Felix Noeggerath on Kant: Transcendental Synthesis as a Principle of System Formation

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Walter Benjamin called Felix Noeggerath (1885-1960) the “universal genius” or simply “genius.” In his 1916 treatise “Synthesis and the Concept of System in Philosophy,” Noeggerath offered a reading of Kant’s concept of synthesis in an original and radical manner. He dares to confront thought with the incommensurability of atheoretical Being. The linkage between logic and incommensurability is what he calls rationalism. In contradiction to this claim, any attempt to exclude atheoretical Being from the realm of logic is anti-rationalism. Noeggerath elaborates on this in a penetrating discussion and modification of epistemological positions, especially those of the Marburg School and Hermann Cohen. Noeggerath constructs a notion of the philosophical system with the help of Kant’s three tables of transcendental judgements, categories, and principles in the Critique of Pure Reason. Each of these tables is known to contain 12 individual elements in four groups of three each. For the systematic division, the third group under the title “Relation” is decisive. Noeggerath assigns one systemic part to each kind of relation: “For it is to be connected: the categorical relation with ethics, the hypothetical with logic, and the disjunctive with aesthetics.” As a result the classical sequence, beginning with logic, is changed. “The order of the limbs is: a) ethics, b) logic, c) aesthetics.” In Noeggerath’s logical outline, specific mathematical concepts of meta-geometry play a decisive role. According to him, philosophy can resemble their preciseness in building a viable concept of the infinite. The prerequisite is that philosophy does not itself behave mathematically but proceeds along its own path in critical distance to the “specialized, act-kindred thinking” of the mathematician.

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The philosopher Felix Noeggerath (1885—1960) is almost unknown today. He is significant for Kant studies because of his 1916 Erlangen dissertation “Synthesis and the Concept of System in Philosophy. A Contribution to the Critique of  Anti-rationalism (With Two Excurses: ‘On the Judgmental Character of Meta-Geometry’ and ‘On the Platonic Concept of μεταξυ’)” [1]1. The work interprets the central concept of synthesis in an original and radical manner.

Noeggerath dares to confront thought with the incommensurability of atheoretical Being [Sein]. The linkage between logic and incommensurability is what he calls rationalism. In contradiction to this claim, any attempt to exclude atheoretical being from the realm of logic is anti-rationalism. Noeggerath elaborates this in a penetrating discussion and modification of epistemological positions, especially those of the Marburg School. The treatise remained unprinted, first due to World War I, and later due to certain publishing obstacles. Only now is it available to the public in a critical edition [2].

First, a few things about the author. Noeggerath was an impressive personality known by many people at the time. Nowadays, he appears only in connection with Walter Benjamin; still, his appearance in this context is noteworthy. Their acquaintance began around 1915—1916 in Munich while they attended university lectures together. Among many other things, Noeggerath was working on his dissertation. Benjamin calls him in his correspondence of the period the “universal genius” or simply “genius”: “The first time I was almost stunned by his absolutely universal education, since he is concerned — this is all at the same time—with the foundation of a philosophical system in very significant way; with mythology from Asia to early America, including all that is thereby related to it; with intensive philological studies; and with the proof of Fermat’s [last] theorem, in addition”2. There is indeed, in the words of Gershom Scholem, “no need to justify that a man of whom Walter Benjamin thought so highly deserves attention” [3. P. 80]. And so it was Scholem who meticulously developed his biography, although we know of no place where Noeggerath so much as mentions Benjamin. Scholem went far beyond the meeting of the two, which was limited to certain years. I mention here only the most salient matters.

Noeggerath came from a distinguished family. After a residency at a Swiss boarding school, starting in in 1904, he studied a whole range of subjects at German universities, primarily in Munich, where he took up permanent residence, but also in Berlin, Bonn, Jena, Erlangen and — this is decisive for his philosophical imprint—in Marburg. At Marburg he came into contact with Hermann Cohen and Paul Natorp in 1907; and there again in the winter semester of 1912—1913 he encountered Nicolai Hartmann. The latter wrote to Heinz Heimsoeth about his Kant seminar: “Noeggerath also does not consider it beneath his dignity to speak; it is touching how he descends from the pedestal of his difficult way of speaking and makes an effort to speak in a completely childlike manner. He told me he expressly learned how to speak in a philosophical manner through participation” [7. P. 132].

Noeggerath had already made a brief appearance the previous summer. On July 4, 1912, Cohen’s 70th birthday was celebrated in the university auditorium. “Two of his students, Candidate Noeggerath and Dr. Schier, addressed him from the tribune resplendent in the most beautiful floral decorations. The first presented a Greek bust, ‘the Hypnos,’ as a token of gratitude. The second read out an address... Moved by this, Cohen thanked them for the veneration and love, and he promised to maintain the bond between him and his students”. Unfortunately, we know of no personal remark by Cohen or Natorp about Noeggerath. This is striking, especially since both of them would exchange letters that discussed many other students. Noeggerath, however, studied elsewhere in the years between these Marburg semesters, and even after his appearance in 1912—1913, he soon left the city again.

The next thing we hear about is the meeting with Benjamin in Munich in 1915, but their exchange of ideas lasted only until “mid-March 1916” [3. P. 97]. This time Noeggerath moved to Erlangen “to complete his studies with the philosopher Paul Hensel (1860—1930), a friend of Wolfskehl’s [and Cohen’s], who was known for his liberal stance, and to begin working on his dissertation, which he completed through lively discussions with Hensel in the summer of 1916 and submitted in October. On December 19, 1916, he was awarded the doctorate summa cum laude in systematic philosophy, Indology, and comparative linguistics. During this time, he met Helmuth Plessner, who also received his doctorate from Hensel (and on the same day). Noeggerath’s dissertation Synthesis and the Concept of System in Philosophy. A Contribution to the Critique of Antirationalism was never printed as a result of the war circumstances and the inflation that occurred afterward. However, Noeggerath had made several serious but failed attempts to get it printed, especially in 1917 and 1922—1923… This is also the only work by Noeggerath before 1945 that has survived with any certainty. Everything earlier, as far as it was in his hands, he later destroyed, or it fell victim to the destruction of World War II” [3. P. 97].

According to Scholem, Noeggerath came to Munich again in early 1917. Benjamin had “the essential conversations with him about the mathematical theory of truth and how this discipline discovered itself for the first time in Europe with the Pythagoreans”3. Because of the war, Noeggerath obtained permission to use the title of doctor on March 23, 1918, even though his dissertation had yet to be published4. At about the same time, he joined the Kant Society5, seeking with his former teacher Moritz Geiger to establish a Munich chapter. The two published an appeal as the Executive Committee, which, however, was unsuccessful at that time6. It is Noeggerath’s last attachment to an academic body about which we know anything for certain. To be sure, however, he remained academically active, for instance, as a translator [8]. Nevertheless, we come across his name just as much in the publishing business and even as an author of children’s books7.

After World War II, Noeggerath had many new plans. “At the beginning of 1946,” he had the intention, according to Scholem, “of publishing four books”: a volume with about 25 poems, a compilation called Imaginäre Portraits (Imaginary Portraits), a Denkfibel (Primer for Thinking) and a book titled Orpheus oder die Spur des Vollendeten (Orpheus, or the Trace of One who Came to Completion). Later, a book on the “Philosophy of the Symbol” was added to the list. Hardly anything was prepared for printing. We can surmise the obstacles only in vague manner. Health problems may have played a role. In the spring of 1949, for instance, Noeggerath told Helmuth Plessner that he had “escaped from the Soviet zone.” He came to Heidelberg at the end of 1948 and was then living in nearby Ziegelhausen. He could sit at his desk only “for a few minutes at a time” because of stomach problems, which lasted for months8. In general, illness is often mentioned in the subsequent period; so, too, is oppressive poverty. Even as Noeggerath “‘was in rags’—that’s how his second wife saw him in 1950 —  ‘he remained a grand seigneur’”9.

There was, moreover, a deep resignation in the cultural Zeitgeist. A 1955 statement makes this clear. Although Noeggerath is only talking about poems here, which he had apparently written in large numbers, it goes beyond this: “Why have I never published any of them? For two reasons. First, not everything was as I wished. Second, I lack any literary ambition, a lack that is related to my thoroughly negative assessment of today’s literary establishment. It is a mystery to me why poems by Celan, for example, are printed, and I cannot believe that a man like Eliot can be considered a great dramatist.” Noeggerath writes similarly about Nietzsche, Ibsen, and Gerhart Hauptmann. Finally, he says, revealingly about Walter Benjamin: “Part of the blame for this state of affairs lies in the fact that the critic is an end in himself and that criticism itself has become literature”10. It will hardly be overlooked that Benjamin, at least since the well-known January 1930 letter to Scholem, claimed the “critique of German literature (critique de la littérature allemande)” as a central task for himself11.

According to the title of Noeggerath’s four planned books, only Die Gedichte (Poems) appeared, but this was not until 1961, a year after his death [13]. A slight recollection, which he communicates, bathes his slightly dazzling personality in a telling light. He laments being “labeled as a philosopher or epistemologist.” With Rilke — Noeggerath had also known him since his student days in Munich — it had been the other way round: “He only knew a few poems of mine and fell out of all the clouds — he almost resented it — when he witnessed a conversation with E[rwein] von Aretin about relativity (who was originally an astronomer): ‘I must first slowly get used to you again,’ Rilke told me at that time”12.

Let's take another look at the planned “Primer for Thinking.” Its subtitle was “Meditationen über ein Thema der Geometrie” (Meditations on a Topic of Geometry). “Intended for interested laymen, and starting from a minimum of presuppositions,” it was supposed to discuss “one of the last, quite central questions of epistemology,” namely “that of the so-called axioms, i.e., of those propositions which, though themselves neither capable of, nor in need of proof, nevertheless underlie every proof”13. Later Noeggerath gave it a new title: Die erkenntnistheoretischen Grundlagen der neueren Geometrie und Physik (The Epistemological Foundations of Modern Geometry and Physics)14. Several systematic sketches that have been preserved belong to the scope of this project15.

And one may also include the only essay printed during Noeggerath's lifetime, “On the Untimeliness of Abstract Art” (Über das Unzeitgemässe der abstrakten Kunst) [14]16. In it, Noeggerath builds a highly original bridge to the philosophical interpretation of modern physics. The connection to the 1916 Synthesis and the Concept of System is also apparent. A “metaphysics of the finite,” which he pronounces as the program of philosophy at the end of the art essay [14. P. 1019]17, was Noeggerath’s endeavor from the beginning.

And so it remained, as he increasingly turned to a “symbol,” a “transubstantiation” of “so-called inauthentic or ‘impossible’ concepts” into sensually perceived objects, , as he put it18. In Synthesis and the Concept of System he discusses something like this via the example of imaginary points of view in projective geometry, to which I will return; in the essay he does so via the reality of the work of art. This extends to the interpretation of spiritualist phenomena. Noeggerath, almost 50 years later, reports about a “materialization” of human figures, which he himself witnessed in 1906 or 1907 during a séance in his mother’s apartment. He does not doubt the real appearance of the figures. However, he contradicts the usual explanations by alleged liaisons into the beyond and the like. Instead, he approaches the occult phenomenon with his concept of a “situational reality.” The observer within the séance is to be considered — and here he quotes his art essay of 1951 in detail — similar to modern quantum physics as a constitutive moment of reality19.

In 1952 Noeggerath married Marga Bauer, with whom, as his health became increasingly impaired, he lived again in Munich. On April 29, 1960, he died  “after an illness of about two months” and is “cremated according to his wishes” [3. P. 120].


In 1916 Synthesis and the Concept of System Felix Noeggerath seeks a new reading of Kant’s transcendental synthesis20. A first hint of its direction lies in the fact that he initially designates the semantic horizon of the word “synthesis” not primarily via Kant but as a citation from Goethe. This happens in the form of the first of three mottoes that Noeggerath prefaces his treatise with. He quotes one of Goethe’s reflections: “The main thing about which one does not seem to consider in the exclusive application of analysis is that every analysis presupposes a synthesis [...] A great danger into which the analyst falls is, therefore, that of applying his method where there is at bottom no synthesis” [16]. We will see why for this fundamental principle, it stems from Goethe rather than a citation from Kant.

The second motto comes from Kant. He warns against neglecting analytical precision: “It is not an increase, but a disfigurement of the sciences, if one lets their borders run into each other” (KrV B VIII). Then, after these two references to fundamental unification and punctual separation, the reconciling whole must now be indicated in a third motto. It finds its symbol in Plato’s Eros, the hermeneutic demon “in the middle” (εν μεσω) between the two, through which — Noeggerath’s third motto — “the whole is combined in one”: “ωστε το παν αυτο αυτω ξυνδεδεσθαι” (Plato, Symp. 202e).

As indicated above: Noeggerath’s guideline is indeed Kant’s critique of reason. Nevertheless, he considers it deficient precisely at its center, i.e., in the thought of transcendental synthesis. On the one hand, Kant unmistakably strives for the idea of a philosophical system in the Critique of the Power of Judgement. On the other hand, in the Critique of Pure Reason, he had determined the concept on which the unity of the system hangs, namely “synthesis,” only in one partial aspect, namely in relation to theory. This may have corresponded to his original intention in the drafting of the first Critique, but more is needed for the later project of a philosophical system. For it is no longer only a matter of theoretical philosophy. The principle of “synthesis” in a system, according to Noeggerath, must also include “atheoretical” objects: areas in which synthesis does not establish relations of thought but relations of will or feeling, i.e., actions (ethics) and works of art (aesthetics). In these a-theoretical directions, Kant did not sufficiently discuss transcendental synthesis. Therefore, the relationship between synthesis and the concept of system must be reformulated.

Taking his point of departure from this task, Noeggerath determines rationalism and thus the critique of anti-rationalism to which the subtitle refers. Rationalism is the search for a synthesis which, on the one hand, creates systematic unity and, on the other, gives each individual part, including a-theoretical ones, its specific form. Anti-rationalism devalues the a-theoretical part; more precisely, it consists in an overvaluing of the theoretical part, i.e., of thinking. One may be of the opinion that it is rational to dissolve all kinds of objects “indiscriminately into relations of thought...” [1. P. 3]. What is theoretically not graspable is regarded as a “possible remainder,” as indeterminately “irrational” [1. P. 3]. Such a “pseudo-rationalism” is Noeggerath’s primary opponent — an “intellectualism” incapable of differentiation [1. P. 3]. Even Kant bears traces of it. For this reason, it needs Goethe: “Compare... the motto from Goethe, which precedes our work, with Kant’s demand that the intellect cannot dissolve anything, which it has not itself connected before! [In Goethe] a synthesis in general is presupposed, here [in Kant] one of thinking” [1. P. 7].

Nevertheless, thinking remains central. Rationalism sets boundaries [Grenzen] to it, but it is precisely rationalism that establishes its own foundation in thinking and, therefore, as a theory. It rests on an investigation into thinking that is in itself conducted by thinking, i.e., it rests on logic. And here Noeggerath proceeds in a strictly Kantian manner. Theory is a cognition [Erkenntnis], and cognition is a kind of knowing [Wissen] that is projected toward and examined for its validity, i.e., science [Wissenschaft]. Consequently, theory is science. This is also true the other way around. Science is cognition. Cognition is theoretical. Consequently, science is theoretical. Logic thus takes shape as a question of knowledge and is, to this extent, scientific. What it lets us know is valid. This is the acid test for Noeggerath’s rationalism. For: How should the logical (i.e., scientific) foundation of rationalism substantiate a possibility of objects that are not scientific, i.e., atheoretical?

The first step is as follows. Logic gets a special role through the question that is at stake here. In other words, it fathoms the ground, its own preconditions. It remains science, but in contrast to other sciences it seeks to formulate the conditions of the possibility of cognition, of theory itself. The cognition of logic, therefore, applies to something that is original [ursprünglich] to itself and to the fact of cognition in general. This original element, however, must, in turn, be a scientific cognition. Otherwise, it would not be verifiably valid. Such a paradox, when made into a concept of its own, is the transcendental synthesis sought by Kant and Noeggerath.

If it succeeds in naming its form, it is the precise indication of something that can be designated only by a double location. On the one hand, the synthesis is, figuratively speaking, in front of the one whose possibility it produces. Moreover, on the other hand, it should be at work in the very thing it precedes. Only in this way, it comes to evidence. It must be validly cognized in itself. Then it can recursively be understood as justifying knowledge. This double place inevitably leads to the boundary [Grenze] of science. This is where Noeggerath starts. More clearly than Kant, he emphasizes that logic, when it reflects on the boundary of its scientificity, lays germs in itself for non-logical, non-scientific, atheoretical objectivities [Gegenständlichkeiten].

Here Noeggerath first follows Marburg’s footsteps. The “boundary” [Grenze] received philosophical significance, especially with Cohen’s second Kant book Kant’s Foundations of Ethics (1877). The work begins with a review of Kant’s theoretical philosophy, more precisely: with a consideration of the “thing-in-itself as a boundary concept.” In Cohen’s work, this retrospective is conspicuously not at the center of his reconstruction of Kant’s epistemology, presented in Kant’s Theory of Experience (1871). Instead, it is already on the way to ethics21. It is only from this second systematic viewpoint that the “Transcendental Dialectics” from the Critique of Pure Reason comes up, and with it the unique boundary logic of the knowledge of ideas, Kant’s so-called regulative principles. In Kant’s Foundations of Ethics, the boundary knowledge, although belonging to logic, is developed from a point of view external to the theory.

Noeggerath's interpretation of Kant’s system concept germinates in this decision, even though he does not mention Cohen’s interpretations. He chooses instead Cohen’s Logic of Pure Knowledge (Logik der reinen Erkenntnis, 1st edition published in 1902) as his philosophically most crucial contemporary source. In it, Cohen integrated meditation on boundaries [Grenzen] into his new conception of a logic of knowledge. This does not mean that he drags ethics into logic. The Kantian separation between nature-being and ethical entitlement remains untouched. Nevertheless, symptomatically enough, Cohen outlines the ethical analogy for almost every form of judgement discussed in his Logic at the end of the respective chapter.

Noeggerath was fascinated by this conception, which combines constitutive and regulative logic. Especially in the first two main parts of Cohen’s Logic, “The Judgements of the Laws of Thought” and “The Judgements of Mathematics,”  he found — in affirmation and criticism, including a remarkable modification — his starting points22.


The inner outline of Noeggerath’s Synthesis and the Concept of System is the following. A boundary is characterized by the laws of the objects whose area it circumscribes. The lawfulness by which this circumscription is determined correlates to those laws within the area. However, only in the territory-inside are there objects: its border is not an object. Boundary cognition seeks instead the principles according to which objects are formed, and special rules apply to principles. Now, transcendental synthesis is the name for such a boundary complex of principles, first of all in cognition.

Consequently, the new rules apply as principles of science. And still more: they must themselves preserve the form of science, for they too are to be known in valid knowledge. Since science is essentially a mode of determination for objects, the boundary knowledge also follows valid guidelines within the field. However, something has to change. To preserve the form of science requires cognizing the original synthesis, with Kant’s expression, as if one cognized it.

What does “as if” mean? Doesn’t one thereby violate the classical prohibition of contradiction from the outset? According to this prohibition in its simplest version, an X is either cognizable or not — tertium non datur. To be cognizable would mean that the X constitutes a specific identity (A is A). To be non-cognizable would mean that the X does not constitute a particular identity. Its inquiry tends toward a non-A. Non-A is denied the step to the object (non-A is not A). With synthesis as a boundary, however, an X is in question, which — because it is not within the domain — is not constituted as a determinate A but which nevertheless is to be cognized as if it were an A. Here, a demand for cognition is obviously held against the prohibition on contradiction.

Is it possible to read the “Non” in the “Non-A” in a way that this “Non-A” is no longer a contradiction? Can this “Non-A” also designate a novelty, an otherness transforming the whole cognitive situation? An adventurous thought! For it demands a revolution of questioning, the venture of a new hypothesis in relation to the material of the traditional knowledge. Noeggerath sees the methodological model for this venture in Kant’s regulative principles of Transcendental Dialectics. His most consistent exposition, however, he finds in Cohen’s Logic of Pure Knowledge.

This is, using Cohen’s phrase, the “adventurous detour” [19. P. 84]: In the negation of the pseudo-identity, as it were, in the middle of the annihilation of the tendency of the X towards something false, a stop is set, an fictitious stopping point. This fictitious point becomes the hypothesis, the hinge of the reversal into a new positive, into a negation of the negation. And so that this does not come to nothing in a thoroughly moving scenery, one must dare everything completely. One boldly asserts that the setting of the fictitious point is the foundation of determinability par excellence. It is the condition of the possibility of cognitive principles in general. The fictitious point achieves this precisely because it is — necessarily  imaginary — not existent. Without blatant violation of the prohibition of contradiction, such a thing is only possible if the method that gives an  X determination is a pure consummation, a self-discovery. This is thinking in Cohen and Noeggerath — completion per se, without a carrier or subject.

The hypothesis runs as follows. The border-X that is subject to inquiry, the transcendental synthesis, cannot, to be sure, constitute itself as A; but it is the way to find an A. Constituting and finding [Finden] are different, and only the latter is concerned here. But as indicated earlier, this cannot be a special path outside of science. So, with transcendental synthesis, science must be newly invented [erfunden]. Also, the objects within the circumscribed area are now different. It is a paradigm shift. If it succeeds, it brings the cognition of the boundary and the cognition of the bounded objects to unity under newly discovered rules. This is done at the following price: it needs a reduction to pure form, a form not already articulated into contents. In question is a cognition as a form without content. This is what Noeggerath in fact intends: that the binary prohibition on contradiction be therefore replaced by a three-valued logic23. It makes a new mode of identity possible. This is to be noted: the circumscribed objects also become new with border cognition. Their contents are dissolved, analyzed. The purification toward form is, as indicated above, decisive. If no new nexus [Zusammenhang] is found, binary contradiction remains. The smallest nuances decide. The questioning driven by the risky curiosity concerning border-knowledge must grope its way between the Scylla of complete annihilation by contradiction and the Charybdis of a delusional system on loan.

Up to this point, Noeggerath follows Cohen. Nevertheless, Noeggerath emphasizes much more strongly that not only scientific reflections discover new things with the help of three-valued logic. Yes, as indicated, he limits science in general to problems of theorizing. He rejects, for example, Cohen’s view that “jurisprudence” may be “called the mathematics of the humanities, and primarily for ethics its mathematics” [20. P. 66]24. In return, Noeggerath expands the capacity of logic beyond the confines of science. With him, a logic that has become suitable for comprehending the original synthesis eliminates the obligation toward science, cognition, and theory for everything that comes into view outward from the newly considered boundary.

The demarcation of boundaries has axiomatic force both inwardly and outwardly. The science of logic brings a freedom to science inward and a freedom from science outward. And indeed both in the form of a realizing justification: science as well as non-science are now possible in a valid form. For logic, this has a remarkable consequence. Logic — which must remain a science — relativizes itself. It strips off all totalitarian behavior. It will no longer grow into a panlogism. Noeggerath’s three-valued logic is a look beyond one’s own horizon. His claim is: Nothing now speaks against synthesis assuming an atheoretical form.


A primordial scenery of the synthetic opens up, a kind of logical substructure. The transcendental theory of finding can identify only germinal points of pure quality. Developing these germs toward real appearance and giving them, per Noeggerath, articulation, quantity, and measure, is no longer its business. With atheoretical objects, this was not to be expected. Yet, in theory, this logic does not supply real objects but only rules to prepare the appearance of possible objects. Therefore, when it is now a matter of systematically presenting these principles of the possible, a new boundary becomes noticeable, this time in language. To give expression to the motility of reflection, it is true that philosophizing must remain close to natural language with its attachment to dynamic objects and things. But its most important problem, synthetic lawfulness, will then be to grasp only metaphorically. Philosophizing risks missing precisely what it wants to say by objectand thing-relevant designations.

Therefore, mathematics serves as a guide. Its symbolism can give an exact form to the imaginary element of that border. According to Noeggerath, philosophy can resemble this preciseness in the non-actual. The prerequisite is that it does not behave mathematically but proceeds along its own path in critical distance to the “specialized, act-kindred thinking” [1. P. 90] of the mathematician. This is the purpose of the two digressions at the end of Synthesis and the Concept of System, one on meta-geometry, the other on Platonic μεταχυ (“between”).

I provide two examples from the Theory of Conic Sections. This theory had — here lies Noeggerath’s approach — united the Euclidean conception of space (under the title of the parabolic projection) with two basic forms of non-Euclidean conception of space (under the titles of the elliptic and the hyperbolic projection) to a unified geometry. He is interested in this because “the problem of non-Euclidean space... has become the formulaic expression of a new view of the nature of science and thus of knowledge in general” [1. P. 87]. But in the end, Noeggerath is not concerned with the question of Euclidean and non-Euclidean. He is interested in the new interpretation of the Infinite.

To show this, the first example leads us away from the naïve assumption that space extends into an indefinite endlessness. For this purpose, Noeggerath uses the theory of the so-called “spherical bush” [Kugelgebüsch]25 [1. P. 78—83]. Intuition is not a criterion in this meta-geometry. Instead, space is defined, against the idea of endless extension, as bent back in itself “spherically” towards a center. This center marks a point with only one determination; it does not belong to the defined space. No construction can positively represent this point. In this sense the point does not exist. But, its positing is the condition of the possibility of constructions. And furthermore: if it is posited, then in the spherical bush — Noeggerath restricts himself to the (parabolic) variant — all basic and doctrinal theorems of Euclidean geometry remain in force.

Thus, the positing of the non existing point becomes the hypothesis of a (Platonic) μὴ ὄν, giving precise determination to the infinite. It frees spatial thinking from the insoluble aporias of an indeterminate endlessness. As a result of the spherical bending, the endlessness becomes the locally determined infinite of a single central point. It is true that the new infinity, as with the (previous) endless, means the non-being of a positive determination. But as punctual “not” it has an exact place. The hypothesis of the spherical bush enables, as Noeggerath puts it, the “apprehension of the infinite as something limited [Auffassung des Unendlichen als eines Begrenzten]” [1. P. 103]. Thus, the limit or boundary [Grenze] is put into effect as a principle of a continuously determined geometry.

The second example shows above all the producing moment of an imaginary point of view (focus imaginarius [1. P. 94—97]). One puts a plane through a cone in such a way that it intersects its central height axis at right angles. The line of intersection with the cone then describes a circle. Now the plane is rotated around a straight line lying in it but outside the cone as around an axis in continuous angular motion. Ellipses, parabolas, hyperbolas are created as intersecting surfaces. The demand is then to determine all conic sections as if they were created purely as projections of the initial sectional figure circle into a changed geometrical environment, despite their differences.

Crucially, the circle must also be dissolved, analyzed as a figure. Its appearance is traced back to elements of construction that generate a circle under the initial constellation but generate other projection shapes when the plane is rotated.  Thus, one does not allow descriptive attributes of finished circles, ellipses, etc. but only genetic predicates of their becoming. The “predicative definition”  [1. P. 92] of the conic section distilled out under this projective consideration exemplifies what we brought up above with respect to the boundary meditation: the tracing back of content determinations to pure form. Continuity (as a form of motility) is paired with discontinuity (of the appearing projections).

This law of continuity governs everything that under the title of transcendental synthesis unfolds into a germinal form, first, of qualitative and, then, of quantitative diversity. Neither a leap nor a dialectical change leads from one content to another. This applies to single regions of the systems and for every transition between different regions, e.g., from theory to practice and aesthetics or vice versa. Thus, one postulates a continuous motility — precisely such synthesis — which generates the parts of the philosophical system in a manner similar to geometrical projection. If this succeeds, the validity of the cultural phenomena correlating the system  parts — knowledge, action, and art — is demonstrated.

 The continuity of the synthetic motility remains fictitious from the point of view of the products, but it is indispensable for their validity. However, these very phenomena provide the basis for asking about this validity. They appeared at first separately from each other or only uncertainly connected. So what unites them? For the sake of the answer a hypothesis of continuity must be ventured. It claims that this separation arises from a unified, purely legal synthesis. This becomes true in the Platonian sense of “hypothesis,” i.e., as a foundation of stable insight if the synthesis can be formalized and a strictly ordered series of actual forms can be developed.

Under this guideline Noeggerath brings together his titular concepts: synthesis and system concept. He obtains the continuity hypothesis with the help of Kant’s three tables of transcendental judgements, categories, and principles in the Critique of Pure Reason [23. A 70, 80, 161/B 95, 106, 200]. Each of these tables is known to contain twelve individual elements in four groups of three each. For the systematic division, the third group under the title “relation” is decisive. In it — Noeggerath takes his key terms only from the tables of judgements and principles — the three principles of substance, causality and interaction correspond to the categorical, hypothetical, and disjunctive judgements [23. A 182—218/B  224—265]. Here, too, Noeggerath makes use of mathematical analogies. At the center, in interpreting the hypothetical relation, this is the theory of the arithmetic series [1. P. 51—54]. As a result, he assigns a systemic part to each of the  three pairs of judgement and principle. “For it is to be connected: the categorical relation with ethics, the hypothetical with logic, and the disjunctive with  aesthetics” [1. P. 10].

It is immediately noticeable that Noeggerath changes the classical sequence beginning with logic. Indeed: “The order of the limbs is: a) ethics, b) logic, c) aesthetics” [1. P. 10]. However, despite this change, Noeggerath, as shown above, also begins with thinking, hence, with logic. This concerns his interest in the regulative potential of the third antinomy (freedom versus natural law) from Kant's transcendental dialectics.

However, we come up against a limit in the text before us. Noeggerath needs to unfold his reflection of the third antinomy in detail. The reason is that the second part of Synthesis and the Concept of System, which is supposed to present it, is — because the work had to be finished as a qualifying dissertation for the  doctorate degree — only available in the manner of a protocol of attained results [1. P. 62—76]. A similar case can be found, for example, in a series of details, where Noeggerath intervenes in Cohen’s “Judgements of Mathematics” [1. P. 47]. What he hints at here, however, demonstrates a profound familiarity with  his subject-matter. The potential of this unusual writing for research is beyond doubt.


1 I would like to thank Peter Fenves for his precise review of the translation. In addition he and Pierfrancesco Fiorato offered extremely helpful support to systematic questions. The directors of the Monacensia (municipal archives in Munich) and of the University Library of Groningen generously allowed the use of their sources.

2 Benjamin’s letter to Fritz Radt of December 4, 1915 [3. P. 87—88]. Systematic interpretations have so far only been given by Benjamin scholars [4—6], esp. cf. Fenves’s extensive afterword to our current Noeggerath edition [2]: Felix Noeggerath and Walter Benjamin Redux.

3 Benjamin’s correspondence to Scholem on May 25, 1917 [3. P. 99].

4 Noeggerath estate in the Monacensia archive in Munich: Biographische Dokumente I, No. 2431/93.

5 Cf. their names on the list of admissions between January and May 1918: Kant-Studien 23 (1918—1919), 167.

6 Cf. ibid. P. 519. — Since the annual volume was not printed until 1919, the editors already note that “the circumstances of the time” had so far prevented a foundation of the local group, in addition to many other things (including a lecture by Max Weber) (ibid. P. 520).

7 According to Scholem [3. P. 105], he became co-owner of the newly founded Berlin children's book publisher Herbert Stuffer in 1926 and anonymously wrote the text for its “Spielfibel” No. 4: “Hurra, wir rechnen weiter!” (1932, illustrated by Tom Seidmann-Freud). By the way: Benjamin published two very appreciative reviews of the first three Spielfibel [9. P. 267—272; 311—314], but not on the fourth Spielfibel with Noeggerath's text.

8 Two postcards from January 11 and March 28, 1949, in Plessner-Archiv der UB Groningen: Brieven van Felix Noeggerath aan Helmuth Plessner (1892—1985) uklu Plessner 143, 010-011.

9 A statement by Marga Noeggerath, cf. [3. P. 115].

10 Letter to the “Merkur” editor Joachim Moras, February 2, 1955, in [10. P. 29—33], here [10. P. 32—33]. Scholem [3. P. 119] mentions that Noeggerath received the first edition of Benjamin’s “Schriften” [11] from the Suhrkamp editor Friedrich Podszus in 1956. Nevertheless, also the letter of Noeggerath to Podszus does not contain any statement about Benjamin.

11 Cf. the overview by Martin Opitz “Literaturkritik” [12].

12 Noeggerath’s letter to Joachim Moras [10. P. 32].

13 Noeggerath in his CV from 1950 [3. P. 116].

14 Noeggerath’s letter to Herbert Fritsche from May 1946 [3. P. 113].

15 Noeggerath estate, Monacensia, Box I, Mss. 1—20, e.g.: “A priori” (Ms. 2, 2439/93; 20 ss.); “Über die Axiome” (Ms. 3, 2440/93; 26 ss.); “Erkenntnistheoretische Fragmente” (Ms. 9, 2446/93; 28 ss.); several parts on “Freiheit” (Mss. 10/11, 2447/93 und 2448/93; in total 17 ss.).

16 See our reprint [2].

17 For the connection with earlier work [3. P. 117].

18 The letter to Joachim Moras [10. P. 31].

19 Citation from Noeggerath’s report [15. P. 225].

20 Page references in the following according to Noeggerath’s typescript [1] (also given in our new edition [2]).

21 The subsequent editions of the book published in 1885 and 1918 brought no change in this point.

22 Natorp’ s “Die Grundlagen der exakten Wissenschaften” is also repeatedly called upon by Noeggerath. The book treats much more comprehensively than Cohen the details of the mathematical-scientific sources (among others, Josef Wellstein), which also became necessary for Noeggerath. But, and this is the crucial caveat, Noeggerath considered Natorp’s essential epistemological act of “fieri” [17. P. 10—14] to be flawed. The “fieri” seemed to be subject to temporality, instead of conversely helping to ground it. Therefore, Noeggerath sees Natorp on the way to his “Allgemeine Psychologie nach kritischer Methode” [18]. The “reconstructive method” of this book has, according to Noeggerath, a certain correspondence with Kant. For the logic of cognition, however, it must be rejected [1. P. 71].

23 Cf. the letter to Joachim Moras [10. P. 31].

24 Noeggerath does not mention that Cohen rejects the fact of an (art) science for his Aesthetics of Pure Feeling (1912) and establishes a “kind of new logic” on the paradigm of poetry [21. P. 367].

25 His most important source is Josef Wellstein’s “Grundlagen der Geometrie” [22].


About the authors

Hartwig Wiedebach

Author for correspondence.
Email: wiedebach@posteo.de
Dr. phil. habil., Independent scholar 37 Georg-Boehringer-Weg, 73033, Goeppingen, Germany


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