February 2, 2008
Philosophy As Science: “Function” and “Energy” in Cassirer’s “Complex System” of Symbolic Forms
By Capeilleres, Fabien
Leibniz geht von dem Funktionsbegriff der neuen Mathematik aus, den er als Erster in seiner vollen Allgemeinheit fasst und den er schon in der ersten Konzeption von aller Einschrankung auf das Gebiet der Zahl und der Grosse befreit. Mit diese neuen Instrument der Erkenntnis ausgeriistet, tritt er an die Grundfragen der Philosophie heran.1 Wenn in der Schriften zur Logik und zur Mathematik ... die allgemeine Methode der Leibnizischen Philosophie sich bestimmte und ausbildete, wenn in ihnen das abstrakte begriffliche Fundament des Systems abgesteckt wurde, so tritt uns beim Ubergang zu den Problemen der Biologie die Leibnizische Metaphysik zuerst in ihrer konkreten Gestaltung mit der Eigenart ihrer besonderes Prinzipien entgegen. Der Entwurf der "allgemeinen Charakteristik," das Bemuhen um eine allgemeingultige Methodik der Forschung und der Beweisfuhrung hatte den Ausgangspunkt des Leibnizischen Denkens gebildet.2
THIS PAPER EXAMINES Ernst Cassirer's specific proposal for the solution to the classic problem: how can philosophy fulfill its ideal of reaching the status of scientific knowledge and become a science? By answering this question, the present study endeavors to fill an important gap in the Cassirerian studies, where that problem was never addressed. It also brings new material to our understanding of the longstanding tradition of Philosophie als strenge Wissenschaft.3 The exposition of Cassirer's solution will open new research in this field, in particular through a discussion with, first, the solutions offered at the same time by other neo- Kantian schools (Wilhelm Windelband and Heinrich Rickert for Bade, Leonard Nelson for the physiological trend) as well as by Husserlian phenomenology, and second, with the contemporary trend of "scientific philosophy" (the Vienna and Berlin Circles or more generally the fathers-and uncles-of analytical philosophy). Such a comparative study goes beyond the explicit scope of the present paper and Cassirer's achievement is where we should start.
This ideal of scientificity is almost as ancient as philosophy itself, since we already find it in Plato's fight against the Sophists. But the problem's articulation as well as the solutions offered took very different guises in the course of history. The late sixteenth and seventeenth centuries, with the rise of novel figures of science, inaugurated a new period of knowledge, and Kant's claim to bring metaphysics to the status of science, being indissociable from the success of the Newtonian physics, inaugurated another one. From then on, this problem can be accurately regarded as the inner force commanding the theoretical development of philosophy. In that perspective, the history of post-Kantianism can be considered as the history of a struggle to gain for philosophy a scientificity of its own. Fichte had no other aim than to achieve Kant's unfinished methodological accomplishment and soon suggested replacing the name "philosophy" by "science.""Transcendental idealism" and "speculative thinking" were the names for Schelling's and Hegel's methodological proposals to reach the same scientific status. Herbart and Fries both acknowledged their debts to Kant but shaped their philosophical identity with specific solutions to the problem of the scientific status of philosophical knowledge. Not only the shining stars of philosophy, but also authors of a lesser magnitude in these constellations participate in this extraordinary expansion of a new philosophical universe; for instance Salomon Maimon's skepticism is indeed a claim for philosophy as a science.4 The numerous and quite diverse neo-Kantian philosophers-such as Hermann von Helmholtz, Eduard Zeller, Albert Lange, and Alois Riehl- and schools-the neo-Herbartian and their journal, the Zeitschrift fur exacte Philosophie,5 the neo-Freisean like Nelson, the Southwest (Windelband, Rickert), Marbourg (Hermann Cohen, Paul Natorp, Emst Cassirer, Albert Gorland, and Rudolf Stammler)understood the "Back to Kant!" motto as a return to science against the wanderings of speculative philosophy and romanticism. The three main movements of the twentieth century, neo-Kantianism, phenomenology, and analytical philosophy, were conceived through the search for solutions to this very problem. Their specificity can be found in the particular solution they suggested, which, in turn, depended in a very large part on the sciences they took into consideration. We can therefore come to an understanding of philosophical modernity only through a careful examination of the development of the problem of philosophy as strenge wissenschaft-"rigorous science" or "rigorous knowledge," to use an expression that does not necessarily take the constitutive relation to logic, mathematics, and natural sciences for granted. This historical reconstitution is essential to the conceptual understanding of our philosophical identity and practices.
Ernst Cassirer's specific proposal for the solution to that problem is of a particular intrinsic interest because of his position within neoKantianism. He presents the accomplishment of the Marbourg School, a trend that offers among the most sophisticated options in neo-Kantianism, he has an outstanding knowledge of the recent developments of the sciences of his time and, last, as the author of Das Erkenntnisproblem and of the methodologically retrospective last volume of the Philosophie der symbolischen Formen (PdsF),6 he is thoroughly aware of the nature of the problem with which we are dealing.
He also carries extrinsic contemporary interests. For instance, in our current perspective, Michael Friedman uses his work as the best example of a "scientific philosophy" likely to help us bridge the gap between the continental and analytical traditions.7
Although Cassirer's philosophy of science is still probably the most studied aspect of his thought, the present problem-the scientific status of philosophy-is addressed neither in the current philosophical use of his work nor in the Cassirerian studies. Concerning the former, Michael Friedman would probably be the author holding the best position to do so, since he pays very scrupulous attention to the historical unfolding of "scientific philosophy" and gives Cassirer a special position in this history. But the Kuhnian background of the study leads to a double limitation. First, because the author subscribes to Kuhn's thesis, the problem of the scientific status of philosophical discourse is not questioned, nor is Cassirer's attempt to reach this ideal.8 Second, such a philosophical frame limits, on the side of the constitution of philosophy, the meaning of the expression "scientific philosophy" to the external relations with the sciences. If the sciences benefit from this relationship in a constitutive way, drawing on philosophy in the elaboration of new paradigms, philosophy seems not to profit from the relations in the same internal and constitutive way, since it gains only a new field of study (that I doubt it ever lost), or possibly some doctrinal elements, but not a new determination of its very concept, method, and status. In other words, I claim that the investigation should not be confined to the examination-however remarkable-of Kant's foundation of Newtonian physics or of Cassirer's analysis of Einstein's theory of relativity, but should start with Kant's original philosophical use of Newton's method to elaborate his entire system, or with Cassirer's philosophical integration of the mathematical concept of function to conceive of symbolization and his use of the energetics to organize symbolic forms in a system. It is only through the understanding of these internal and originally constitutive relations between philosophy and science that the expression "scientific philosophy" can take its full meaning, a meaning that was shared by the most important continental rationalist philosophers and by the members of the Vienna and Berlin Circles, principally Carnap and Reichenbach. In such a perspective, "scientific philosophy" will clearly appear as a distinctive branch in the tradition of Philosophie als strenge Wissenschaft.
As for Cassirerian studies, they are no exception to an unfortunate state of the history of philosophy that rarely addresses this question. Only one very particular aspect of the question appears, namely the query for unity and systematicity in the philosophy of symbolic forms. Even if unity, systematicity, and scientificity are intrinsically related to each other in the philosophy of symbolic forms, such an approach does not address the specific problem of philosophy as rigorous knowledge and its constitutive relations to science.9 The present paper is an attempt to begin filling this void.
More generally, this article forms the outline of a chapter for the history of philosophy as rigorous knowledge that I started to write a decade ago.10 At the root of that project lies the conviction that the gap between continental and analytical philosophy is more a historical and sociological matter than an effective conceptual problem leading to irreconcilable options. The reconstruction of the history of philosophy (starting with Leibniz and Kant) in the perspective of its claim to be rigorous knowledge can show that this "gap" is in fact only a crack delineating figures in a family picture, not the (conceptual) abyss separating, for instance, the rationalist and the romantic traditions within continental philosophy. But to sketch such a family picture, we have to take seriously into consideration the common aim of both continental rationalist and analytical philosophies-to "lead philosophy on the safe way of a science"!11-and to thoroughly analyze the philosophical and scientific means they used to fulfill this claim. It should also bring mutual respect, as well as peaceful and constructive debate among the heirs in order reasonably to share and cultivate this extremely rich inheritance. Against the current contempt for systems and strong doubts in the Cassirerian community concerning the scientific status of philosophy, I will start (1) with a reassessment of how Cassirer claimed scientificity and systematicity for every level of philosophy: for its idea as well as for the historical movement to which he belonged, neo-Kantianism, and for his philosophy of symbolic forms. Addressing the solutions offered to conceive of this systematicity, their inadequacy will be explained. I will then (2) show that the solution should be found in the function of symbolization. As it were, it is conceived of by Cassirer as a relation of integration and derivation that can be formulated as a mathematical function of the form (p(x). In a third step (3), using Cassirer's own modelization of the system of the Naturwissenschaften in Substance & Function (F[Phi^sub 1^(psi^sub 1^, psi^sub 2^), psi^sub 2^(psi^sub 3^, psi^sub 4^),Phi^sub 3^3 . . . ]),12 we will see that it should be extended to the Geisteswissenschaften. It produces the following formalization of the whole system of the symbolic forms: F[M(xyz), L(xyz), A(xyz), P . . . ], in which F represents consciousness conceived as integral, M the law of mythical thought (and its typical moment of symbolisation, expression), as a differential from F (it is a mythic consciousness), but integral for the relations x, y, and z (space, time, objective connections that, under this law, are mythic space, mythic time, and so on), L language, A art, and so forth.
This model provides two quite different aspects of scientificity. The first aspect addresses the question of the general status of philosophical knowledge. If philosophical operative concepts are "functional" concepts that reach "pure signification," philosophy can claim to be a knowledge that has reached scientificity. The second aspect addresses the more specific question of the status of philosophy as a systematic doctrine. The organization of the symbolic forms in a philosophical system constitutes philosophy as a doctrine. The general question of the status of philosophy ought to be specified to the problem of the system. We will see that the possibility to formalize the structure of the system shows that the model for this organization is itself functional. It is built in the continuity of Cassirer's understanding of the general theory of relativity and opens the way for a more meaningful analogy for systematicity, namely, that of an energetics of the spirit similar to the doctrine of energetics in physics. Through the fulfillment of this double aspect, Cassirer's philosophy of symbolic forms strives to be a scientific doctrine and carries on the classical ideal of philosophy as rigorous knowledge.
I will conclude with a few implications of such a solution regarding the problem of the scientific status of philosophy, with respect to both the history of Continental philosophy and the philosophical consequences it carries concerning the common history, the current dialogue, and the possible collaboration of continental and analytical philosophies.
(a) Science and System in the Idea and the Reality of Philosophy. What is the configuration of the problem of scientificity of philosophy in Cassirer's thought? Cassirer's claim for a scientific status is asserted for three embodiments of philosophy: (1) its very idea ("idea" is here understood in a Kantian meaning, as a methodological horizon for research, leading to various concrete results), (2) neo-Kantianism as the historical current that revived the methodological means necessary properly to pursue that aim, and (3) his own work. To grasp the structure and signification of the problem of scientificity according to Cassirer, I will briefly expose the way it appears in these three levels. This will provide an insight into Cassirer's specific answers.
Among the numerous texts in which Cassirer describes the idea of philosophy and delimits its features, the inaugural conference at the University of Goteborg, Der Begriff der Philosophie als Problem der Philosophie (1935) is the most explicit and concise. "Philosophy claims to be the true unified science."13 The status of science that here appears in the mere designation of philosophy as a "Wissenschaft" has to be understood in a strict signification, as the end of the talk makes explicit: "the struggle is for an independent, objective and autonomous truth."14 The other distinctive character is unity. Not only does philosophy claim to be true knowledge, but it claims to be a knowledge of the unified totality. The quotation continues: "The whole of its striving and its conceptual longing appears to be aimed at absolute unity, at the unity of being as well as at the unity of knowledge."15 So we are dealing with three essential traits: truth, unity, totality.
In its sheer ideal figure, truth manifests only a requirement for universality: philosophical propositions should not express individual opinions. But the relation with unity and totality brings another dimension: the truth of philosophical judgments should not be relative to a particular field of being or of knowledge, without any consideration of the other fields, for their validity would then claim an illicit universality. In other words, the truth of the propositions should be ascribed by a strict delimitation of their field of validity, which is possible only through a systematic organization of all the fields, not only because of the logical completeness it brings, but for the mutual limitation it produces. So the three features of the idea of philosophy are synthesized in the concept of system, and it is no surprise that Cassirer, when he wants to summarize this question, quotes Hegel's famous sentence taken from the Phenomenology that the truth is the whole.16 It allows the philosopher to draw attention to the fact that the delineation is not only, so to speak, horizontal or operated between constituted fields, but also vertical or- between strata of the constitutions of each field.
For Cassirer, this idea is the regulative ideal underlying the historical and conceptual development of philosophy since Heraclites. Actual philosophies are the result of determined work within the scope of this idea, and their specificity is produced by the very methodological concept that commands the configuration of the system. Descartes's Mathesis universalis, Leibniz's Scientia generalis, and Kant's transcendental method are examples of this methodological concept of philosophy that plays the role of a principle of the understanding in order to realize the idea into a detenrrined result-the body of knowledge called a philosophical system.
We can conclude that, at this level, the scientific status of philosophy is a goal immanent in its very idea, and that it carries methodological implications, the main one being systematicity. Let us now move to the second level, the idea of philosophy as embodied in neo-Kantianism.
If we examine the 1928 article "Neo-Kantianism," we find that Cassirer's description pictures a characteristic implementation of the idea of philosophy. The simple feature of truth and universality is immediately asserted: "The individual thinkers who belong to this movement differ from each other in their interpretation of the Kantian doctrine as well as in the result which they reach from the Kantian premises. But, notwithstanding differences of detail, there is a certain methodological principle common to all of them. They all see in philosophy not merely a personal conviction, an individual view of the world, but they inquire into the possibility of philosophy as a science with the intention of formulating its conditions."17 "Science" here carries for Cassirer the same meaning as Kant's concept of Wissenschaft, when the latter designates the expected state of future metaphysicsa level of knowledge equivalent to mathematics (only, for Kant, discursive instead of intuitive).
How was such a goal achieved? "They take their cue from the most general statement of the Kantian problem in the Preface to the Critique of Pure Reason and in the Prolegomena."16 It is the methodological dimension that is now stated. If the references are to the B Foreword to the Critique of Pure Reason and to the Prolegomena, it is because these texts emphasized the scientific status and methodological characters of the critique. The Prolegomena are not only a prolegomenon to metaphysics as science; following an analytic exposition, they also give a clear illustration of the transcendental method that allows scientificity to be attained. Roughly speaking, this method is to start with a set of determined established facts (Euclidian geometry, Newtonian physics, moral consciousness)19 and inquire into their a priori conditions of possibility.
Is it a systematic task? Indeed: "Beginning with certain epistemological enquiries, it extended gradually over the whole field of philosophy," is among the first sentences of that short article. The last one is: "[W]e may say by way of summary that it [the neo-Kantian movement] has gradually encircled the total orbit of knowledge by trying to advance more and more from the 'abstract' to the 'concrete,' from the general principle of knowledge to the specific content of mental culture." So not only does "Neo- Kantianism find itself confronted with a new task inasmuch as it must face a different state of science itself"; not only does this movement have to face a new state of mathematics and physics; it also has to follow the enlargement of the field of inquiry that post- Kantian systems had started, and it was in this way led to a philosophy of culture. From this point of view, and even if in that text the philosophy of culture mentioned is Windelband and Rickert's philosophy of value, there is no doubt that Cassirer's philosophy of symbolic forms, which claims to extend Kant's "critique of reason to a critique of culture,"20 carries on that dynamic enlargement of neo- Kantianism. I hope that these schematic suggestions suffice to indicate how, for Cassirer, scientificity and systematicity express each other, s'entr'expriment as Leibniz would say. This conception first appeared with Descartes and, more clearly, with Leibniz. It reached its full development with the so-called German Idealism, in the works of Fichte, Schelling, and Hegel. In this context, it already rhymes with scientificity of knowledge. But before we examine the third level, Cassirer's claim of systematicity and its relation to scientificity, it is necessary to correct a deeply misleading understanding of systematicity.
According to a widespread interpretation developed by Heidegger, systems are the late accomplishment of onto-theo-logy. "Onto" because, since the ontological difference between being as a verb and the substantivation of its present participle is not assumed, the origin of things is itself conceived of as a thing, namely God. Hence the "onto-theo": a system is always the projection or the shadow of the totality of being conceived of as God in its figure of Summum ens. As for the "logy": the logos here at stake (as opposed to the logos of poetry, originally apophantic) has several defects. As an ontology, it is synonymous with the pure mind of God. In other words, the categories of being are its operative ideas, its reason. So whatever is considered as being can be grasped only through that kind of logos, namely reason. Sein is therefore missed again since it is precategorial, and all things are put together and conceived of via the principle of reason, which ultimately leads to technology. The modern figure of the system adds to the classic Summa the feature of subjectivity, Hegel's motto, "We ought to think the Absolute not only as substance but also as subject," being the crying illustration of this unfortunate fate. This late feature superimposes two figures of the fundament, God and the ego, the second adding to the first the idea of a process within the substratum. After Hegel, the meaning and significance of the system is supposed to decline. Schleiermacher, Herbart, Schopenhauer, more or less contemporaries of the former authors, already do not attribute the same value to systematicity and, to sustain the claim of philosophy as a rigorous knowledge, they use different tools. With the split of the Hegelian School, the unity of knowledge, reflecting the unity of being, is dismantled. Figures like Kierkegaard, Marx, and Nietzsche follow, each showing, in his own way, vacuity of systematicity.
Such a picture is misleading for at least five reasons. First, since Leibniz and Kant, neither substance nor subject is conceived of as a metaphysical substratum. And at least since Kant, the reality of the Summum ens has vanished to the profit of an analytic of human reason. In other words, the systems are systems of concepts of functions and of significations, not concepts of beings or things. second, the ontological difference is, indeed, an essential object of reflection, but it never takes, as it does for Heidegger, the structure of a negative theology ("Semn\). Onto-theo-logy and metaphysics of subjectivity are therefore irrelevant here. Third, radical critiques of systems are just as traditional as systems. Within the context here addressed, one can mention Hamann's and Jacobi's oppositions to Kant as well as Gottlob Ernst Schulze's skeptical attacks, Holderling's early dissociation from Schelling and Hegel, as well as the very large and diverse group of thinkers we refer to as "German Romanticism" (Herder, Goethe, Schiller, Schlegel, Novalis, and so on). When compared to the critique of rationality and systematicity that was accomplished then, contemporary critiques have little accuracy and no substantial originality; they should not justify a historical category such as "the age of systems." Fourth, not only are great philosophers, such as Dilthey and Husserl, caricaturized or omitted, but so is neo- Kantianism, the main movement of German philosophy between 1870 and 1910. Within neo-Kantianism, systematicity was, as it had been for Kant, "that which first makes ordinary cognition into science."21 If these philosophers disagreed on what the system of philosophy should be, they nonetheless agreed that philosophy ought to be systematic. And fifth, the concept of "reason" has changed drastically, precisely with the extension given to that concept by eighteenth- and nineteenth-century systems. These systems (a) had much wider fields than the one of classical reason (myth, language, art, technology, economics, and so on), and (b) put their own operative rationality as well as the whole categorical structure in perspective (although, indeed not to the point to give it up to poetry), a point that Heidegger, given his reading of the late Natorp and Emil Lask, could deny but not ignore.
We now move to Cassirer's systematic conception of philosophy. In order to dissociate the philosopher's aim from its (possibly defective) result, we first have to make clear his claim in favor of a systematic philosophy and assert its relation to scientificity.22
During his philosophical apprenticeship in the Marburg School, Cassirer worked with philosophers for whom either philosophy was a system or it was simply not philosophy. Both Cohen and Natorp argued that philosophy can be developed only in the perspective of the system.23 Although this inheritance does not imply that Cassirer accepted the elements, structure, and specific method of the systems built by his masters, he did endorse a concept of philosophy as a system.
Because I will return to how this question is treated in 1910 in Substanzbegriff und Funktionsbegriff, let me skip this stage and briefly expose this question in the PdsF.
First, from a genetic point of view, it is interesting to note that in the first mention of the project of the PdsF, in the last chapter of the 1921 Einstein's Theory of Relativity, the systematic dimension of the project is strongly emphasized: "systematic philosophy .. . has to embrace the totality of the symbolic forms and to refer each individual form its fixed place in this totality."24 Far from being a formal requirement, systematicity appears to be the necessary condition for a critique, a philosophical and true determination of the concept of objective reality (Wirklichkeit, the objective or effective reality, as constructed in every dimension of objectivity, not Realitdt, any given)25 and the subsequent concept of truth. For the philosophical lesson of the doctrine of relativity in physics is not that knowledge is relative in the skeptical sense of negative value unable to reach absolute validity, either because the thing itself cannot be grasped or because the truth about a given phenomena is scattered in different fielda of knowledge (that might in turn be considered as dependent from a common absolute thing), but that it is possible to articulate all the different determinations of objective reality in a unified system (that does not claim to ultimately grasp a preexisting absolute reality).26 Systematicity is therefore immanent in the very essence of the project, and we will later see the importance of the concept of relativity in the construction of the system.
In 1923, the problem of systematicity was at the very core of the philosophical project, which sought:
A standpoint situated above all these forms and yet not merely beside them-a standpoint which would make it possible to encompass the whoke of them in one view, a view which would try nothing else but to make visible all these purely immanent relations of all these forms to one another, and not their relations to an external, "transcendent" being or principle. We would then obtain "a philosophical "systematic"27 of the spirit in which each particular form would take its meaning purely from the place where it stands, a system in which the content and signification of each form would be indicated by the richness and the specificity of the relations and concatenations in which it stands with other spiritual energies and ultimately with their totality.28
So in the formulation of the general project of the philosophy of symbolic forms-symbolic forms described beginning in 1921 as "spiritual energies"-the systematicity is not only a property of a philosophy of the spirit but also, as it was for Cohen and Natorp, a guiding thread, a part of the method to understand the meaning of each form and of their totality, that is, culture. In other words, Kant's transcendental topic, as reinterpreted by Cohen in his general comprehension of the transcendental method makes systematicity not only a requisite of philosophy but also a category of reflection for its elaboration.29
When Cassirer moves from the project to its realization, he gives a useful but nonetheless obscure indication. Refusing the speculative (that is, for Cassirer, Hegelian) concept of system, and wishing to enlarge the epistemological conception at work in S&F, the philosopher, far from condemning systematicity, claims a more subtle elaboration of the system: "And yet, in such a perspective, we by no means abandon the interconnection [Zusammenhang] of the particular forms, but, on the contrary, this perspective sharpens the idea of the system by replacing the concept of a simple system with the concept of a complex system."30 So in 1923 not only is (the project of) the philosophy of symbolic forms a system, it is a "complex system." In 1924, the second volume of PdsF still strongly asserts that mythical elements have to be understood within a systematic unity, and that myth as a symbolic form is to be situated in the global system of symbolic forms since "the globality of these forms really constitute a systematic unity."31
In 1929, Cassirer not only insists on the systematicity of his philosophy, writing, for instance, that each problem takes a different shape when it is related to "the fundamental systematic question of the 'philosophy of symbolic forms.'"32 He also makes a retrospective insight: "The third volume of the Philosophy of Symbolic Forms represents a return to the investigations with which I began my systematic and philosophic work two decades ago."33 Cassirer refers here to S&F, an indication to which I will return.
Did Cassirer ever renounce this conception of philosophy as a system? In the conclusion of his 1944 book, An Essay on Man, he writes: "A philosophy of culture begins with the assumption that the world of human culture is not a mere aggregate of loose and detached facts. It seeks to understand these facts as a system, as an organic whole."34 Can this assumption be confirmed, or must it be renounced? The last paragraph responds, returning to the concept of a complex system: "Philosophy cannot give up its search for a fundamental unity in this ideal world [of human culture]. But it does not confound this unity with simplicity."35
We can conclude that from his early works until his death, Cassirer upheld a systematic concept of philosophy. His philosophy of symbolic forms must therefore be understood as a system. However, this statement of systematicity does not imply that Cassirer was not highly aware of the difficulties and precariousness of systems. Indeed, at each step of the historical and conceptual development of his philosophy, he warned his reader that the ideal of systematicity remains an ideal that can be fulfilled only on a temporary basis and inadequately.36 But, according to the author of the PdsF, philosophy cannot renounce this ideal without renouncing its own essence.
As for the requirement of scientific status, Cassirer seems to think that it is quite obvious, the task of philosophy having always been a search for truth (concerning the answers to determined questions). Explicit statements are therefore present, but not as numerous as those for the claim of systematicity. I find interesting to note that, even in the most difficult period of his life and in one of his most modest (not to say "pessimistic") texts, Cassirer still claims that the philosophy of symbolic forms is striving to be a science. In the 1938 discussion with Conrad Marc-Wogau, Cassirer reasserts the filiations with Kant and in particular with the two main references to the scientific status of the critique, the Prolegomena and the transcendental method: the philosophy of symbolic forms "strived only to give the 'Prolegomena to a future philosophy of culture.'"37 To do that, it not only started from the "fact of science" (an expression used by Cohen to characterize the starting point of the transcendental method) but also from "the 'fact of the Geisteswissenschaften' that stands in front of us and that Kant did not know and could not expose in its actual form."38 Just as the Critiques undertake the foundation of the metaphysics of nature and of morals, the PdsF exhibits the original functions that found the "globus intellectualis," the whole of the Naturand Geisteswissenschaften, and it will provide a philosophy of culture that is somehow still to come. In Cassirer's words, the PdsF "did not strive to erect a finished edifice, but only wanted to sketch a groundplan (Grundrifi)."39 If we keep in mind the Kantian context of theses sentences, the parallel with the first page of the Architectonic of the KrV is striking. Then Cassirer continues, "Such a schema is, I believe, a science in progress, a science still in many ways in statu nascendi, hardly satisfactory."40 So indeed Cassirer shows some reservation here, but he nonetheless conceives of his philosophy as a science.41
So the real question is not if philosophy should be a rational activity producing a body of true sentences, but what the correct conception of truth is, and how philosophical practice can lead to a scientific result. The unfolding of the problem of systematicity will provide an answer to these two questions. Our problem should therefore now be: what is the structure of his system? I shall begin with an examination of the solutions offered in Cassirerian studies.
(b) The Aporia of the Problem of Systematicity. The preceding discussion allows us to characterize certain components of Cassirer's system, components that any exposition of the nature of this system has to take into account and elucidate.
This system seeks to be a "sharper idea of the system," and this more rigorous idea of the system is characterized as a "complex system." Further, it is opposed to a speculative system in the following two ways. First, the system is not an "abstract universality" but a "concrete totality." This requirement was recognized by Hegel too (as well as by Leibniz and Kant), but, in the eyes of the members of the Marburg School, was never fulfilled in his philosophy.42 This general claim is important because it gives the logical status of the concept of system: as we will see, only a functional concept can reach this concrete universality. Second, the system is what we usually call, rather vaguely, an "open" system: systematicity is an aim, an ideal of unity that cannot be achieved once and for all.43 Philosophy as science is therefore an ongoing task.
Interpreters of Cassirer's philosophy most commonly understand the system of symbolic forms in the following way. First, they usually refer to what Cassirer calls "phenomenology" with a limited reference to Hegel. In the terms of this interpretation, the principle of organization seems quite simple: the process of symbolization unfolds teleologicaly (although there is no metaphysical necessity in this development): starting with expression (Ausdruck), it goes through presentation (Darstellung) and finally reaches pure signification (reine Bedeutung). This journey of the spirit through the levels of symbolization leads it to intellectual freedom. The objectified symbolic forms (myth, religion, language, art, technology, ethics, law, history, science) should-according to this interpretation-obey this general process, but the question remains: how? In other words, how do the various figures of the spirit perform the symbolic dynamic of the spirit, and how does the system of symbolic forms organize them in order to understand and explain the function they accomplish within this dynamic?
In Cassirerian studies, the earlier solution offered consisted in a linear classification, ordering the figures along the axis leading from expression to pure signification. This interpretation starts with myth, for it is, so to say, the matrix of all figures and the closest to expression, and it ends with science because of its relation to pure signification. But we know nothing of the organization of the forms in between these two poles. Moreover, building a linear connection of the figures between myth and science is meaningless and impossible for several reasons. The most general reason is that Cassirer conceives symbolic forms as "different directions of objectivization" and writes, while discussing Natorp's polydimensionality of the spiritual world: "The difference between the fields of spiritual meaning is a specific difference, not a quantitative difference.... The globality of the possible stages of the objectivization of the spirit cannot be projected upon a single straight line without, by such a schematic model, obscuring essential traits."44 It is therefore impossible to understand the system as a linear development of successive forms. Moreover, such a schema could hardly be called a "complex system."
These difficulties led from the image of the line to the very traditional metaphor of the tree. Symbolic forms differentiate from the mythical trunk like several branches striving, each in its own way, to reach the light of pure signification through the half shade of presentation. This schema is more appropriate to Cassirer's own explanations, but it is merely metaphoric, and, as a metaphor, it poses two problems. The first one is similar to the use of myth and allegories by Plato: although a philosophical explanation might use metaphors, it cannot rely on them because they belong to a kind of thought which, in philosophy, cannot reach pure signification; philosophical knowledge would remain, at best, at the level of presentation. second, this metaphor does not give a philosophical explanation of the process by which forms differentiate themselves from myth and from each other. Nor does it provide the principle of their differentiated unity within the whole, or indicate up to which level each form can develop (besides myth, do they all reach pure signification?). Even if this metaphor is not necessarily wrong, it remains a metaphor and is therefore quite insufficient.
If one really wants to use a metaphor, a recent study, Michael Bosch's Das Netz der Kultur, Der Systembegriff in der Kulturphilosophie E. Cassirers,45 suggests a much better one, namely, the image of a network. This metaphor has many advantages, Cassirer's use of it being an important one.46 But the problems it raises are no less important. First, although more accurate, it still is only a metaphor and as such, in philosophy, belongs to presentation, not to pure signification. second, it is an ambiguous metaphor it is not differentiated from the picture of the web, also used by Cassirer in similar contexts, and it refers to several fields (theory of communication, biology). This imprecise meaning might also allow a conflation with certain fashionable contemporary interpretations such as the poststructuralist determinations of the concept of structure and some of its models: concepts of "rhizome" and other "thousands plateaus" (Deleuze and Guattari) or Barthes' semiological systems. An operative model of the system cannot therefore be build on the basis of this picture. To solve this problem of systematicity, my thesis is trifold: (1) I claim that Cassirer uses the mathematical model of the function to conceive of the process of symbolization. (2) I uphold that, as the process of symbolization is "one and the same function" common to all forms, the philosophical system describing the unity of these forms extends to the unity of the whole, the abstract structure of the function of symbolization as formalized in a mathematical model. (3) Cassirer's understanding of the energetics and of the theory of relativity provides the model to conceive of the relations of the forms within the whole system. The structure of the system of symbolic forms then becomes a generalization of the structure of the process of symbolization. Philosophical thought appears as a specific symbolic function that builds philosophy as a doctrine according to its understanding of a rigorous knowledge.
In order to apprehend the unity of the system of the philosophy of symbolic forms, we have to understand the function which Cassirer describes as providing "a standpoint situated above all these forms and yet not merely beside them-a standpoint which would make it possible to encompass the whole of them in one view."47 If there is a general agreement that this function is symbolization, the nature of this function is still debated. I shall now explain it, starting with the definition of a symbolic form.
(a) Structure of the Function: Quality and Modality of Relations. The definition of the symbolic form most commonly quoted because of its explicit nature is the following: "Under "symbolic form," one should understand each energy of the spirit, by which a signification content is attached to a concrete sensitive sign and internally belongs to that sign."48 Cassirer defines the concept of "symbolic form" in terms of a concept which is just as enigmatic, that of "energy of the spirit," and he seems to designate by this certain activities of meaning production, activities specific to myth, to language, to technology, to history, to science, and so on. With respect to the very project of the philosophy of symbolic forms, each of these forms is therefore described in terms of energy.49
In this way, the symbolic form is a production (according to a law) before it becomes a product, an objective domain (a point which is the fundamental postulate of critical idealism): it is a "unitary activity" which synthesizes the diversity of conscience in a unitary signifying framework according to a specific rule or principle, not the cultural domain we think of when we say "myth," or "science."50 It is important to notice that two different characters are interwoven in this concept of "symbolic form": the "form" is the determined expression of a rule, while the "symbolic" dimension refers to the "energy," that is the dynamic connection between the elements and the law that unify them. For Cassirer, each representative element must consequently carry the mark of this unifying relation. To use a metaphor, this mark is like the monogram of the law, the condensed expression of the more general form. It confers the element the status of a sign since it expresses the law. But, as Cassirer's definition states, this mark is not an external or extrinsic label, it is the very form of the element itself as an element of Kant's expression "formaliter spectata" is here to be remembered and actualized. An element of a group can only be regarded as an element through the relation (a law) that defines the group. When we take the element into consideration, it is only through the consideration of the relation in it. If we now go back to the element of consciousness, philosophy should be able, by moving from the form of a defined element to the most general moments of the synthesis, to discover the general rule, the principal of global unity and thus the semantic system that configures the sign. It is therefore necessary to focus on the way in which a lived aspect of consciousness, carrying necessarily the mark or stamp of the synthesis, is unitarily linked by it to the rest of the diversity and permits us to rediscover the principal of the stamping. Following this process is to address symbolization.
According to Cassirer, symbolization consists in a "fundamental character of consciousness, namely, that the whole is not obtained from its parts but that each position of a part already conceals in itself the position of the whole, not as to its content, but as to general form and structure. Every particular belongs here originaly to a determined complex and brings with itself to expression the rule of this complex."51 In other words, all representative content, to the degree that it is the lived aspect of consciousness, is determined formaliter spectata by the rule of the globality of the structure in which it appears and of which it carries the mark. "Here" is a sign only by implicit reference to a topology also defining "there" and "over there." This structure, which is none other than a rule of consciousness, is thought of in terms of a relational structure. Thus the element represents the whole, that is characteristic of a symbol, but this presentation occurs in terms of a relation or link which can be approached in a formal manner. It is by questioning the conditions of the possibility of this reference of the element to the whole that it is possible to disengage the general principle of symbolization.
The most abstract moment of this link, or, in other words, the most formal relational structure that Cassirer disengages is precisely that which he calls the relation, according to its quality:
As first moment, we encounter here a difference, which we may designate as the difference between the quality and the modality of the forms. By the 'quality' of a given relation we here understand the particular type of connection by means of which it creates, within the whole of consciousness, series whose members are subject to a special law of order.52
We can already observe that the representative elements that constitute the contents of consciousness are organized as a unity consisting not in a sum but in a series that depends on a law. Because these elements are still organized in a serial fashion by a relation, that one can discover the law through which the part-that is to say, in fact, the element-relates to the entirety: the possible whole of the elements. That which links the "here" to the "there" and to the "over there" is not a visible agglomeration, it is, rather, the placement in a series based on the relation of juxtaposition. Space (the law of juxtaposition), time (the principle of succession), the conceptual connections (called, in a Kantian vocabulary, categories) and number constitute the formal relationships fundamental to symbolization. These relationships structure the unity of consciousness and the unification of the contents that result through symbolization. The diversified unity of consciousness is, in this respect, thought of as diverse ways of setting relations: space, time, and objective connections. Through such an analysis, the philosopher reaches the transcendental sphere: "it is precisely the pure relation which governs the building of consciousness and which stands out in it as genuine 'a priori' as the first [factor] according to the essence."63 Cassirer declares that he is in perfect agreement with Natorp when the latter asserts that consciousness is relation.
The formal unity of consciousness in representation finds itself thereby deduced as terminus a quo.54 Cassirer conceives of the last term of the subjective pole as pure spontaneity of the I, the originary position of all relations. In other words, position, conceived of as the original synthetic unity of perception, as the act of the imagination (and not of understanding) is the fundamental relation. It appears as such only to the philosopher and, on the one hand, displays itself in post-predicaments (the enumerated relations), and on the other hand, as we shall soon see, receives modalities.
These relational unities must be unified in turn within a single framework. Although space, time, and objective connections cause punctual unification of contents, these relations themselves must be unified within consciousness in order that one can conceive of, on one hand, the unity of the subject, and, on the other, the global unity of representations, that is: a world. In other terms, the lived aspect of consciousness must have a spatial, temporal, and categorical unity, but space, time, and objective connections must be homogenous, unified within the same framework. It is this global unitary and general process that Cassirer designates as energy or as the specific direction of the spirit, and which is identical with the symbolic form as such. At this abstract level, all forms consist in the same process. As soon as it becomes necessary to disengage the legal principal of the putting in form, it is necessary to question the specificity of each symbolic form.
Cassirer thematizes this aspect in terms of the modality of relation.56 Qualities of relation experience a different actualization depending on the specific framework, the symbolic form, or even the specific nature of the formal network in which they are inserted. Indeed, "[t]hus, taken abstractly, both the mythical and the scientific explanation of the world are dominated by the same kind of relation: unity, and multiplicity, 'coexistence,' 'contiguity' and 'succession.' Yet, each of these concepts, as soon as we place it in the mythical sphere, takes on a very special character, one might say a specific 'tonality.'"56 It is not the quality of fundamental relations (space, time, categories) that are different in science and in myth, for instance, but their modality. We see then, that in order to characterize a specific form of relation in its concrete application and concrete meaning, we must not only state its qualitative attributes as such, but also the whole system in which it stands. If we designate schematically the various kinds of relationssuch as the relations of space, time, causality, and so on-as Ri, R2, R3 ..., we must assign to each one a specific "index of modality" mu^sub 1^, mu^sub 2^, mu^sub 3^ . . . , denoting the global context [Zusammenhang] of function and meaning in which it is to be taken. For each of these global contexts of signification, language as well as scientific cognition, art as well as myth, possesses its own constitutive principle which set its seal [Siegel], as it were, on all the particular figures within it.67
This is to say that the qualities of the relations, while remaining valid in their abstraction, experience inflections depending on their relational context, be it one of myth, geometry, or aesthetic intuition; the juxtaposition-the relation of spatiality- is different based on whether the line is perceived as a boundary between the sacred and the profane, a mathematical plane, an artistic ornament, and so on. We thereby rejoin the specific symbolic form as such.
In terms of symbolization, any perceptual element is integrated within the series of a symbolic form by its integration in what Cassirer calls the "quality of relation," that is, the serial of space, the serial of time, objective connections, and number. These qualities of relations are submitted to a higher law which we can discover by analyzing the "modality of relation," the specific shape of space, time, concepts, and number as they appear in myth, art, science, and so forth. We then reach the specific law which commands the series of the relations and therefore the serial order of their perceptual elements (for instance "the law of concretion" in mythical thought, common to mythical space, time, concepts, numbers, and pervading all mythical element conceived as spatial, temporal, and so on).
The relational structure of consciousness is thus conceived of, on the one hand, as the collection of functions or the "originary forms of synthesis" that we have looked at, collection which, on the other hand, must be conceived of according to a transformation prompted by the semantic system or the symbolic form in which it operates: myth, religion, language, art, technique, morals, law, history, science, and so on.
This general relational structure of consciousness is intrinsically a symbolic structure, since it is the relation that constitutes the symbol. A more concrete example can now be supplied. If I say, "at the orient," its antonym, "the Occident," immediately comes to the listener's mind, or at least is negatively present in the understanding of the former expression. The position of a spatial term is thereby correlative to the position of another spatial term within a unity because, according to Cassirer, the totality of the topographic system is formally established with the first term. The quality of this relation is obviously space. What is its modality? Certainly language, but in what sense? The antonym of "orient" is not "west" and we cannot imagine Shakespeare writing "Lo! In the east where the gracious light Lifts up his burning head";58 it is not the opposition of abstract magnetic coordinates we are dealing with here. One of the first coordinates of the mythic consciousness finds itself within this lexical couple, the schema served to fix both space (orient and orientation, from orienter, face the east) and time, that is, the trajectory of the sun. Moreover, with this simple orientation, a symbolic charge associated with this scheme is also put in place: sunrise is the place of the origin, of day, of life, and so forth, whereas sunset is that of the end, of night, of death and these first coordinates embrace the human universe.59
The fundamental tie (the relation as a determined serial rule) which unites the given element with the global structure of consciousness appears in the said element, making it pass from the status of a simple given (an isolated and crude element, "nonrelational," one might say) to one of a symbol. The element as such, in its formally determined essence, conveys transcendence and refers to an alterity. This symbolic charge of a determined sensory element is what Cassirer calls "symbolic pregnance": "the way in which a lived perception [Wahrnemungserlebnis], as a 'sensory' experience [Eriebnis], contains at the same time a certain nonintuitive 'meaning' which it brings to an immediate and concrete presentation."60 Thus he designates by this term the "ideal interwovenness," the "reciprocal relatedness" between the single phenomenon of perception and a totality of meaning which configures it, transforms it into a sign or a symbol, a symbol which it, in turn, inhabits.61
(b) Process in the form: Integration and Derivation. We presently possess the constitutive elements of the general process of symbolization. To understand how this process can be called a function in a strict meaning of that word, and to grasp how it can provide Cassirer with a perspective for the systematic unity, it is now necessary to examine how the paradigm of integration and derivation, which it relies on constantly in the three volumes of PdsF, intervenes in this process.
We have seen that consciousness is conceived of as a pure relational fabric and that each element of consciousness comprehends its globality:
Accordingly, there is no 'something' in consciousness that does not eo ipso and with further mediation give rise to 'another and to a series of others' such as the very nature of representation as a setting forth in a sign. For what defines each particular content of consciousness is that in it the whole of consciousness is in some form posited and represented."62
This fundamental tie, which unites the element with the global structure of consciousness, the individual and the universal, is thought of in terms of a mathematical model: "If we want to explain this property, by a mathematical analogy and symbol, despite the fact that it goes beyond the limits of mathematics, we can, in contradistinction to mere 'association,' chose the expression 'integration.' The element of consciousness is related to the whole of consciousness not as an extensive part to a sum of parts, but as a differential to its integral."63 The fundamental structure of symbolization is therefore conceived of by an analogy to the integral and the derivation.
We should also notice that consciousness is nothing less than the symbolizing structure as understood in terms of this mathematical model. "The 'integral' of consciousness is constructed not from the sum of its sensuous elements (a, b, c, d, ... ), but from the totality, as it were, of its differentials of relation and form (dr^sub 1^, dr^sub 2^, dr^sub 3^,.. .)."64
In the perspective of the history of philosophy as rigorous science, this conception relies directly on Hermann Cohen's interpretation and transformation of Kantianism firmly grounded in the 1883 study Prinzip der Infinitesimal-Methode and the second edition of his Kants Theorie der Erfahrung (1885). The transformation occurs within the Leibnizian framework of (a) the unconscious summation of petites perceptions (the infinitesimal small perceptions) that ends up producing a content of apperception and (b) the mathematical apparatus that Leibniz invents and uses to conceive the "labyrinth of the continuous" that is involved. This framework was then used by Salomon Maimon in his Essay on Transcendental Philosophy,65 to transform the meaning of Kant's anticipations of perception: the sensory data constituting reality (Realitat) do not necessarily refer to the affect of an external thing but can be unconsciously produced by spontaneity. In other words, the receptivity of sensibility can in fact be a lesser activity of the understanding. By such a transformation, transcendental idealism falls into a skepticism (we cannot know that the object of knowledge is a correlate of the thing) that is extremely close to Leibnizian idealism. Cohen's transformation assumes the Leibnizian tradition but rejects the filiations with Maimon because of its psychological formulation and the resulting skepticism. The Kantian Transcendental Aesthetics disappears as an autonomous part,66 the specific role it fulfills becoming a part of the pure transcendental Logic, ruled by the "principle of origin."67 Cohen's reelaboration of the aesthetic allows Cassirer to understand the process of symbolism as integration, or, more specifically, to understand the relation between the element of consciousness and the whole as a relation between integration and derivation. This interpretation of Kant as well as the conception of knowledge it induces was common to the three major members of the Marburg School.68 Indeed, this mathematical model intends to carry on the elaboration of critical idealism: the "sum of [discrete] sensuous elements" is the usual thesis of empiricism. It is a common misunderstanding to see in this idealism either an absolute idealism or a speculative subjectivism. To avoid such a mistake, one has to remember that Cassirer (like Cohen and Natorp) uphold a methodological idealism.
If we return to the different moments of this relation of symbolization, both in terms of its qualities and in terms of its modalities, how is integration conceived? On the first level, singularities are organized in a series and integrated into the relation based on its quality: the elements are determined based on spatiality, temporality, objecfive connections, and number. However, the qualities are always shaped by a modular index: space can be mythic (the frightening ocean beyond Hercules' pillars), aesthetic (wonderful cliffs over the sea!), legal (territorial waters), historical (the Mediterranean under Perikles, Carthage, and so on) or geometric (geography or the fractal shape of the coast). Moreover, these modalities are themselves integrated within a unique determination of consciousness: mythic consciousness consists of the modular unity of all qualities of relations, within a determined unity of space, time, concepts, and number. But as a process, symbolization is "like a single stream of life and thought."69 It is in order to name this global and living unity Cassirer coined the term "symbolic pregnance." This unity is a concrete unity, a unity of the particular and the universal, and the relation between integration and derivation is the only one that can describe it.70 Finally, at the last level, it is necessary to think of a unity of the individual concrete consciousness that can assume concurrently a point of view that is religious, artistic, historic, and so on (a Hegelian example: when the religious [artist] enters the church the power of expression involved in religious thinking makes him "bend the knee," but when the [religious] artist sculpts the wound of Christ he does not identify himself with Longinus, the Roman centurion inflicting the wound). In this manner, the modalities of consciousness are themselves integrated within the global unity of consciousness. We can consequently think of the human as a "symbolic animal," to reuse the expression taken from An Essay on Man.
What are the implications of such a mathematical analogy for the conception of the philosophy of symbolic forms as a complex system and its possible status of science?
We have seen that Cassirer formalizes three things. First, in an initial step taken in S&F, he (a) makes explicit that the functionality of scientific concepts is accurately expressed by a theory of knowledge that describes their form as a mathematical function of the type F(x); and (b) extends the validity of this mathematical form to the philosophical conception of the fields of physics and of their unity. He is then able to put into a formula the system of the sciences of nature. In a second step taken in the PdsF, he (c) formalizes the process of symbolization. This is accomplished by broadening the same conception of functionality, and we saw how this extension is made both horizontally or in width, to embrace not only science but also myth language, and other such things, and vertically or in depth, to understand not only conceptualization of laws, but also symbolization in forms. In this second step, a stage (d) that would construct the system of symbolic forms in the same way the system of sciences of nature where modelized in (b) is, as we will see, just suggested.
At this point, my thesis is quite simple: I claim that we should and can do for the second step what Cassirer did in the first one: add to point (c) a moment (d) that formalizes the complex system of the philosophy of symbolic forms by using the models Cassirer gives us. In other words: my interpretative hypothesis rests on a simple structural implication: if we take seriously Cassirer's attempt "to apply [his] findings [of S&F] to the problems of cultural sciences,"71 we should be able to develop the following analogy a:b :: c:d. Constructing (d) on the basis of the symbolic function should give us the functional modelization of the system of the symbolic forms exactly in the same guise Cassirer modelized the system of the Naturwissenschaften in (b) on the basis of the conceptual function.
We can expect two main benefits from such a (re)construction. The structure of the "complex system" of symbolic forms would clearly appear for the first time, and this structure would likely be functional, bringing the philosophical conception of the "morphology of the spirit" to pure expression, a kind of knowledge that can legitimately claim to be scientific. The main purpose of the present article would then be fulfilled. A couple of secondary benefits might also be worth mentioning: Cassirer's evolution from 1910 to 1921 would assume a remarkable coherence; the consistency and the completion of the mature philosophy of symbolic forms would be exhibited through an exegesis that uses only internal (Cassirerian) principles, and so on. So now let us see if such a (re)construction is possible.
The first stage of this reconstitution is to check the extension of the mathematical model Cassirer constructs for symbolization. The second stage will be the possibility of a formulation of the system of all symbolic forms analog to the system of the 1910 formulation of the system of Naturwissenschaften. I shall then explain the meaning of this formulation regarding the concept of energy that constitutes a key notion in the definition of a symbolic form (gamma).
(1) That the Mathematical Model of Function is Valid to Conceive "Forms of Any Kind." In the General Introduction to PdsF, where Cassirer introduces symbolization as integration and builds the general analogy with the mathematical function, he warns his reader: this mathematical analogy "goes beyond the limits of mathematics."72 The third volume offers more information:
In fact, all our preceding inquiry has repeatedly shown us that what we call the symbolic formation of the perceptual and intuitive world does not begin with the "abstract" concept, and certainly not with one of its highest expressions, the concept of exact science. In order to understand this mode of formation and its fundamental direction, we had to begin our inquiry at a much lower level-we had to go out of the dimension of the scientific concept of the world, b