in sentences such as the following: The sematological field is closely connected from a central point with all the others; sematology interferes everywhere (Gätschenberger 1977: 144). Surprisingly, Gätschenberger also chooses an approach consisting of four axioms, to which he adds fifteen maxims. The axioms developed by Gätschenberger are: • Real (or thought to be real) can be symbolized by the signs for at least two unreal (or thought to be unreal) objects. • To create an artificial sign or symbol - To pontificate an object artificially. • One goal of sign-setting is parallelism between sign contexts and existing object contexts. • One goal of sign-setting is to form the necessary maximum of symbols with a minimum of signs (ibid.: 32-38). The following fifteen maxims, which I will not list in detail (cf. ibid.: 39-45), are rules of most different nature: On the one hand, they are sematological transfers of the identity, the contradiction, and the proposition of the excluded third party, which can also be seen as unfolding of a single axiom, which would then have to read: “ A is A and not Non-A and shall always remain A ” (cf. Austeda 1962: 34 ff.). On the other hand, Gätschenberger lists among the maxims such propositions that are very strongly reminiscent of the sincerity criterion of speech act theory and that admit the demand made by Mauthner (1980, I: 67) to revive the relation between axiomatics and axiology already known to the Ramists. Third, and finally, among the maxims appear those sentences that could perhaps be characterized as preserved principles of scientific work. Gätschenberger himself comments on his draft as follows: The first two axioms or laws of thought are sematological descriptions translated into the language of the signified and as such require a justifying connection with the other propositional objects. A second group of so-called axioms consists of generalizations of inner experiences. There are retrospections by which one states that one must and cannot do some things. Certainty about it or evidence exists only in each first, second, third case, and so on. That it is always true can only be justified if an ideal system can justify the generalization (Gätschenberger 1977: 143). From this latter statement of Gätschenberger, we can draw some important conclusions about his assessment of the role of the axiomatic method in general and of sematological axiomatics in particular, as well as about the question of the establishment of axioms. To answer the last question, we read him as saying: Conventionally, one demands from a system, that it begins with axioms, postulates, and supreme laws of thought. The demand is first unclear, secondly incomplete. By axioms, one understands Karl Bühler ’ s Axiomatics and the Axiom (1984) 73 secretly or openly gifts of reason, by laws of thinking laws of a thinking ability instead of the thought. Sematological demands are missing completely (ibid.). Reinforcing this tendency, it is said elsewhere: One can be of the opinion that sematological sentences do not belong to a system, but rather that one has to decide on the meaning and mode of use of the signs before their establishment and then only apply the signs correctly. This may be true for systems that deal only with limited areas. But the larger the area of a system becomes, the more the bad consequences of the decisions become apparent (ibid.: 142). If we interpret these two passages as a plea against the apriorism of more geometrico constructed axiomatics, however, the question immediately arises how then axiomatics should be conceived. Gätschenberger ’ s answer, which we have already encountered in a comparable way in Whewell and Mill, and which is also at the heart of Bühler ’ s thought, states: But the axioms do not speak in the language of the given of the retrospectively perceived, but in the language of the demanded for the sake of the given. Axioms are generalizations of retrospectively perceived things translated into the language of the demanded. [ … ] The retrospective perceptions form an exceedingly rich treasure of experiences, which is certainly not inferior to the ‘ external ’ perceptions and accomplishes just what is attributed to reason and still some more. These inner experiences, by not knowing anything about them, do not become less important for cognition than the outer ones (ibid.: 84). In short, then, axioms are generalizations of everyday experiences, which Gätschenberger expresses in this way elsewhere (cf. ibid.: 144). Against this background, an answer to the still open question about the role of sematological axiomatics is then possible: if axiomatics takes up the experiences of successful sciences - to speak with Bühler - and if axioms are translated sematological resolutions, without the axioms thereby becoming corollaries of the resolutions, then we may - according to Gätschenberger - “ put the axioms next to the sematological principles ” (ibid.: 144). I will try to show later that this conclusion of Gätschenberger ’ s must be corrected to the effect that axiomatic and sematological firsts are not in a symmetrical relation, but are to be set off against each other without remainder. Although Max Bense ’ s work Axiomatik und Semiotik is the latest and most comprehensive work in this field, I will only briefly discuss it, since Bense, on the one hand, directs his investigation towards a goal that is fundamentally different from ours - his considerations are directed towards “ mathematics and knowledge of nature ” . In contrast, here it is about the axiomatics of linguistics resp. the sciences of experience - which, on the other hand, explains his deductive procedure that proceeds via axioms to definitions, postulates, theorems, etc., whereas here an apagogic respectively the abductive procedure is chosen. Beyond these conceptual divergences with respect to the subject matter treated and the procedure adopted, which are, however, not negligible methodological differences of opinion, there are assumptions underlying Bensen ’ s understanding of semiotics that I cannot endorse: I see one of the decisive points of contention in Bense ’ s definition of semiotics as an “ operational theory ” (Bense 1981: 151), which I would like to counter without further discussion, which will be conducted elsewhere, with a conception that understands semiotics as a method of reflection critical of basic principles. 74 Karl Bühler ’ s Axiomatics and the Axiom (1984) Despite these divergences, I would like to take up three of Bense ’ s suggestions and examine them for their applicability in the present context. Bense starts from the assumption “ that certain decisive properties of dyadic representations on the logical level are already determined by corresponding or equivalent ones on the categorically lower semiotic level of triadic relations ” (ibid.: 152), from which he draws the conclusion that it is obvious to “ abandon the well-known requirements of completeness, independence, and freedom from the contradiction that is imposed on axiom systems of logical-mathematical provenance, pro-axiomatically, i. e., by correspondingly determinative demands on the semiotic level of representation ” (ibid.). Although Bense considers this conclusion obvious, it seems to me to imply at least three problematic aspects: The first issue, however, which already casts doubt on the premises of Bense ’ s conclusion, concerns the possibility or impossibility of ‘ dyadic representations. If this is not just a superficial way of speaking, which I would like to leave out of consideration, one would have to assume that there are representations that consist of only two relational foundations. What is a very common phenomenon from the point of view of relational logic turns out to be an impossibility of thinking from the perspective of the problem of representation. As, for example, C. S. Peirce and Bühler have shown in their detailed treatment of the problem of representation in the case of the scholastic formula “ aliquid stat pro aliquo ” , representation is precisely not of a dyadic nature but is only put into function when the representative is regarded as the representative of the represented, i. e., when the “ stare pro ” is systematically taken into account as a medium or third party (cf. Bühler 1934: 40). The second problem concerns whether the semiotic level is categorically deeper than the logical level. A satisfactory clarification of this question, to which the discussion will return later, would require a lengthy argument for which this is inappropriate. Instead of a detailed argument, I would like to counter Bense - again with reference to Peirce and Bühler - that semiotics cannot justify logic because they are not only on the same level but because logic should be conceived as semiotics (cf. Peirce C. P. 8.377), which also corresponds to Bühler ’ s opinion, who explicitly equates logic and sematology in the unpublished draft of his Axiomatik der Sprachwissenschaften (Axiomatics of Linguistics) (cf. Pre-Axiomatik: 27). The third disagreement stems from the attempt to transfer the requirements of completeness, independence, and non-contradiction from the logical-mathematical context to the semiotic level of representation. As nice as it may be to build up axiomatics along these three demands, such an attempt is at the same time inappropriate, for it would amount to a metabásis eis álio génos, as Bühler called such an attempt since mathematical axiomatics (more correctly geometrical axiomatics) has in principle different constitutional conditions than logical-dialectical-semiotic axiomatics, which is strikingly evident with respect to the hypothetical nature of the semiotic axioms, which never want to and can deny their origin in generalized judgments of experience. Idea and plan of Bühler ’ s axiomatics Even if Karl Bühler only published a paper in 1933 in the Kant Studies, which already dealt with the ‘ axiom ’ problem in its title, the impression would be completely wrong that the axiomatics of linguistics was the inclusion of a thought which was new for Bühler; Rather, Karl Bühler ’ s Axiomatics and the Axiom (1984) 75 Bühler dealt with this problem throughout his life, with the first approaches going back to his medical and his philosophical doctoral theses (Bühler 1903 and 1904), while the last studies, which are as yet unpublished, were made during the time of his American emigration. That this way of looking at the development of Bühler ’ s axiomatic thinking is not a post festum constructed unity or dynamic of the approach, but that such a way of looking at it is completely in accordance with Bühler ’ s self-assessment, can be gathered from the memoirs in the preface of the Theory of Language (Bühler 1934: X), in which Bühler reviews some of the most important stations on the way to his theory of language. In his opinion, his system “ was founded in 1907 after the discovery of the ‘ syntactic schemes ’ in speech thought [ … ] and in 1908 after the highlighting of the representational function of language in my collective lecture on the processes of understanding [ … ] ” (ibid.). He concludes his review of the development of his work so far with the statement: “ Since I have been able to think scientifically, my interests have revolved around the phenomenon of language ” (ibid.). However, it would be too little if we merely wanted to state that Bühler ’ s axiomatic model of 1933 or 1934 had precursors in his own work, just as there were still important developments after 1933. Bühler ’ s approach is only justified by Hilbert ’ s expression of the progressive deepening of the foundations, which Bühler interpreted not only as meaning that he elaborated, refined, and supplemented axiomatics once it had been designed; this expression also implied for Bühler the obligation to establish the foundations of the empirical sciences on his part, namely - as we will see - in axiomatics of the theory of signs. Before the publication of Axiomatics of the science of language, two directions of axiomatic thinking in Bühler can be distinguished, which at first seem to be mutually exclusive and only in the course of the twenties merge into a consistent system. In Bühler ’ s medical dissertation, which has already been described as an axiomatic of Helmholtz ’ s color theory, the starting point of the experiments is the assumption of the validity of the persistence and proportionality theorems established by J. v. Kries, from which Bühler deduces (cf. Bühler 1903: 10). His philosophical dissertation on the Scottish philosopher Henry Home is also oriented in a quite comparable way. In this case, he did not go to work experimentally, but endeavored in theoretical discourse to find the “ underived elements ” (Bühler 1904: 59) in Home ’ s thought. A third study, in which this view was practiced, determines the axiomatic method as the “ kind of deductive procedure beginning with axioms ” (Bühler 1922: 5). The first elaborated system of axioms comes in the Krise der Psychologie, first published in 1926, which, in Bühler ’ s opinion, is at once about the axiomatics and the method of psychology (cf. Bühler 1978: 1). Bühler sees the goal of this critical stocktaking in a deduction, i. e., a “ derivation of the three psychological aspects from the tasks facing our science and from the means of investigation at its disposal ” (ibid.: 57). But if one asks how the term ‘ deduction ’ is to be understood here, Bühler answers: The deduction presented is formally, logically a syllogism with the upper proposition, lower proposition, and conclusion. The upper proposition states that all three aspects are necessary to justify a theory of language. The subordinate clause subsumes the phenomenon of language under the objects of psychology. From this, it can be concluded that some things belonging to psychology require three aspects (ibid.: 57 f.). 76 Karl Bühler ’ s Axiomatics and the Axiom (1984) This explication of the concept of ‘ deduction ’ shows that the axiomatic approach hides Bühler ’ s basic question, which he poses in the following key passage: How is psychology possible? So Kant would ask in our situation. It is indeed incumbent upon the philosopher to reflect soon on the possibility, soon on the necessity of the given. And we need philosophical reflection on our axiomatics, their character, and viability. It is a transcendental deduction in Kant ’ s sense that is necessary and is sought here. Each of the three aspects is possible, and none is dispensable in the one science of psychology. Each of them demands the other two for their complement so that a closed scientific knowledge system comes into being. From each of them spring its own tasks, indispensable to psychology, which become meaningless or insoluble if abandoned. Thus, the initial object of psychology belongs to the experiences, the sensible behavior of living beings, and their correlations with the entities of the objective mind (ibid.: 29). With this formulation not only the actual concern of axiomatics is clearly stated, but also the system built up from three axioms is presented, which Bühler presented in an overview as follows: I Wherever there is genuine community life, there must be a mutual direction of the meaningful conduct of the community members. Where the points of the direction of the control are not given in the common perceptual situation, they must be mediated by a contact of higher order, by specific semantic devices. II If the self-need and the self-determination of the individuals involved in a community act are to be brought to bear in the mutual control, they must come to manifestation. III By assigning the expressive signs to the objects and facts, they gain a new dimension of meaning. Thus an incalculable increase in their efficiency as means of communication. The one through the other (ibid.: 50 f.). In the Krise der Psychologie, however, Bühler not only established these three axioms constituting the field, which in his opinion “ constitute the cosmos of pure language without remainder ” (ibid.: 51), but in the preface to the second edition of this book, written during his stay in America in 1928, he developed a model consisting of four axioms, in which the controversies of psychology are to a certain extent bundled (I quote from the manuscript, which differs from the printed version): 1. The subjectivist axiom: The only legitimate outcome of psychology is self-observation; its object is experience. 2. The atomistic axiom: The analysis of the experiences finds firmly circumscribed elementary contents of consciousness; the so-called entangled or higher phenomena are complexions from them. 3. The sensualistic axiom: Genetically original contents are only the sense data with the inclusion of the elementary feelings. (Feeling tones, of which there are only two: desire and dislike). 4. The mechanistic axiom: The formation of complexions and the course of experience are subject to the law of contiguity, the principle of association; there are simultaneous and successive cementations or both in one (MS of the preface to Bühler 1929: 1). Measured against the Krise der Psychologie, in which some scholars certainly not unjustifiably see Bühler ’ s most important work, Bühler ’ s Ausdruckstheorie, first published in 1933, is less productive from an axiomatic point of view, although this work is also axiomatically oriented in large parts since Bühler assesses the approaches of the various theorists of expression treated precisely in terms of the axiomatics on which they are based Karl Bühler ’ s Axiomatics and the Axiom (1984) 77 (cf. Bühler 1968: 3). Particularly noteworthy, however, are some remarks which are suitable to clarify and inculcate what has been said so far. The first group of these remarks concerns the logical status and dialectical origin of axioms, emphasizing their hypothetical character. For example, Bühler, like Meinong, speaks of axioms as “ general assumptions ” (ibid.: 74) and characterizes the first sentences as finder rules, regulae ad directionem ingenii (ibid.: 97), which can be understood as an elucidation of the concept of induction ideas introduced earlier. A second point of view that is significant for the present context of discussion concerns the question of how Bühler himself places his axiomatic studies in the history of dogma, i. e., the history of axiomatics (cf. ibid.: 195): He argues that there were phases in the scientific process that were primarily concerned with the unification and harmonization of the knowledge achieved (cf. ibid.), in order to be able to derive from it the direction of future work. Literally, it says: It is instructive to break down the knowledge possessions of today into aspects and to realize what future tasks await us in the field of axiomatics (ibid.: 195). The third and perhaps most important set of issues, which will occupy us in more detail later, relates to the leitmotif-recurring demand that the work of the theorist of science should not yet end with establishing axiomatics of linguistics. The deepening of the foundations must find its continuation in sign-theoretical axiomatics, or Bühler ’ s words: But a comprehensively new plan in these matters must be dominated and supported by deepened sematological axiomatics (ibid.: 88). The unpublished draft version of the Axiomatics of Linguistics, which I have called Pre- Axiomatics, cannot be reproduced here in extenso, but only in some particularly striking aspects. However, I would like to quote the complete table of contents of this draft, which already allows an insight into the later significant deviations in the printed version: The system of axiomatic sentences I The key theorem of the sign nature of language. II The decomposition theorem of speech acts and speech entities (aspects). III The manifold theorem from the structural model of language. IV The proposition of the logos-character of semantic synthesis and semantic synthemata. V The theorem of the three sense relations in language signs (representation, expression, appeal). VI Postponed is the sociological consideration. Unfulfilled is a thesis about the speech act. How closely Bühler follows the great Greek thinkers “ in matters of principle research ” can be seen from the fact that he derives the first two axioms directly from Greek thought developed in unsurpassed straightforwardness of approach: Where Plato in the Cratylus takes up the thinking of his contemporaries about the nature of human language and continues it in his own way, he firstly states the proposition that language is an organon, a device of mental intercourse, through which one is able to communicate something to the other about things. This is a definition of language from the point of view of its performance, a definition of performance. Secondly, he recommends that one should do the same in the research of this organon as one wants to obtain reliable information about the nature of any other tool. There is, for example, the weaver ’ s wheel, the loom. Go to the weaver, he knows how to handle the loom and has the most intimate knowledge of the properties of this organon from his craft practice. Or even 78 Karl Bühler ’ s Axiomatics and the Axiom (1984) better: Go to the one who made the weaver ’ s shuttle, the carpenter. There you will certainly learn the most reliable about the construction of the weaver ’ s chest. This is a methodical instruction for the philosopher. It is transferred to the language, applied to the object language, the recipe of the socalled Socratic induction (MS Pre-Axiomatics). Bühler did not think of simply borrowing his axiomatics from Plato and the Greek thinkers. Still, he had in mind a contemporary renewal of the classical approach, which above all should also take into account the rich results of successful linguistics in an appropriate way: My opinion in matters of linguistic theory is that a Plato redivivus today, after due insight into what has been accomplished in linguistic research, could take up his old scheme of thought, reinterpret it, and thus develop a clear and fruitful program of linguistic principles research (ibid.). The last-mentioned point of view, which frees Bühler ’ s conception from any suspicion of apriorism, he himself considered so important that he emphasized it again in a modified formulation: The philosopher of today can do nothing else than that he gets his information from the linguist of the subject. There in his theoretical workshop the Platonic Socrates would have to open his discussion of principles today. But the actual sense of the procedure can remain granted. In other words: the philosopher of today has every reason to assume that in the large-scale business of empirical linguistic research, which has now been going on for a century (continuously, in spite of all the twists and turns that have occurred in it) from success to success, that in this secular research business what the philosopher is looking for, the axioms of linguistic theory, are already alive. It is only a matter for him to find them in the bosom of linguistics, to formulate them exactly, and thus to raise step by step to the range of a system, which in general assumptions about language has always carried and fertilized empirical research. In the conception of the best empirical linguists, explicitly or implicitly, the axioms or some axioms of the theory of language are already contained. This is the assumption from which I start (ibid.). If, on the basis of these explanations, the procedure of Bühler ’ s research into principles is basically clarified, it only remains to discuss what Bühler meant when he spoke of the fact that everything else could be “ logically or semeologically deduced ” (ibid.) from the basic assumptions mentioned. He cautions not to be frightened by the word ‘ deduce ’ and explains his use of the word as follows: It does not mean that one can suck this knowledge from the fingers, that one can win it materially apriori. No, this ‘ deduction ’ is only the last step that belongs to every completed induction. Just as Kepler, once he had found the elliptical idea, was able to deduce the facts in a certain sense, in a certain whole, i. e., to make them logically coherent and transparent, the theory of language can and must if it is to be of any use, try to deduce certain basic results of comparative linguistic research (ibid). As clear differences between the axiom system of the Pre-Axiomatics and the later print version can be stated, as do the approaches developed in the Axiomatics of Linguistics, the Theory of Language, and the Paris Lecture of 1937 differ. Messing (1982: 60 f.) is even of the opinion that the axiomatics presented in the Krise der Psychologie does not necessarily lead to the organon model. A comparison of the axiom systems in question should answer the question of whether, despite certain differences, this is an elaboration of one system, or whether the rearrangements and accentuations ultimately lead to fundamentally different approaches: Karl Bühler ’ s Axiomatics and the Axiom (1984) 79 The system of axiomatics of linguistics, consisting of four axioms, includes the following propositions: A The organon model of language B Speech action and speech formation C The structural model of language D The scheme of speech functions In the Theory of Language the system, which is also built up of four axioms, has taken the following form: Axiom A exposes the basic structure of human language; Axiom B expresses the sign character of linguistic phenomena; Axiom C names the four different moments that can be distinguished in the overall object of linguistics; Axiom D characterizes language as a multiclass sign device (cf. Dempe 1935: 246 f.): A The organon model of language B The sign nature of language C Speech act and speech work; speech act and speech formation D Word and sentence. The S-F system of the type language The lecture Bühler gave on the third main theorem of language at the 11th International Psychological Congress in Paris in 1937 betrayed a view of linguistic axiomatics that had changed in essential respects: I know four main theorems of language theory. The first, the organon model of language, deals with the functions of the speech act; the second, the structural model of language, deals with the structure of the linguistic entities (la langue). The pair of terms function and structure is familiar to science and needs no explanation here. - The third main proposition deals with speech traffic and the fourth with speech work; this new pair of terms presents itself at the moment when one raises the question of the main uses of language (Bühler 1938: 196). If we now put the three systems in relation to each other, it very soon turns out that it is not only about the elaboration of a perspective that is uniform in its basic structure, but that on the one hand the three axiom systems are complementary to each other in several respects, whereas on the other hand there is also at least a serious change to be noted: 1. Language as a sign phenomenon 1933: Axiom A 1934: Axiom B 1938: Axiom A 2. Language as a relational phenomenon 1933: Axiom D 1934: Axiom A 1938: Axiom C 3. Language as a four-sided phenomenon 1933: Axiom B 1934: Axiom C 1938: Axiom D 4. Language as a two-class system 1933: Axiom C 1934: Axiom D 1938: Axiom B (cf. Kamp 1977: 202). Even this simple comparison shows that the three axiomatics, understood as constitutional schemes, are each directed at a different object: While the axiomatics of linguistics is primarily concerned with the constitution of the object of linguistic research in general, the axiomatics of Theory of Language is the constitution scheme of language linguistics, and the axiomatics of the Paris lecture is the constitution scheme of parole linguistics, or in other words, while the main interest in 1933 is the constitution of signs and meaning, in 1934 the structural and functional thought comes to the fore, whereas in 1938 the accent is on the 80 Karl Bühler ’ s Axiomatics and the Axiom (1984) speech traffic, the speech act and the actual use of linguistic signs. From the fact that this change of perspective can be achieved by a simple regrouping of the axioms, one can see that. Bühler in no way thought of rejecting the respective earlier drafts as wrong: Such a remark is nowhere in Bühler ’ s work. Instead, we must assume that the various axiomatic drafts were systematically developed by Bühler in order to do justice to the complex task of constituting the object of ‘ language ’ and its scientific treatment in a comprehensive sense. If further above, besides the complementarity of the three drafts, also a serious change was mentioned, this was meant to articulate the impression that has arisen during the screening of the three axiomatics: If one can say that. the axiomatics move from the general, abstract, and supra-individual to the particular, concrete, and individual, one could be inclined to evaluate this movement as a progressive pragmatization of Bühler ’ s approach, the consequences of which can only be pondered today. For Bühler himself, in the twenties and thirties the demand for the construction of linguistic pragmatics did not yet arise in the same way as it does today, since before this task could be accomplished, important preliminary work still had to be done: What is meant here is the double function of axiomatics, insofar as they should, on the one hand, reject or prevent threatening erroneous developments as critical theories, and insofar as they must, on the other hand, become active in a field-constituting way. The first point of view, which appears in a particularly concise way in the preface to the second edition of the Krise der Psychologie, does not contradict the second function; on closer examination, it turns out that the two functions are nothing else than the two sides of the same coin. Therefore, in the following, we will only deal with the question of which conclusions Bühler was prompted by the field-constituting function of axiomatics. In order to answer this question, we have to revisit the concept of the induction idea discussed earlier; now, however, we shall no longer be concerned with which theorists Bühler joined in adopting this concept, but rather with the extent to which the induction ideas may be regarded as formulations of Bühler ’ s research program. That this interpretation of the term “ induction idea ” is not only permissible but even necessary, is proven by a number of passages, which in their essence all boil down to the following view: When and as far as this [the question of whether the procedure of the experts in their structural recordings can be grasped from the highest, axiomatic guiding principle but the language as appropriate] succeeds, we gain a usable, i. e. scientifically fruitful answer to the question, which we can first of all put in general terms, following Kant ’ s well-known formula, like this: How is pure linguistics possible? Indeed, in the special field of linguistic research, a kind of basic research is conceivable, as Kant conceived and conceived it for the mathematical natural sciences. [ … ] We ask whether the three aforementioned pre-expectations of linguists can be brought into a connexus logicus, a mutual order of reasoning, e. g., can be regarded as the outflow of a single axiom about the structure of human language; this will suffice for the time being. Whether these pre-expectations of the linguists are to be regarded as the highest ideas of induction in the sense of an empiricist conception or whether they can be obtained epistemologically by other means, we leave completely undecided here. Well, if the theory of language is to be of any use and to bear the proud name of a theory with honor, then it must not stop at the gate to the last abstractions, but must resolutely think things through to the end just as the theoretical physicist or mathematician of today has long been accustomed to do in his field (Bühler 1932: 119 f.). Karl Bühler ’ s Axiomatics and the Axiom (1984) 81 Bühler ’ s axiomatics is thus directed at isolating the all-encompassing induction idea that programmatically guides the research business of linguistics, whereby he hastens to add every time he comes to speak of this idea that such an induction idea belongs to the trivialities of practical linguistic research (cf. ibid.: 98). But how must such an idea of induction be constituted, so that, on the one hand, it completely grasps the whole of language and its parts in a constituting way, on the other hand, it is at the same time fruitful from a research programmatic point of view and, thirdly, finally, it is to be regarded as a triviality of practical linguistic research? The only idea that Bühler considers capable of developing such a far-reaching inductive force is the induction idea of the sign nature of language, which at the same time also indicates how the research programmatic must be constituted. If the induction idea of the sign nature of language “ constitutes the cosmos of pure language without rest ” (Bühler 1978: 51), then a general sign theory or sematology must be developed for linguistics as well as for sociology and psychology, without sematology being derived from the mentioned sciences (cf. Bühler 1933a: 35). The consideration of the critical and area-constituting double function of Bühler ’ s axiomatics has led to the concept of the idea of induction, which has been interpreted as the establishment of a research program centered on the establishment of a general theory of signs. This last step of argumentation must now be clarified in order to be able to concretize the very general demand for the establishment of a theory of signs and to satisfy its content. Similar to Ferdinand de Saussure and other important sign theorists, Bühler has repeatedly emphasized the necessity of building up a general theory of signs, and he has also collected numerous important individual findings that are of decisive importance for the semiotics yet to be developed. Still, he has not presented a comprehensive theory of signs. In a few places, however, there are hints in Bühler ’ s work suitable for reconstructing the picture Bühler might have had of the sematology to be developed. Significantly, these clues stem from the context in which Bühler addresses the logos problem. (I do not want to conceal that in one of our last conversations before his much too early death, Gerold Ungeheuer pointed out to me that the roots of semiotics are hidden in the well-known double sense of logos). Bühler discusses the thesis to what extent it is permissible to describe language summarily as an instrument of logos, of logical “ mental functions ” (cf. Bühler 1933a: 62). That this thesis stands on shaky foundations is evident from the fact that Aristotle ’ s logic, including the table of categories, would undoubtedly have turned out differently if Aristotle had not accidentally “ grown up as a Greek, but as a Chinese, Eskimo, or Bantunean ” (ibid.: 63). Bühler ’ s proposed solution to this old controversy is as simple as it is original: He suggests to think through the proof process of those who have explained the concept of ‘ homo sapiens ’ in terms of language in reverse, in order to arrive at a new definition of the relationship between logic and language structure. In my opinion, Bühler ’ s own proposed solution contains in nuce the program of Bühler ’ s theory of signs, just as against the background of this proposed solution a redefinition of his main work on language in terms of scientific theory becomes necessary: I set in principle agreement with the respectful modern reform movement in the logic of the concept equation: Logic (in the broadest sense of the word) = general representation theory. If there should be any other problems in the research business of science, which should be counted to the logic, but not to the problems of representation, then we are not interested in that here, but it is only 82 Karl Bühler ’ s Axiomatics and the Axiom (1984) the “ element theory ” , which is important for our purpose. And this element theory of logic can be developed completely and purely as the general theory of representation with the help of symbolic sign systems (of the type of language). It does not contain a word about mental functions, which of course belong to the factual completion of representations, to dealing with the symbolic signs of representation. Psychic functions also belong to dealing with numbers and geometrical forms and yet the number theory and geometry keep themselves free of any statement about them. The same abstraction must be demanded of sematology and, within its framework, of the scientific treatment of linguistic entities (ibid.: 63 f.). If we summarize what has been said so far in a short formula, we have to add another link to our earlier equation of logic and semiotics, so that the equation now reads: logic = semiotics = general theory of representation. With this equation it is indicated, on the one hand, that the “ deepening of the foundations ” of linguistics must result in a general theory of representation or sematology, or, viewed the other way around, that the representational function of language, as the subtitle of Bühler ’ s main work on language reads, is a form of manifesting sematology. On the other hand, the research program of sematology is now openly apparent, for if language is to be understood - as Bühler says - as an intersubjective representational device, i. e., as “ an organum for one to communicate something to another about things ” (ibid.: 64), it follows that sematology, within the framework of this organon model, has to ask about the general principles of sign traffic, with logic at its disposal as an instrument. Further above I have made the claim that in Bühler ’ s work, there were only a few indications that allowed the reconstruction of his picture of the developed sematology. I would like to qualify this claim at the end of this section insofar as it refers only to the published texts. After 1938, i. e. after his emigration from Europe, Bühler consistently worked on the construction of a general theory of signs in a series of partly larger and without exception unpublished studies, which I will report on elsewhere (cf. Eschbach 1984c) and which will find their way into the Bühler-Werkausgabe. Bühler did not write an axiomatic theory of signs, but in scattered remarks, he gave a large number of suggestions for such an enterprise, which in the final part will be “ gathered up ” according to his pattern and connected to a system design. The axiom system of the sign theory Since Gödel ’ s incompleteness theorem makes it clear that the completeness of an axiom system cannot be decided system-immanently, axiomatics is forced to check its theorems elsewhere. In the following considerations, however, it is not primarily about the proof of the incompleteness or completeness of Bühler ’ s axiomatics, which would already be a futile undertaking insofar as he always expressed himself very cautiously on this point and always left the possibility of extensions open, but rather about a “ lowering of the foundations, ” i. e., about the substantiation of the axiomatics of linguistics in axiomatics of sign theory. One could ask oneself whether this further step of justification makes sense and whether, in a process that threatens to lead to an infinite regress, the axiomatics of the theory of signs should not be justified next. This is countered by the fact that if a justification seems Karl Bühler ’ s Axiomatics and the Axiom (1984) 83 conceivably possible, then this next justifying step should be taken because any other attitude would amount to a ‘ genetic fallacy. ’ Nevertheless, an extra-systemic justification of sematological axiomatics seems to be difficult to imagine, which is manifested, for example, in the fact that the aloe Stoa determined the semeion as an axiom (cf. Pohlenz 1978, I: 49). For the axiom system of sign theory presented in the following considerations, it is true to the same extent as for Bühler ’ s axiomatics of linguistics that it would be quite conceivable if this system consisting of seven propositions were supplemented by further propositions. However, a renunciation of one or more of these propositions does not seem to be possible, since each of them and all of them together are necessary for the constitution of the object of sign theory. In the long series of attempts to define man as a human being, man has been described, for example, as a rational being, or there has been talk of man being distinguished from all other living beings and from his environment by his gift of language. In a third respect, man appears as a working being; still, other questions make man appear as a zoon politikon, etc., etc. Each of these attempts at definition can claim a high degree of plausibility, and not a single one of the definitions mentioned would have to be rejected as false. In spite of their different emphases, the attempts at definition mentioned have one thing in common: they are all much too one-sided to be considered a definition of the essence of man. Instead, one could be tempted to arrive at the desired definition by combining all the above-mentioned definition attempts in one formula. However, this solution would be opposed by its heterogeneity and unwieldiness. We will therefore have to consider what underlies all the above-mentioned definition attempts and at the same time does justice to the complexity of the previous definition attempts in a comprehensive sense. The first and guiding idea I see in the specific sociality of humans, i. e., in the community life of humans, which I regard as the source point of all actions, be they of symbolic or nonsymbolic nature. With the axiom of sociality, I consider George H. Mead, Alfred Schutz, Ferdinand de Saussure, and Karl Bühler. Mead, in his philosophy, of sociality, as in mind, identity, and society, focused on the question of how an individual can conceive of himself as an individual, and he saw the answer to this question in the fact that the individual in the community of other individuals must at the same time distinguish himself from the others and learn to assume the role of the other. Karl Bühler also pointed out in the Krise der Psychologie that not the individual but the community is to be considered as the origin of all human activity, because no human being lives exclusively under his own skin, as Mead ’ s Chicago colleague John Dewey once formulated, which means for our present question that the transgression of one ’ s own perceptual situation, which of course requires appropriate means, i. e. the assumption of the perspective of sociality is the condition for the constitution of the ego identity of the individual. Throughout the history of philosophy, there have been attempts to isolate the initial and unmediated elements in the process of engaging with our environment. In order to lend at least a certain degree of plausibility to the idea of the unmediated elements of cognition, one has had to resort to nebulous concepts such as ‘ intuition ’ or the imputation of ‘ innate ideas ’ , which at the same time implies that one voluntarily leaves the realm of rational thought and is willing to engage in magical whispering. 84 Karl Bühler ’ s Axiomatics and the Axiom (1984) Since the works of Wilhelm Wundt, Charles S. Peirce, and Karl Bühler it has been proven beyond doubt that not only complex thought processes take place in the form of judgments, but that already on the level of perception and experience we can correctly speak only of perceptual judgments and experiential judgments. If, however, already the process of perception is to be described as the formation of perceptual judgments, which applies a fortiori to all higher activities, then it is also expressed that the question about the unmediated elements of mental human activity is in principle wrongly posed because such unmediated elements cannot exist in principle at all. Instead of continuing the vain search for the unmediated elements of cognition, I suggest changing perspective and to ask instead what it is that is responsible for the principle mediatedness of perception, experience and cognition. We have already heard that perception, experience and cognition take place in a judgmental way. Now a judgment is nothing else than a sign, so that we can say that. all perceiving, experiencing and thinking happens in signs. In analogy to an expression coined in the German philosophy of language, I therefore call the second axiom the axiom of the non-interpretability of signs. In the colloquial way of speaking we speak occasionally of dark clouds as a sign for rain, we call traffic signs signs, or an injury in the proximity of the heart is evaluated as sign of the near death, as we read with Sextus Empiricus. If, however, we ask more precisely what is supposed to be the sign in the examples given, we will notice very quickly that it cannot be clouds or tin signs or wounds that would have been transformed into signs in a peculiar process of transubstantiation; it is rather the case that a material appearance, or as Bühler said, “ a perceptible something hic et nunc ” assumes the role of a representative pointing to something else. From this last-mentioned determination we can infer that, besides the material sign-bearer or representamen, there must always be something that is represented, i. e., the signified object or state of affairs. In his perceptive analysis of the scholastic formula “ aliquid stat pro aliquo ” , Bühler has shown that we have not yet grasped the sign relation to its full extent if we merely assure ourselves of the material representamen and the signified object or state of affairs, because these two foundations of relation continue to diverge as long as we do not explicitly refer them to each other. If we call a dark cloud a sign for threatening rain, then we put the one as a sign for the other, i. e. we constitute in the act of the ‘ as if-observation ’ first of all the sign, which would not exist without this constituting act. We can therefore formulate the third axiom, which I call the axiom of interpretation: Only that is a sign which is interpreted as a sign. If a sign owes its constitution to an ‘ as if ’ relation, we must further ask how this process of constitution takes place. Again, it was Bühler who, with reference to Trubetzkoy, gave the decisive clues as to how the constitution of the ‘ as if ’ relation is to be thought. Other important suggestions in this context come from de Saussure and Peirce. Above we have stated that all thinking is thinking in signs. This insight resulted from the fact that perception and experience take place in the form of judgments. If something enters our perceptual space, we analyze it in a comparison as something known or as something still unknown. While in the first case the judging activity comes to rest after the formulation of a tautology of the form ‘ A is A ’ , in the second case, the conclusion to something still unknown, it is a question of a genuine extension conclusion, which proceeds in the form of a Karl Bühler ’ s Axiomatics and the Axiom (1984) 85 hypothetical judgment. Ferdinand de Saussure discusses the extension inference as a characteristic feature of the constitution of signs on the basis of the two fundamentally different relations ‘ simile - simile ’ and ‘ simile ’ whose common occurrence in an inference process is suitable for describing innovative movements. Gottlob Frege answers this question of meaning-constituting extension judgments almost casually when he writes that we can only move from one thought to another if the meaning of one thought also has a part of another thought. An example of such a movement could be: ‘ run: proceed as ask: x ’ . This analogical principle goes beyond what was said in the premises as the conclusion not only repeats or joins what is already known but opens up a new state of affairs not yet known in this way. However, since the extension stroke is a hypothesis that infers from fuzzy and incomplete premises, the judgment reached is in principle tentative. On the basis of these findings, we can formulate the fourth axiom of sign theory, which I call the diacrisis axiom: A sign can be determined only in demarcation from a second sign; the meaning of a sign is fuzzy. From what has been said so far it is clear that signs can only exist if there is the intention to refer to something else with the help of a medium, whereby the attention is not directed to the medium but to that to which the medium refers, which of course does not exclude that the perceptible medium is also specifically thematized. Furthermore, it was established that establishing a sign relation necessarily involves a material or immaterial object or state of affairs that is signified. Finally, the discussion has yielded the result that signs are independent of and inconceivable outside the performances of an interpretive consciousness. If we relate these three findings to each other in an integrating approach, we can say that any genuine sign relation is a three-figure relation characterized by some peculiarities. The first peculiarity is to be found in the fact that - as C. S. Peirce proved - a genuine triadic relation is not reducible to the sum of dyadic relations, which will not be further substantiated here. The second peculiarity of the sign can be explained by a simple example: While it makes sense to consider an ambassador as the representative of his country, it does not make sense to reverse this relation and refer to the country as the representative of the ambassador. Although in principle everything can be interpreted as a sign, this openness to designation then experiences a significant limitation once a sign relationship has been established, because it is then no longer possible to reverse the relationship. The fifth axiom of sign theory, called the relation axiom, thus reads: A sign is a non-reversible triadic relation. The diacrisis axiom takes into account the fact that a sign can be determined only in demarcation from a second sign. If one continues this line of thought, one arrives at the assumption of a plurality of signs, about whose relation to each other, however, nothing would be said yet. Parallel to this assumption, it also has to be taken into account that there are many different contexts in which signs play a decisive role. Since it would not only be uneconomical and technically hardly realizable to adapt to each sign its own specific regularity, but which would also disavow the function of the sign to fulfill its social role, and since man as the creator of signs is existentially dependent on bringing order into the chaos of the multiplicity of sense data in order to be able to orientate himself in his environment at all, the sixth axiom, which I call the system axiom, formulates that signs are systemically organized. 86 Karl Bühler ’ s Axiomatics and the Axiom (1984) Johannes v. Kries, Charles S. Peirce, and Karl Bühler have repeatedly pointed out that the possibilities of human experience are inextricably coupled with certain concepts of space and time, which are to a substantial extent neurophysiologically conditioned. beyond the biological conditions of human possibilities of experience, all the cultural parameters have to be taken into account which leads to the fact that people think the way they think. In summary, however, biological and cultural conditions cannot explain why the sign-based actions of humans are as they are until it is systematically taken into account that the interpretation of signs as signs is a process. If we also take into account that the interpretation of signs must always be based on the delimitation as well as on the transfer of what is already known, we can make the previous formulation more precise and characterize the sign process as a continuous process. 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