THE CONCEPT AS A FUNCTION: A NEO-KANTIAN INNOVATION AND ITS IDEALIST LIMITS

The author defends the thesis that with the neo-Kantian concept of the concept determinacy is conceived of as mediation but not also as self-mediation. In terms of Hegel, neo-Kantianism conceives of the concept as an essence, not as a concept. Consequently, neo-Kantianism does insufficient justice to its own claim of transcendental idealism to be the self-knowledge of reason. This thesis is substantiated by scrutinizing, first, the functional account of the concept as developed by the Marburg neo-Kantian Ernst Cassirer and the Southwest neo-Kantian Bruno Bauch. Subsequently, the transcendental idealist conception of the concept as a function-concept is problematized by taking Hegel’s speculative-idealist doctrine of concepts into account. It becomes clear that concept progresses from itself as a concept of substance to the function-concept, and finally to the concept.


THE CONCEPT AS A FUNCTION: A NEO-KANTIAN INNOVATION AND ITS IDEALIST LIMITS
While the fruitfulness of an in-depth study of neo-Kantian interpretations of Hegel for the purpose of appropriating their critique is more than questionable given the advanced state of research on Hegel, it is very worthwhile to confront the respective philosophies with one another from the point of view of the matter at issue.This applies in particular to their basic concepts.The concept of the concept undoubtedly belongs to these basic concepts.In both neo-Kantianism and Hegel, it even has a programmatic status.
In both cases, however, it is also characterized by a doctrinal status, i.e. it is a specific function of validity.What is the significance of the specificity of this function of validity?
In what follows, I defend the thesis that with the neo-Kantian concept of the concept determinacy is conceived of as mediation but not also as selfmediation.In terms of Hegel, neo-Kantianism conceives of the concept as an essence, not as a concept.Consequently, neo-Kantianism does insufficient justice to its own claim of transcendental idealism to be the self-knowledge of reason.
First, I will discuss the functional account of the concept as developed by the Marburg neo-Kantian Ernst Cassirer and the Southwest neo-Kantian Bruno Bauch.Both endeavored to achieve a functional understanding of principles and both rendered outstanding services.I then problematize the transcendental idealist conception of the concept as a function-concept with the help of Hegel's speculative-idealist doctrine of concepts.The interpretation of the concept as a function is a characteristic of the neo-Kantians' understanding of philosophy.Philosophy is a theory of validity, a theory of the determination of the validity of our theoretical and atheoretical (practical, religious, aesthetic, etc.) performances.In developing their theory of validity, the neo-Kantians are not merely committed to Plato's conviction that philosophy is only possible as idealism; at the same time, they emphasize a fundamental insight of Kant's critical philosophy, namely that the determinacy of human performances or objectivations, as the products of reason that they are, can only be determined via the determinacy of their validity, more precisely, via the principles of the validity of these performances.
Kant's contribution to philosophy is valued by the neo-Kantians in terms of his insight into the problem of validity (cf.paradigmatically the quid iuris question of the "transcendental deduction of the categories"). 1At the same time, it is important for them to refine Kant's idea of a philosophical method, a method neither lost in metaphysical speculations -as, according to the neo-Kantians, is the case in post-Kantian idealism -nor positivist reductions of the problem of validity.For the neo-Kantians, philosophy is not about recognizing things in their being but about understanding the validity with which the being of things is thought (COHEN, 1910, p. 27;ECW 3, p. 542).The much-invoked "transcendental" is nothing other than the whole of the principles of validity.
The enthusiasm for Kant's philosophy is shared by the neo-Kantians just as much as the post-Kantian idealists' demand for a perfection of Kant's transcendental idealism.Kant's early idealist successors were already very much impressed by Kant's transcendental revolution in philosophy.Nevertheless, they were not convinced by Kant's implementation of transcendental thought.Whether Reinhold, Fichte, Schelling, or Hegel, all set out to bring Kant's transcendental philosophy into a form that would do justice to the claim of critical philosophy itself.
Geltung, vol.2, n. 2, 2022 For the neo-Kantians, at least for the two most important schools of Marburg and Southwest German neo-Kantianism, the same applies ceteris paribus.They conceive of philosophy as the philosophy of the determinants of human behavior, as, to formulate it with the Southwest Germans, a philosophy of values or, to use an expression of the Marburg philosopher Cassirer, as a philosophy of symbolic forms, or, to use a term applied across schools, a doctrine of ideas.As a comprehensive philosophy of such determinants of orientation or determination, philosophy proves to be a philosophy of culture: it brings the foundations of culture to its concept.This conception of philosophy is not least the result of an appropriation of Kant's transcendental philosophy, aiming to renew Kant's transcendental turn to master the philosophical problems the neo-Kantians were facing in their own time.
Against a Platonic reification of ideas, i.e. metaphysical idealism, for the neo-Kantians, the sphere of philosophical foundations is shown to be a sphere of principles that constitute the ground of our thinking and acting.Principles are not to be understood as a kind of being but as fundamental determinants of validity, i.e. as conceptual ("logical") conditions that make the object reference of our thinking and acting possible in the first place.Therefore, principles are conceived of as something that precedes "experience" and is at the same time intrinsically related to it.Any ontology presupposes a logic of its object.Kant accordingly grounds cognition in the cognitive relation itself qua the whole of a priori conditions that underlie both our cognition and the objects of our cognition.Transcendental philosophy as a doctrine of principles of cognition does not find the ground of validity of cognition in a concrete contentual knowledge of objects but solely in the pervasive validity structure of cognition itself.
For the Kantian type of transcendental philosophy of the post-war period, paradigmatically the advanced positions of Hans Wagner (1980;1992) and Werner Flach (1994;1997), this orientation of philosophy as a comprehensive doctrine of the principles of validity of human performances Geltung, vol.2, n. 2, 2022 has also proven to be decisive.Philosophy as a fundamental philosophy is only possible as a doctrine of the principles of validity that proceeds from Kant and thereby perfects Kant. 2   Ever since Kant, transcendental philosophy has been constantly confronted with a rather naive accusation of formalism.Its forms are supposed to be merely empty shells that are somehow applied to a formless content.
However, since transcendental philosophy conceives of principles of validity as "conditions of the possibility" for something, as principles for principiates and nothing detached from them, the transcendental philosophical understanding of principles overcomes such vulgar formalism -at least seen from a systematic perspective: "principles", "forms" are nothing that is somehow "external" and "abstract" to the concrete.Rather, they are always already at work up at any level of the determination of objects.Thus they are not characterized by an abstract universality but rather by their object-enabling function, that is to say by a content-logical nature.The formality of the formal as understood in transcendental philosophy consists in precisely this function of being the determining condition of the concrete.It contains the determinations of the concrete in its concreteness, the concrete as "grown together" from principles.
The transcendental is the concrete-universal structure of objective meaning.
The neo-Kantians clearly saw and succinctly elaborated the reciprocal and well-ordered relationship between principle and concreteness.Rickert (1921, 50ff.;1924, 8ff.), for example, overcomes a formalistic view of principles through his heterology: content itself proves to be a form and consequently a necessary moment in the whole of thought.And, as indicated, Cassirer and Bauch in particular have made great efforts to achieve a functional 2 The impulse to perfect Kant's doctrine within the framework of transcendental idealism is an important feature of neo-Kantianism.See, e.g., Windelband (1915, I, IV), Cohen (1902, p. 7), Rickert (1924/25, p. 163), Natorp (1974, p. 243), Cassirer (ECW 11, p. 9).
Geltung, vol.2, n. 2, 2022 understanding of principles, not least in critical discussion with the abstraction theory of the concept and the picture theory (Abbildtheorie) of truth. 3assirer, for instance, holds that all objectivation is "mediation,"4 having the "far-reaching idealist consequence" that the determination of the object of cognition can only be achieved through a "peculiar logical structure of the concept."(ECW 11,p. 4) The idea of a "purely functional unity," a "rule," now takes the place of the "unity of a substrate," the "unity of a substance," so that the "new task" of a philosophical "critique of knowledge" arises (ECW 11,p. 5).
In his epistemological deliberations of Einstein's theory of relativity, Zur Einsteinschen Relativitätstheorie. Erkenntnistheoretische Betrachtungen, a text relevant to Cassirer's concept of function alongside the first chapter of Substanzbegriff und Funktionsbegriff as well as the Introduction to the Philosophie der symbolischen Formen and the chapter on "Concept and Object" in its third part, Cassirer formulated what he had said against the background of Kant's philosophy of the special sciences in such a way that what these call "object" is not a "given in itself," but only determined by their respective "point of view"; only through certain "form-concepts," "logical conditions," does the "uniform mass of the given" become its object (ECW 10, p. 7).This new task does not arise in a merely regional sense, i.e.only as a task of an epistemological critique, but in a universal sense as a clarification of the foundation of all ways of objectification or reality formation (ECW 11,p. 6), such as cognition, language, myth, art, and religion.Kant's "revolution of the way of thinking" (ECW 11, p. 7) or "Copernican turn" thus takes on an Geltung, vol.2, n. 2, 2022 "expanded sense."(ECW 11,p. 8) The foundation is the "function": the "'primacy' of the function over the object" is the "basic principle of critical thinking" (ECW 11, p. 9).All content of culture, insofar as it is more than mere individual content, is based on a "general principle of form" and therefore has an "original act of the spirit" as its precondition (ECW 11,p. 9).Philosophy needs to determine the "system of the manifold expressions of spirit" by pursuing the various directions of the "original formative power" of spirit; all of them reach beyond the "individual manifestations of consciousness" in that they make a "claim to objectivity and value" and insofar present something "universally valid" (ECW 11,p. 19).
So much for the programmatic meaning of the concept of function and its transcendental philosophical profile.Whatever is, is based on the functions of validity that constitute it as that what it is.These functions can only be captured by starting philosophically to analyze what is.

THE VALIDITY-FUNCTIONALITY OF THE CONCEPT
In addition to the programmatic meaning of the concept as a function, the concept also has a particular validity function in the whole of validity functions.First of all, this concerns the meaning of the concept as a function.
That is to say that the constitutive conditions of the object, in Kant's terms, the conditions of the relation of the concept to its object, cannot be clarified by recourse to "determinations of being" in the sense of "some properties of given things," and thus to an "already existing reality."Rather, it requires recourse to the "conditions of the positability of a 'reality' in general."(ECW 13,p. 375) These conditions include the "concept."Logically, it is the "propositional function" F(x) (ECW 13,p. 375).The function "applies" to the singular values but it is not a singular value itself.The singular values "are" only insofar as they stand in the relationship expressed by the function: the "singular, discrete" exists only through some form of the "universal."(ECW 13, p. 376) Likewise, Geltung, vol.2, n. 2, 2022 the universal only manifests itself in the "particular" (ECW 13, p. 376) and has no existence independent of it.It is not accidental and important concerning Hegel that Cassirer (like Bauch) does not make a strict distinction between the particular and the singular in this context.The universal, which is here the concept, is regarded as the "order and rule for the particular" and can only be "authenticated and proven" in this way (ECW 13,p. 376).For Cassirer, one of the most important achievements of the Kritik der reinen Vernunft is that the relation between concept and object is fundamentally reconceived (ECW 13,p. 362).The concept shows to be the "consciousness of the rule" that determines the manifold of intuition into unity; in this way, it expresses the necessity of synthesis, which is the object (ECW 13,p. 362).It is no longer the "object" as an "absolute object," but the "objective meaning" that forms the "central problem."(ECW 13,p. 363) Consequently, the performance of the concept is no longer merely "formal," it is not a "mere generic term," (ECW 13, p. 363) not an abstraction.Instead, its performance is "productive and constructive."(ECW 13,p. 362) The concept is therefore also not an "image" of an absolute reality that exists in itself; the concept functions as a "precondition of experience" and thus as a "condition of the possibility of its objects": the "question of the object" has turned into a "question of validity."(ECW 13,p. 362) In his doctrine of the concept, Cassirer articulated the outlined opposition of object and validity in terms of the substance-concept and function-concept.Since Kant, the concept is no longer, as in "older metaphysics and ontology," a "concept of a thing," as a "substantial" unity (of the identical and persistent in all changing states), as an "independent thing existing for itself."(ECW 13, p. 363) Rather, the concept is related to the object because it is first and foremost the "precondition of objectification."(ECW 13,p. 364) The concept is thus, in the strict sense, the function of the objectivity of the object.A "logical structure of conditions" (ECW 13, p. 365) takes the place of a subjectobject ontic.In the words of the late Cassirer, the object is a "symbolic relation" (ECW 13,p. 365); expressed functionally, it is a "functional unity," a unity that Geltung, vol.2, n. 2, 2022 has its determinacy through a certain "form" or "function" of cognition (ECW 13,p. 369).Seen more closely, the concept turns the "fragmentary data of perception" into the whole of an object (ECW 13,p. 370).
The outlined idea of the concept as function can be found in many places in Cassirer's work, in detail and illuminatingly, as indicated, especially in the first part of Substanzbegriff und Funktionsbegriff, which significantly bears the heading "Thing-Concepts and Relations-Concepts," (ECW 6, 1ff.) or, for example in the first chapter of Zur Einsteinschen Relativitätstheorie, with the equally telling title "Measure-Concepts and Thing-Concepts," (ECW 10, p. 1) For my purposes, it suffices to only emphasize something that Cassirer himself continually repeats in many phrases, namely that a "manifold of perception is conceptually grasped and ordered" if its "members" do not stand next to each other without relation but emerge from a "generating basic relation," (ECW 6,p. 14) and that the connection between the members is thus created by a "law of assignment," i.e. determined by the function F(x) (ECW 6,p. 16).In Kantian terms, the concept is the principle of the synthesis of the manifold into the object as its unity, of the singular content into the general, of the given into the object of cognition.The object of cognition is always only because it is singled out from the "uniform mass of the given" using certain "concepts of form" or "ideal points of view" (ECW 10, p. 7).
So much for Cassirer.The same can be found in a systematically much stricter mode of development and articulation in the southwest German neo-Kantian Bauch.Before I critically discuss the neo-Kantian conception of the function-concept with the help of Hegel, I aim to supplement the theory of the concept as function presented above with a few aspects that are found particularly succinctly in Bauch.
They relate in particular to the unsaturation or need for supplementation of the function as a function of something.The function is generally the "principle of determination, of belonging together, of assignment."(BAUCH, 1914, 323 ff.;1926, 131 ff.;1923, 283 ff.) Accordingly, Bauch conceives of the concept, as the Geltung, vol.2, n. 2, 2022 universal that it is, neither as abstract but as "abstrahent" (abstrahent, abstracting); nor as concrete but as a principle of something, of the concrete, as "concrescent" (konkreszent, concretizing), as a condition of determination and thus a presupposition of concrete determinacy.It is the "universal condition of the particular."(BAUCH, 1923, p. 276) The objective validity functionality of the concept consists in being the "objective law of formation of the object to be recognized in general."(BAUCH, 1982, p. 265) Bauch also describes it as a totality of the conditions of particularization and the invariance of the conditions for the variance and variation of the particular features (BAUCH, 1914, p. 326, p. 329;1923, p. 256, p. 258, 283 ff.;1926, 101 ff., 131 ff., p. 188;1982, p. 266).
The concept thus has a specific validity function in the constitutional structure of objectivity (KRIJNEN, 2008, ch. 5.3.2).Concerning the cognition of real objects, the object-giving order of the contents of sensation forms, so to speak, the lowest level of constitution.Of course, for sensation itself to exist or to be a sensation at all, it must be placed in a context.For Bauch, this context is the objective validity function of the category.Both for Bauch and Kant categories are principles of objective determinacy.Sensations and objects are integrated into these categorial relations qua truth relations.They are presupposed for everything real.While a category never constitutes the whole object but only one of its aspects, the categories, which are themselves already relations, stand in turn in a relational context of categories that determine the object.Precisely this object-determining connection of categories is the concept.The categories have their connection within the concept; at the same time, the objects themselves are constituted by concepts and thus by categories.And in that Bauch (1923, p. 259) conceives of intuition as the inclusion of the manifold material of cognition in the categorial context of validity according to the law of the concept, the concept is for him "in the proper sense" the "embedding of sensation in the context of categories for the particularity of the object of intuition."(BAUCH, 1923, p. 275) The relationship between the concepts, in Geltung, vol.2, n. 2, 2022 turn, is the basis of the relationship between the cognition of the objects as well as the objects of cognition.The concept is not only in need of supplementation in the direction of the concrete but also in relation to the whole, the totality of conditions of particularization, the connection par excellence.For Bauch, this encompassing connection is the idea, i.e. the system of concepts and thus that objective relation of validity that, as a whole of conditions of objects, constitutes reality and its cognition.
Bauch has articulated this consistent interrelatedness of the validity functions as "logical continuity" (BAUCH, 1923, 289 ff.).The conditions of validity form a "constant relationship, a continuum" and therefore a "universal system of relationships," a "continuous relationship" between the principles of validity (BAUCH, 1923, p. 290).As indicated, the material of cognition is also included in this layered apriority.Apriority in the transcendental sense is from the outset content-related in nature (BAUCH, 1923, p. 290).In his elaboration of logical continuity, the moment of the relatedness (Verwandtschaft) of validity relations is of the essence.Bauch conceives of it as a "bordering" (Angrenzung) in the sense of being "bordered" (Hingrenzung) to a goal, i.e. as a "logical relationship in terms of content."(BAUCH, 1923, p. 298, vgl. 299 ff.)The relationships of validity determine the material or content.In accordance with Rickert's heterology, Bauch wants to avoid any χωριςμός, any strict dualism of form and content.Form and content themselves form a "unity a priori."(BAUCH, 1923, p. 303) The concept is the "universal functional condition of the particularity of the objective intuition and the intuited object," the object a whole of contents that are united in its concept (BAUCH, 1923, p. 303).The principle of logical continuity concerns the affinity of the concepts in such a way that the contents are included in the system of categorial validity relations to the system of concepts in the manner of a serial order (BAUCH, 1923, p. 307).
As a moment of cognition, sensation is that which is moved by the category and the concept towards objectivity (BAUCH, 1923, p. 308).

THE EXTERNALITY OF THE FUNCTION-CONCEPT
From the outlined idea of the function-concept together with the associated idea of logical continuity, it is clear that the function-concept is conceived of as mediation.It is conceived of as a functionality in which function and variable, form and content are joined to form a unity, i.e. cognition of the object.The concept as a function is thus determined in relation to something else that it is not itself.In Bauch's terms, the concept is unsaturated and in need of supplementation.In a critical departure from Hegel, for Bauch the concept as a universal condition of the concrete is not, "as Hegel said," (BAUCH, 1926, p. 134;1914, p. 325;1923, p. 283), 5 itself concrete but rather concrescent, i.e. determining, conditioning the concrete.There is no identity between concrescence and the concrete, the conditional and the conditioned.Rather, a "distance" remains between them (BAUCH, 1926, p. 134).Each requires the other but this other is not the other of itself: the concept is not the concrete, the concrete is not the concept.Instead of an identity, there is a logical continuity, a bordering (Hingrenzung) towards a goal.
The neo-Kantian functional theory of the concept undoubtedly makes the constitutive performance of the concept for the cognition of the object transparent.This is the strength of the doctrine of the concept as a function.It concerns a strength that is also its greatest weakness: as a function-concept, the concept is unable to determine its own functionality.It is a determining function for something else.From Hegel's point of view, one would have to say that in transcendental philosophy, the concept is conceived of as essence, as mediation, not as concept, self-mediation.The so conceived concept is only relative mediation, not absolute mediation.
5 Also the Neo-Kantian Richard Hönigswald thinks that Hegel fails to recognize the nature of the concept as a "function" (HÖNIGSWALD, 1966, p. 170).Like Cassirer and Bauch, Hönigswald to fails to recognize himself the speculative meaning of Hegel's doctrine of the concept.See on this Krijnen (2024a).
Geltung, vol.2, n. 2, 2022 Doubtlessly, Cassirer wants to do justice to the idea of a "strict systematics" of the forms of spirit and the "genuine and true autonomy" associated with them.He does so by means of a moment that is common to all basic forms of spirit and constitutes the "ideal relationship" between the several realms of culture (ECW 11,.This relationship is the concept of symbol. The Southwest neo-Kantians would say it is the concept of value, as it functions in the fundamental axiotic relationship (KRIJNEN, 2022c).But the transcendental concept of symbol or value is characterized by a formalism that contradicts the idea of a strict systematics and instead lives from an externality between form and content that annihilates strict systematics precisely by introducing from the outset an other that does not owe itself to the form and thus undermines its true autonomy nolens volens.Regarding the functionconcept, this can be demonstrated, for instance, by looking at the relationship between intuition and concept, or, related to this, that between form and content, regardless of whether in Cassirer or Bauch.The content is never conceived of as a self-differentiation of the form, the relationship between function and variable(s) never as a manifestation of the function.For methodic reasons, the mediating power of the concept or form always takes precedence at the expense of self-manifestation.
If the performance of the function-concept takes place entirely within the opposition of consciousness, then either way a pre-conceptual content comes into play, irrespective of whether this content, as with Cassirer and Bauch, is conceived of as a correlative moment of the concept or form, so that their relationship is not an ontic of mutually independent quantities but of determinations of meaning.
According to Cassirer's theory of the sign, for example, the sign offers a consciousness of the "first stage and the first proof" of objectivity, since it overcomes the "constant change of the contents of consciousness" by determining a permanent thing in it; thus it is "a first universal" in relation to the content: the "flowing content" is replaced by the "self-contained and self-Geltung, vol.2, n. 2, 2022 retaining unity of form" (ECW 11,p. 20).More precisely, the sign provides a "mediation" for the transition from the "mere 'matter'" of consciousness to its spiritual "form."(ECW 11,p. 43) Although in neo-Kantianism Kant's dualism of the material and formal moment of cognition, sensibility and understanding, is rejected as abstract and replaced by an original relationship, it is precisely with Cassirer and Bauch that the constitutive power of the concept emerges in such a way that it moves from the multiplicity and changeability of impressions to the unity of the object.The basic function of giving meaning is, on the one hand, already effective before positing something; on the other hand, it is only applied to the content.On the one hand, to grasp the singular, consciousness is not dependent on the "stimulation of the singular," (ECW 11, p. 39) but creates content for itself as an expression for certain complexes of meaning; on the other hand, it is again the "chaos of sensual impressions" that takes on a fixed shape through the "freedom of the activity of spirit," transforming itself into form (ECW 11,p. 41).This structure is by no means limited to the 'sign'.In general, the relationship between concept and object is understood as it has become decisive for Neo-Kantianism according to Kant's critical philosophy: Cognition of the object is not the representation of a given reality but, as Cassirer puts it, the "manifold of intuition" is to be subjected to a "rule" that determines its order; the concept is nothing other than the "consciousness of this rule" and of the unity that is posited by it (ECW 13, p. 362).The concept makes the object and its cognition possible.In terms of the Kritik der reinen Vernunft, Cassirer overcomes the discreteness of the "empirical individual data" and unites them in a spatialtemporal continuum (ECW 13, p. 364).There is a "strict and precise correlation" between concept and object, not as an ontic relation, as a "thing-relation" but as a "relation of conditioning," a symbolic relation: the concept refers to the object because it is the necessary condition of objectification (ECW 13,p. 364), that is to say that the object of cognition only receives its specific meaning through a specific "form" or "function of cognition" (ECW 13, p. 369).The forms or Geltung, vol.2, n. 2, 2022 functions also form a correlative relationship with one another (ECW 13, p.

369). The ground of validity of cognition is a whole of correlating functions of validity.
The lowest level of this whole of principles is formed by the stream of consciousness of impressions.As such, this stream is validity indifferent.
Cassirer never tires of emphasizing that even the "mere object of perception" is not directly given; rather, it is only represented "mediated" by perception and can thus be assembled into an object: the determinations are determined as "belonging" to one another (ECW 13, p. 369).Cognition establishes new connections between the "contents of perception" and expresses them conceptually (ECW 13,p. 370).In this way, the "world of the senses" becomes an "ideal" world, a "world of meaning."(ECW 13, p. 371) An "ontic transcendence" is replaced by a "transcendence of meaning"; it transforms the content of perception and with this enters first the realm of knowledge (ECW 13,p. 371).This model of constitution of the object is oriented towards the paradigm of consciousness, whose stream of consciousness is contained by the concept so that the object can be recognized as what it is.The model is also decisive for other texts in which Cassirer expands on the concept as a function.
Continuously, the concept replaces the "original indeterminacy and ambiguity of the content of the concept" with an unambiguous "determination" (ECW 6, p. 4); a "manifold of intuitions" counts as conceptualized when the members do not remain unrelated to one another but are brought into a necessary order according to a "generating basic relation" (ECW 6, p. 4).Thus concepts are brought into play as principles of the synthesis of the manifold (whereby the manifold is admittedly not restricted to the sensually given).This dependence of the concept to what is given, to what is to be synthesized -even if it concerns a relationship of correlation -and therefore the limitation of the concept and its mediating power for something else, can hardly be expressed more memorably than in Cassirer's view that the "logical nature" of pure function-concepts has Geltung, vol.2, n. 2, 2022 found its "clearest expression" in the system of mathematics.The reason being that in mathematics we are dealing with a realm of "freest and universal activity" of the concept; mathematical objects are only ideal, all determinacy arises only from the law of their construction (ECW 6, p. 121).Consequently, Cassirer holds that the mathematical concept of construction cannot be regarded as the paradigm of the "concept as such": the mathematical concept lacks a reference to being (ECW 6, p. 121).The concept, however, should relate to being.Accordingly, the function of the concept must be determined in a "final and completed" way in the "concepts of nature."(ECW 6, p. 122) In short, in a doctrine of validity as rendered explicit in transcendental philosophy, a way of thought that remains caught up in the perspective of the opposition of consciousness, there is an unbridgeable distance between concept and being.Although the concept does not throw away "its own form and its own presuppositions" as they arose for Cassirer in mathematics, it attempts to "prove itself" against the "resistance" that it experiences from the "'given'."(ECW 13,p. 470,cf. p. 468) Physics, for example, transforms the "uniform mass of the given," the "reality of immediate perception," into something "measurable."» (ECW 10, p. 7) This may be described as the "irrational moment" of the existent, as it eludes complete determinability through the concept (IHMIG, 2001, p. 215).In any case, the concept is not conceived of as pure self-determination.It is not pure self-mediation but mediation of the one and the other for the cognition of the object.In this mediation of the concept, however, the pure concept is presupposed.
The same can be found in Bauch's work, albeit again in a systematically more stringent development.Here too, the mediating or determining performance of the concept is not only overstretched to the detriment of its selfmediating or self-determining function, but it becomes also particularly clear.
For Bauch, the concept as a function of determination is incomplete, in need of supplementation, unsaturated, and thus dependent on an other that is not conceived as the other of itself.Thus the concept is not a concrete Geltung, vol.2, n. 2, 2022 universality in the Hegelian sense but abstrahent and concrescent.Accordingly, Bauch conceives of the relationship between universality and particularity in such a way that particularity is that which we "experience in immediate life" (BAUCH, 1923, p. 225); the "basic characteristic" of particularity is that it stands in a certain relationship to "sensation." (BAUCH, 1923, p. 227) Taken by itself, sensation is validity indifferent and hence does not yet mean anything for cognition, even though to be even just sensation it must always already be classified in the relationship of categories; in the same way, the particular as cognitive material is always already classified in the universal relationship of categories (BAUCH, 1923, p. 257).The concept is a relationship of categorial relationships and thus establishes the universal relationship of categories: concepts as "principles of order" organize the particular into the universal relationship of categories (BAUCH, 1923, p. 257).Although the universal and the particular are correlatively related to each other, they are not conceived of as self-differentiation.In contrast, they are thought to be an ordering of what is ultimately the content of sensation.In such a way, the concept is the "condition of the possibility and the law of the unity of the universality of its particulars."(BAUCH, 1923, p. 258) According to this logic of presupposition or the conditions of the possibility, Bauch also conceives of the relationship between intuition and concept: Intuition is the inclusion of the "manifold material in the categorial relationship of validity according to the law of the concept."(BAUCH, 1923, p. 259) The concept mediates it to cognition.This certainly rejects sensualism insofar as intuition or sensation and the concept are not, as in Kant, two heterogeneous sources of cognition: both are subordinated to the one law of validity of knowledge.Consequently, they each are differentiated functions of validity: intuition embeds sensation in the universal relationship of categories for the determination of intuition by the concept (BAUCH, 1923, p. 268, p. 275, passim). 6The "content or being-foundational (seinsgrundlegende) character of the concept" (BAUCH, 1923, p. 287) guarantees a functional Geltung, vol.2, n. 2, 2022 relationship between universality and particularity, intuition and concept.The concept is the precondition of particularity; it determines through which differences a particularity is specified, i.e. which particularity can be determined.The concept is precisely the totality of the conditions of particularity (BAUCH, 1923, p. 289).
Their relationship is not that of self-differentiation or self-determination of the concept or the universal.Instead, it is a relationship of "logical continuity."(BAUCH, 1923, 289 ff.)The conditions of validity form among themselves a "continuous relationship of relations of validity," (BAUCH, 1923, p. 290) in which the material of cognition is also included.This continuous relationship takes the form of what Bauch (1923, p. 300) calls "bordering" (Hingrenzung) qua direction towards a goal as a limit (limes): the limitation regulates the course towards continuity.The lowest level of constitution is also formed for Bauch by sensation, which enters into the concept as the "quality of its content."(BAUCH, 1923, p. 300, passim) Sensation, as "content," "supplements" thought qua the formal structure of validity relationships of a categorical and conceptual nature (BAUCH, 1923, p. 302).The affinity of concepts in logical continuity is "content-relatedness" (inhaltliche Verwandtschaft) (BAUCH, 1923, p. 303).Hence, it is not identity or selfmediation, and as a limitation it is certainly not self-mediation through selfreferential negativity.In the perspective of transcendental philosophy, concepts determine and govern the objects as laws of validity; they are neither objects themselves but their condition of possibility, nor are they conceived of in the fashion of a χωριςμός, a strict separation.The concept is a function and relationship.The concept and the concrete form a one-sided relationship of justification and reciprocal relationship of conditionality; the conditional and the conditioned are neither without each other nor do they coincide; rather, a "distance" remains; "each requires the other," which it is not itself; the concept is unsaturated and in need of supplementation (BAUCH, 1926, p. 134).

THE SPECULATIVE CONCEPT AS THE PRESUPPOSITION OF THE FUNCTION-CONCEPT
Like the neo-Kantians, Hegel is also intent on perfecting transcendental idealism as initiated by Kant.And, as in neo-Kantianism, the motif of the unity of reason, which Kant had insufficiently rendered explicit, plays a decisive role for Hegel too (KRIJNEN, 2016).However, thinking through the presuppositions of transcendental idealism does not lead Hegel to an improved transcendental idealism but to speculative idealism, or to be more precise, speculative idealism is the improved transcendental idealism (KRIJNEN, 2024).Speculative idealism, however, is not a pre-Kantian metaphysics of spirit, as is the common prejudice in the transcendental philosophical discourse. 7Rather, it is a radicalization of the transcendental idea of justification, a radicalization that arises in the course of an immanent critique.
Accordingly, Hegel conceives of the concept, as of all determinations in his Logik, free of any "substrata […] of representation" or otherwise pre-given.
He considers them in their "nature and value in and for themselves."(GW 21,49) The determination of pure self-determination of the concept must take place without any recourse to external conditions.The concept is pure selfdetermination and in this determination of itself at the same time determination of the other of itself.It is precisely in its functionality for others that it proves itself to be self-determination.In Hegel's terms, the essence passes over into the concept.Transcendental philosophy, in contrast, thinks of the concept as an essence, not as a concept.It is an absolutized logic of essence (KRIJNEN, 2021;2022b).It is true that transcendental philosophy treats concept-logical topics such as concept, judgment, conclusion, idea, and the like.Yet it does so not in their concept-logical determinacy.Hegel's logic of the concept too shows that transcendental philosophy, whether Kantian or later, cannot be a radical 7 Regarding Cassirer, see Krijnen (2023), regarding Kant, see Krijnen (2022a).
Geltung, vol.2, n. 2, 2022 doctrine of justification but must for the sake of its own claim to cognition develop into a speculative logic.
Hegel's logic of the concept in particular makes the radical selfdetermination of thought explicit, while transcendental philosophy, to articulate it with Hegel, is and remains cognition under the "theoretical idea."(GW 12,199,231;GW 20,§ 225) For this reason, it cannot get rid of its formalism, as it manifested itself, for example, in the above-mentioned as the externality of the function-concept.The methodical moment of the "realization of the concept" through the concept's own moments of the universal, particular, and singular is missing."Forms" are not primarily conditions of the possibility for what is made possible but must first be determined in themselves in terms of their truth content.The concept as a concept is presupposed in the determinacy of the concept as a function-concept, that is to say as the determination of the other: in determining the other, the concept is presupposed as pure selfdetermination.
At its end, Hegel's Logic of Essence has identified essence as pure selfmediation that is transparent to itself: as a "perfectly transparent difference" between universality, particularity, and singularity, which is the "concept, the of subjectivity or freedom."(GW 11,409) As a self-transparent relationship of self-mediation, essence has turned into the concept.While in the Logic of Being the self-determination of the concept appears only as an immediate determination ("passing over," Übergehen), the self-determination of the concept in the Logic of Essence is thematic but does not yet appear as self-mediation.
The Logic of Essence determines thought in its reflection and mediation, not, like the Logic of Being, in its immediacy.Initially, in the logic of reflection of the Logic of Essence, the mode of movement and relationality of the thought determinations themselves become an issue.The Logic of Essence transforms the unrelatedness of the determinations that predominates in the Logic of Being into relationality: that which is, is only within a relational structure of determinations, has its ground in essence as that which grants determinacy Geltung, vol.2, n. 2, 2022 (posits, determines, mediates).Essence is "being that has gone into itself," (GW 20, § 112 R) "being coming into mediation with itself through the negativity of itself."(GW 20, § 112) Nevertheless, the determinations of essence are only "relative," not yet "reflected in themselves"; they are an "imperfect" combination of immediacy and mediation (GW 20,§ 114).In the Logic of the Concept, on the contrary, determination is expressly self-determination, a perfect combination.The Logic of the Concept is a true logic of freedom as a logic of self-determination (KRIJNEN, 2021;2022b).
It is precisely in its abstract or formal universality that the concept proves to be inadequate (incomplete, deficient, insufficiently determined); it realizes itself through the determination of this inadequacy as the unity of itself.In this fashion is the concept the ground and source of all determinacy.It has its content or reality in itself; in its realization it does not fall back into what is supposedly given.If it were to fall back into what is somehow given, the concept would not be the founding unity of immediacy and reflection or of being and essence; it would merely form one side of the relationship.However, the concept as such contains the moments of "universality" (equality with itself), "particularity" (determinacy), and "singularity" (as the reflection in itself of universality and particularity and thus as that which is determined in and for itself, i.e. the determined universal).
Since the concept as self-referential self-determination is the unity of being (logic of immediacy) and essence (logic of mediation), it is not only selfdetermination but determines itself as self-determination.The activity of determination is not carried out on others but on itself.If the determination of thought takes place in the manner of a reflective constitution -regardless of whether in transcendental or speculative idealism -then this reflective constitution as such becomes thematic in the concept. 8The concept posits itself as what it is, and in this it remains entirely with itself.In this respect, the positing of a new determinacy of the concept is its concretion, self-enrichment, self-development, self-interpretation, absolute negativity.The self-relation that is the concept is a self-referential determination, a determination that mediates itself.Thus the reflective constitution that only took place in (thought as) being and essence is determined in the concept.The determinations of the concept are the determinations of the forms of its own actualization.
First, the concept is pure, simple self-determination. 9As such an immediate self-determination, the concept is the pure universal, for although it is initially totality, it is still completely indifferent about any determinacy.In this respect, as a pure concept, it is the indeterminate concept.Nevertheless, the universal is not an "empty" universal that is dependent on a given manifold for its determination.Rather, the concept is absolute determination and therefore has its content in itself.As the universal, it is self-determination.The particular and the singular are for it determinations of self-determination.A universal that is only indeterminate with regard to possible fulfillment through content is an "abstract" universal.The speculative (speculative-idealist) concept of the universal is not external to its particularity and singularity; these belong to it.
The universal is a "concrete" universal, a universal that determines itself in a reflective-constitutive fashion, that is to say that it develops its determinacy from itself.Without the precondition of a concrete universality, the abstract universal in contrast to the particular (and singular) could not even be thought of; there would only be respective determinations, no universal and particular.
The universal particularizes itself just as it singularizes itself.As a concrete universal, it has its determinacy only in relation to the particular and the singular.As something purely universal, it is indeterminate self-determination.
As such, the universal is self-particularization and self-singularization.It contains the moments of particularity and singularity in itself; thus it remains Geltung, vol.2, n. 2, 2022 entirely with itself in its determinacy.It is equality with itself in its determinacy -i.e.particularity -and the reflective-constitutive unity of the universal and the particular -i.e.singularity as the universal determined in and for itself.As an indeterminate self-determination, the universal exposes itself as its own determinacy.For Hegel, the universal as a free power "is itself and reached out to its other," but without doing violence to it as it is in its other with "itself," relates to that which is different from itself only as itself and consequently returns only to itself in the process of determination (GW 12,35).
Consequently, the universal is a "creative" or "free" power qua selfreferential negation: pure self-negation (GW 12,p. 35).Thus it is at the same time an infinite unity, absolute identity with itself, identity with itself and mediation.The concept as the universal or the universal that is the concept is this identity as self-referential negation, negative identity, self-positing, selfdetermining identity, indeterminate self-determination.If this is the case, then the concept is an absolute concept.The universal is not an abstract universal but exposes itself: concrete universality.It refers to nothing other than itself, does not require anything existing outside itself to realize itself, i.e. to achieve its determinacy.The concept as the universal is reflection reflecting itself in itself (not against something else), total reflection, absolute mediation in itself, purely intelligible self-relation as such.So is the universal a concrete universality.It is a concrete universality through its negative self-reference.Thereby the universal presents itself in the particular and the singular.It gives itself existence in the element of thought.
While transcendental philosophy conceives of the principles of what is cognized in terms of a layered (graded) whole of (constitutive and regulative) apriority that makes up its foundation, covering the entire spectrum of determination from the origin of thought to concrete objectivity, Hegel's Logik is divided into being, essence, and concept.The Logic of the Concept thematizes the pure self-determination of the concept; it does so as a reflective-constitutive pure self-determination: determination as an infinite relation of the concept to Geltung, vol.2, n. 2, 2022 itself.Initially, the concept is merely pure self-relation, i.e. thematic as selfdetermination, not only as immediacy, as passing over into something else (Logic of Being), or mediation, as the positing of something else (Logic of Essence).The Logic of the Concept is the reflective constitution that determines itself.The determinations dealt with here are thematic -and thus determinedas forms of the realization of absolute self-determination.
Kant's transcendental revolution is taken into account in such a way that the concept is not only the form of comprehension but also the form of what is comprehended.Subjectivity, as the idealist basic formula for philosophical comprehension reads in this or that accentuation, is the foundation of objectivity.Thoughts are, as Hegel also says, "objective thoughts": in that thought seeks to form a "concept" of things, this concept cannot consist of determinations that are "alien and external" to things (GW 20, § 24, incl.R).
Also in accordance with Kant's philosophy, which arrives at the pure concepts of understanding or categories as principles of objective determinacy via the forms of judgment as the principles of thought, Hegel develops the determinations of the concept via its subjectivity as forms of comprehension (GW 12,p. 31;GW 20,§ § 163ff.).He starts from the subjective, formal, or immediate concept, arrives at the objective, real, or mediated concept (GW 12,127ff.;GW 20,§ § 172ff.)and finally at the adequation of subjectivity and objectivity in the idea as absolute self-determination.This absolute selfdetermination has passed through both subjectivity and objectivity and is therefore self-mediated self-determination (GW 12,173ff.;GW 20,§ § 213ff.).
What distinguishes Hegel from Kant and the subsequent transcendental philosophy in principle, however, is that the determination of the unconditional self-determination of the concept gets by without recourse to external conditions.In contrast, transcendental philosophy generally lacks a "principle of determination" (GW 20, § 508) as understood by Hegel, i.e. the realization of the concept through its moments of the universal, particular, and singular, which abolishes all externality (cf.GW 12,17).The content of the objectivity of Geltung, vol.2, n. 2, 2022 the concept as unconditional self-determination, which does not include any recourse to externality and thus excludes formalism, arises in the transition from the subjective to the objective concept: the subjective concept has objectivity in itself.In Kant's terms, its objective reality is thus deduced.
The model of a layered apriority is typical of transcendental philosophy.
Certainly, it arises from the origin of thought qua original synthetic unity and extends from the principles of the origin to the singularization of thought.
However, the origin does not singularize itself to itself but to others.Against this, with Hegel's transition from the Logic of Essence to the Logic of the Concept, the substance proves itself to be the subject, the substance is liberated into the concept.The mediation of the concept has become a "mediation of the concept with itself," "immanent reflection," "absolute negativity that what forms and creates."(GW 12, p. 34) Hence, not only is the development of the Logic of the Concept from the concept to the idea conceived of as a manifestation of the concept, but nature and spirit as the parts of the system of philosophy that follow on from logic are also manifestations of the concept in a specific way.By implication, they are manifestations of freedom as a manifesting self-relation: being-and-remaining-with-itself of the concept in the other.
In contrast, in the apriority model of transcendental philosophy, the relationship of form to content remains characterized by externality, despite all attempts to overcome Kant's dualism of stems of sensibility and understanding or intuition and concept respectively through a pervasive structure of the validity of knowledge that is supposed not to be an abstract universality but a constituent of all objectivity.The form does not determine itself to content, the concept itself not to reality.Rather, the content remains non-form regardless of its form-determinacy as content, the reality also non-form despite its formdeterminacy.
While Bauch and Cassirer do not make a strict distinction between the particular and the singular in their explanations of the function-concept, it is crucial for Hegel.Singularization, as Bauch would say, concretization, Geltung, vol.2, n. 2, 2022 concrescence, is conceived of in Hegel's Logik as the manifestation of the universal through the particular to the singular.By completely mediating its moments of universality, particularity, and singularity with each other and with itself, the concept comes to a new immediacy, a new being: the "objectivity of the concept."(GW 12,126,cf. 92 and GW 20,§ § p. 192) Here, the concept as the subject has not united with another but with itself.It is precisely this realization of the concept that for Hegel is the "object" (GW 20,§ 193).The concept determines itself as objectivity (GW 12,127,130).It is not an abstract universal detached from being but immediately contains "being" -admittedly not in the logically primitive form of pure immediacy but in the richer form of "singularity."(GW 12,128) Looking at Hegel's Logik as a whole, we can also say that the concept progresses from itself as a concept of substance to the functionconcept and finally to the concept.