From Monism to Pluralism: Cassirer’s Interpretation of Kant

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Introduction

Kant is known as a philosopher who revolutionized the theory of knowledge. Kant compared his changes in the field of knowledge with those of Copernicus in astronomy. Like Ptolemy’s astronomy, the pre-Kantian theory of knowledge relied on ordinary understanding. Before Kant, philosophers did not doubt that man acquires knowledge of the objects already given in the world in which he or she lives. Such a process of acquiring knowledge¹ can be represented as an arrow going from the objects to the minds. Philosophers of modern times raised the question about the reliability of knowledge and the source of knowledge. Nevertheless, no one raised the question about the direction of arrow acquiring knowledge. Kant’s revolution changed the direction of this arrow: not from the objects to the cognition, but from the cognition to the object. A man does not live in a given and known world. Instead, a man’s cognition forms the world by the laws of this cognition. In other words, The Critique of Pure Reason (CPR) considers cognition as a process of constituting the laws and forms of the objective world.

Kant’s method of investigation is called the critical method. It discovers what should be the functions of cognition to discover the natural world as it is in scientific research. Kant’s process of constituting the world integrates two sources of knowledge: intuition and understanding. The first source is direct knowledge given in “pure” or a priory form of receptivity: space and time. It gives initial order to the reception of sense data [1. P. 155—192]. The second — is an indirect source of knowledge. This knowledge is produced by concepts that are the functions of understanding under which multifold representations are united [1. P. 205].  The concepts are arranged into judgements, which, in turn, create a system of knowledge. The highest principle of cognition is the unity of transcendental apperception in which all representations of intuition are synthesized. Without this unity, the representations would not be “my” representations [1. P. 246—247]. Thus, the possibility of the objects is conditioned to the unity of “my” consciousness [1. P. 250]. This is, in brief, the revolutionary knowledge system developed by Kant. This system provided a way out of the impasse into which modern philosophy had driven itself when it asked for the reliability of knowledge. In Kant’s theory, the required reliability should not be found in the objects of experience but in cognition. Thus, cognition as a process of acquiring knowledge becomes a basis that ensures the reliability of knowledge.

The Kantian revolution of thought was also a revolution in worldview. Henrich Heine compared the destruction made by Kant in the realm of thought with the terrorism of Robespierre [2. P. 109]. The wonderful organization of nature, which previously seemed to be proof that nature was made by the hands of the creator, now turned out to be a creation of human cognition.

Ernst Cassirer was a student of Herman Cohen — one of the leading figures in the Marburg school of the neo-Kantian philosophical movement. The starting point of Cassirer’s multi-volume work, The Philosophy of Symbolic Forms (PSF), devoted to the philosophy of culture, is the “revolution in the way of thinking” made by Kant [3. P. 154; 4. P. 78—79; 5. P. 29]². Cassirer defined this revolution as a radical change in the theory of cognition, the change that reorganized the relationship between man and the world. Under Kant’s new theory of cognition, objectivity is not found in the objects but in the cognitive judgements about objects. However, Kant’s theory of cognition is applied to the scientific knowledge of objects exclusively and does not embrace entire objectivity. Therefore, the CRP is not the last point of Kant’s inquiries. In his following books, Kant analyzed the forms of objectivity that go beyond scientific cognition. The Critique of Judgement examines non-cognitive judgements. There are aesthetic and teleological (relating to life sciences) judgements. CPR answers how mathematics and physics are possible but does not answer how life sciences are possible. In Kant’s cognitive system, there are no means to explain an organism’s plausible existence. How can we explain the life and growth of organisms in a world where the concept of causality explains everything? According to Wilhelm Windelband, this is the riddle for our cognition [ein groβes Rätsel für unsere Erkenntis], which Kant discovers in the Critique of Judgement [8. S. 163]. From Cassirer’s view, the incompatibility between the teleological and cognitive judgements will not be a riddle if the capacity of cognitive judgements is expanded. Kant understood that the CRP approach is too narrow [4. P. 79]. Consequently, Cassirer defined the task of his philosophy, the PSF, to extend Kant’s critical method to different forms of objectivity, such as the pre-scientific world of living beings: the mythical and aesthetic forms. “A critique of reason thus becomes a critique of culture.” [4. P. 80] Kant’s inquiry was not aimed at what a being is. Rather Kant asked: how natural science is possible? Whereas Cassirer set the task of exploring how different cultural forms of world-making are possible.

This new task is very different from Kant’s original intentions. The analysis of the functions of cognition in the CPR was aimed at confirming the necessity of scientific knowledge. It must explain the reliability of knowledge. The functions of cognition constitute the only objective form of the world. They do not allow different possibilities for organizing the world’s structure. Intuition is immediately given; therefore, only one form of space and time exists. Similarly, there is only one a priori or pure synthesis. Althought, Kant called synthesis “the effect of the imagination” [1. P. 211]. In this context imagination does not mean the arbitrariness of action. It is a “blind” imagination that strictly follows a priori concepts of understanding. The necessity of these concepts excludes the possibility of a different synthesis.

“The gist of his [Cassirer’s] comments [on Kant] may be summarized this way: Kant has failed to account for a great variety of synthesizing acts by which sensory data may be ‘spelled out in order to be read as experiences’ ” [9. P. 41].

This paper examines how Cassirer derived the different synthesizing acts out of the Kantian notion of pure synthesis in CRP, more precisely, how the “Copernican revolution” of Kant paved the way for various cultural forms in Cassirer’s PSF.

The Shift in the Theory of Concept

Cassirer stated that the revolution of Kant’s thought lies in changing the model of the concept [10. P. 97]. Cassirer clarified this changing in Substance and Function (SF), written in 1910³. In the old model, the concept is derived from a common property of existing things and is called a generic concept [10. P. 4]. Cassirer emphasizes that this kind of concept formation matches the model of the individual existence of things because this concept is part of reality. So, Cassirer called the generic concept “thing-concept” (Dingbegriff) [10. P. 2—3]. By contrast, the functional concept is not a quality of individual things but becomes a function that determines the order of moments in the series⁴. It means that moments are the inner components of relation, and there is nothing outside of relation.  While the generic concept exists in the same mode as a thing perceived by the senses, the functional concept (Funktionbegriff) is pure relation. It is called here “concept of relation.” Cassirer came to the very radical statement that the meaning of judgement depends on various relations [13. S. 152]. In SF, Cassirer still needed to develop the theoretical platform for the plurality of objective forms, and all the examples of concepts in this book refer to the concepts in the natural sciences. However, he stated that SF’s results brought him to PSF’s ideas [4. P. 69]. The thesis of this article is that with the help of the concept of relation, Cassirer justified the plurality of synthesizing acts. By the term “plurality,” Cassirer did not mean worlds with different natural laws but different modes of existence in one world. He denied scientific cognition as the only way to establish objective reality. The world of nature results from a “special form of cognition” [3. P. 154] or “one of the many forms” [3. P. 77]. We will inquire what Cassirer’s theoretical assumptions led him to this conclusion.

 Cassirer assumed a variety of cognitive acts to arrange worlds that go beyond the physical world. The laws of these worlds are not derived from scientific judgements. These worlds can be defined as “modes of existence,” “forms of objective reality,” or “directions of spiritual activity.” All these terms refer to what Cassirer had named “symbolic forms” [4. P. 73—85].

“Twofold Opposition” of A Priori Synthesis

Cassirer stated that the different symbolic forms depend on the forms of space and time. What did he mean by this? Cassirer analyzed the form of space in the article Mythic, Aesthetical, and Theoretical Space [14]. He seemed to follow the Leibnitzian definition of space. He defined space as an order of things in a spatial position. It is a functional concept or concept of relation. The concept of relation does not depend on any given element; it does depend exclusively on their connections. For example, the rule for ordering the series of natural numbers is the same rule that defines the members of a series. Although the relation between order and the content of the series is necessary, the order itself is not necessary. The different principles of the order will form different content. The space is identified with one specific order but is not bound to only this order.

Cassirer argued that the shift from the definition of space as the universal ground of knowledge to space as “order” is “a victory of pluralism over abstract monism, of a multiplicity of forms over a single form” [14. P. 8]. Space as a concept of order is the condition for the plurality of worlds. The different order of arranging sensory impressions in space set up different ways of world-making. The pluralistic theory about space becomes a foundation for developing the two symbolic forms: mythic and scientific-theoretical [5]. These two forms are the outcomes of different forms of space and time.

Scientific space and time are characterized by three essential features: continuity, uniformity, and infinity. Continuity means that points in space and moments in time are not independent elements. Uniformity means that all the “points” and directions of scientific space are the same; they do not possess individual qualities. Every ‘moment’ taken from this continuum is defined as a position in space or in the procession of time. Infinity means that space and time can be expanded without end. It has no borders and lacks a beginning and an end [5. P. 83].

By contrast, the aesthetic and the mythic forms of space and time are characterized by discreteness, heterogeneity, and clear borders [5. P. 84]. The ‘points’ in the mythical space and time do not have the same meaning. There are ‘points’ of greater and less articulation. The structure of this space and time is organized as a dichotomic system. It is expressed in the division between more articulated and powerful “sacred” moments and less articulated, ‘profane’ points [5. P. 73—83]. The mythical space and time reflect the structure of bodily perception⁵. Unlike points in scientific/theoretical space and time, those in aesthetic/ mythic/perceptive space and time are not subdued to a causal relationship. They have a particular “type” of causality [5. P. 46]. This type of causality is called metamorphosis or miracle. Everything can be transformed into anything else, as is well-known from ancient myths and the Bible.

Thus, the natural world exists in one form of space and time, whereas the realm of art, myth, and the immediate world of living beings — in another. Space and time as the forms of subsuming particular to the universal, can be organized in two ways. The first characterizes by the concept of order, the concept of relation. The particulars (moments) in this form have no other meaning than their position concerning other moments. Their position is determined by the primary order (concept, universal). The second way characterizes the particulars, which have their meaning as robust and routine moments. However, the position in the structure also determines the degree and specialization of their power. The moments in the center are the most powerful and have the most potent emotional effect. In both cases, the meaning of particulars is determined by their relations to the universal. So, in both forms, the universal, that is, the form, precedes the particulars. However, doesn't that look paradoxical? The structure where the whole defines the order of particulars is intuition. Intuition means that there is no synthesis of a particular, but there is a given structure. Indeed, despite the functional understanding of space and time forms, in PSF, Cassirer continued to call them spatial-temporal intuitions [Anschauung]. This issue needs to be considered in more detail.

In Kant’s Life and Thought, Cassirer examined the correlation between pure intuition and a priori synthesis in CRP. Synthesis is “the action of putting different representations together with each other and comprehending their manifoldness in one cognition” [1. P. 210]. The unification of manifoldness is the faculty of understanding and not of sensibility. This means that synthesis refers only to the concepts of understanding and not to the forms of receptivity. Yet Cassirer stated that all syntheses must be related to intuition. Pure intuition is not only a container but also the place of connection between the concept (universal, rule) and the impression (particular) that takes place in space and time. To support this, Cassirer has referred to Kant’s essay in correspondence with Eberhard [3. P. 160]. Cassirer argued that exactly there Kant discovered the principle of synthesis. This principle implies that all synthetic a priori judgements are related to pure intuition, but the character of this relation needs to be clarified in the CPR. “Thus the result is that all synthesis a priori is separably linked with the form of pure intuition, that it either is itself pure intuition, or else is mediately related to and rests on some such intuition” [3. P. 160]. Hence, “pure” synthesis is not only a priori “as is that in space and time,” as Kant put it [1. P. 210], but it requires the necessary relation to pure intuition. This relation reveals the characteristic peculiarity of a priori synthesis. It is the character of “twofold opposition” [Doppelte Gegensatz]  [3. P. 159]. What does it mean?

In the definition of “a priori synthesis,” Cassirer highlighted two contradictory statements. One statement refers to “synthesis” and the other to “a priori.” According to the first statement, synthesis is the action that combines sensory elements. Synthesis is described here as a mechanical operation that unites sensual manifold into one concept. The second statement is that unity precedes synthesis. Thus, in a priori synthesis, the correlation of the particular with the universal can be done in two opposite ways: by connecting the particular to the whole and by dividing the given whole into the particulars. The first is an empirical connection, when a general concept is formed from a particular experience. The second is an action of formal logic, which does not produce new knowledge but analyzes what is already given. A priori synthesis includes both directions. Cassirer defined this synthesis as: “a constructive connection, in and through which simultaneously a profusion of particular elements [zugleich eine Fülle besonderer], which are conditioned by the universal form of the connection, arises for us” [3. P. 159]. The whole, therefore, is both composed of the elements and is already somehow present in the “fullness” [eine Fülle] of these elements. Therefore, an a priori synthesis is a whole that is synthesized and initially given.

Cassirer stated that Kant explains this structure of a priori synthesis with the help of pure intuition. Intuition is a form of receptivity in which the whole is initially given and composed. Let us take an example from geometry, the science of space [3. P. 147—148]. The rule — the angle sum of a triangle is equal to 180°, is discovered in a particular observation. However, this rule is given as a general principle concerning any three straight lines that could intersect in geometry. This principle ensures universal objectivity, that is, its correctness about all possible triangles. The rule of a triangle is a priori. It is given before any observation. This and other geometry rules are derived from intuition, which is the primary structure of space. Besides, this principle is creative and synthetic because drawing the lines of a certain triangle is an act of actual connection of points, so it is not a result of formal logic or propositional thinking. This rule may serve as an example for all the principles of space. Space includes two directions of correlation between the particular and the whole: it is at the same time the act of connection and the form of intuition where all elements are present initially. According to the first, the particular is subsumed under the concept. The second direction, in fact, is not the correlation since particular is already filled with universal. Cassirer argued that these two directions of arranging are contained in the Kantian definition of pure intuition. Since the form of space and time is based on the concept of order, it can arrange manifold in two forms of objectivity: theoretical and mythical-aesthetic. Since the forms of space and time are pure intuition, it allows us to explain the possibility of the pre-scientific and aesthetic form as an immediate perception whose features cannot be explained by conceptual thinking. When Cassirer pointed out that every pure synthesis comes with pure intuition, he also explained the nature of this synthesis by the double nature of pure intuition. Thus, the concept of a priori synthesis is ambivalent; it includes twofold opposition since it implies, at the same time, a synthesis and an original wholeness [3. P. 159].

The Logic of Non-Identity as the Basis for the Diversity

The concept of a thought containing a double-thinking (Doppelgedanken) characterizes Cassirer’s functional concept [16]. This returns us to the beginning of the article. Already in SF, Cassirer criticized the non-functional approach to the concept, that is, the approach according to which the concept is defined in the same manner as an existing thing. This notion of a thing cannot be ambivalent. Nevertheless, the concept of relation is a concept of a new kind; it is a function that defines the order of the moments. In the functional concept, the moments are determined by a relation. From the logical point of view, the concept of relation is inconsistent because it presupposes both the unity of the elements and their separation [17. S. 291]. The relational theory of concept breaks the logic of identity. To answer the criticism about inconsistency, Cassirer argued that the new model of a concept presupposes a double-thinking.⁶ This thinking includes two divided moments that remain in a relationship; they are neither wholly divided nor completely united [16. S. 116].

Cassirer worked out the concept of relation into the concept of a symbol — the central notion of the philosophy of symbolic forms. The two-sided character of the concept of a symbol challenges the contradiction between symbolic and intuitive knowledge. In the commonly accepted view, a symbol is a sign that represents (or stands for) something else; it is a material object that is used to represent something different from itself. For Cassirer, the “symbol” signifies the link of the universal (meaning, concept, rule of the function) to the particulars of sensory impressions. Symbolic knowledge is knowledge received through concepts, that is, through interpretation. Such knowledge results from cognition which constitutes objects and does not grasp “reality” as it is. Therefore, Kant’s theory of cognition in the CPR is the process of acquiring symbolic and not intuitive knowledge. Intuitive knowledge is immediate cognition. This knowledge needs neither concepts nor synthesis. Cassirer considered the immediate knowledge as fiction. The concept is the only instrument of philosophy, and philosophy has no other way to reach knowledge. Philosophy “knows” only one way to investigate: using concepts. “To philosophy, which finds its fulfillment only in the sharpness of the concept and in the clarity of ‘discursive’ thought, the paradise of mysticism, the paradise of pure immediacy, is closed” [18. P. 113]. Cassirer stated that the notion of immediate knowledge had been inherited from mystical religious tradition. The philosophy of mysticism needed immediate cognition to distinguish between the divine direct apprehension and the limited consciousness of mortal man, which needs concepts for achieving knowledge. This division was inherited even by the rational philosophy of Kant, in which human cognition needs concepts as means for knowledge compared to divine immediate intellectual intuition.

Cassirer stated that the conflict between intuitive and conceptual knowledge had become the main problem of philosophy over the past 150 years. This contradiction has caused opposition between phenomenology and neo-Kantianism, philosophy of life and positivism, irrationalism, and rationalism [19. P. 136]. In the introduction to the PSF is written: “The cleavage between these two antitheses [concept and intuition] — it would seem — cannot be bridged by any effort of mediating thought which itself remains entirely on one side of the antithesis”  [4. P. 112]. The phrase “it would seem” from the above citation points to Cassirer’s doubt about the validity of this statement. We argue that Cassirer resolved this conflict by the logic of non-identity. The concept of the symbol is functional one, that is, the concept of relation. According to the logic of non-identity, the concept of relation means the connection and separation of moments simultaneously. Consequently, the concept of a symbol presupposes both the connection of sensory manifold with meaning (as two separate elements) and the primary wholeness of manifold and meaning.

Cassirer’s revision of the old tradition of the distinction between symbolic and intuitive knowledge began in his book devoted to Kant [3] with a consideration of a priori synthesis and intuition in Kant’s CPR. This synthesis and intuition contain two different notions about the correlation of manifold with the concept. The first notion involves the synthesis of the sensory manifold, and the second is the original unity. This is the meaning of the “twofold opposition” of a priori synthesis. On the one hand, synthesis is a combination. It presupposes a conceptual construction of reality. This is a symbolic aspect of knowledge that denies the cognitive role of intuition. On the other hand, unity (concrete wholeness) is already given in each element of the synthesis, even before the synthesis itself. This unity presupposes intuitive rather than symbolic knowledge. These two aspects of a priori synthesis manifest that pure intuition and concept are not opposed to each other: intuition contains the act of binding and arranging, and the concept — the givenness of sensibility.

It should be noted that Cassirer’s solution to the contradiction between the mediated (that is, concept, symbol) and the immediate (that is, intuition) does not mean to “sublate” this contradiction. This is not the Hegelian “Aufhebung” in which two opposites are sublated and synthesized into a new concept. For Cassirer, contradictions remain opposite notions. Exactly the twofold opposition or double-thinking makes it possible to avoid the mere givenness of the elements, the “ossification” of knowledge. This characterizes pure synthesis as a creative process. This is the main strength of the Kantian “revolution in the way of thinking” — the revelation of human knowledge as a “divine” boundless creativity. Double-thinking prevents cognition from turning into dogmatic monism of concepts (rationalism) or sensibility. This doubleness paves the way for explaining the plurality of free forms of world-making.

Conclusion

The present study is examined how Cassirer explained the possibility of symbolic forms based on Kant’s theory of cognition. In the CPR, Kant set a completely different task. His “revolution” was designed to provide a method of scientific cognition that guarantees objectivity and truth of knowledge.  Neo-Kantians considered Kant’s critical method the solid basis for scientific knowledge. Unlike other neo-Kantians, Cassirer argued that the Kantian revolution is a key to understanding scientific knowledge as a particular but not a unique function of cognition. It is vital to a variety of symbolic forms.

Cassirer inherited the Kantian method of inquiry from facts to conditions of these facts: there must be conditions in cognition that determine the facts as they are. This paper examined Cassirer’s position, where the starting point is the facts. Cassirer proceeded from the fact of existing different symbolic forms: myth, religion, and aesthetics. The existence of these forms is a fact of culture. Whatever explanations philosophers have found for these forms, they cannot deny their existence. These forms show that the critical method should not be limited to just the scientific form of cognition. It must be extended to other areas of culture. All cultural forms should be included in the Kantian critical method.

We also examined how Cassirer turned to analyzing these symbolic forms. He demonstrated that the difference between scientific and non-scientific forms lies in the difference between space and time forms: the first is characterized by continuity, uniformity, and infinity, whereas the second — by discreteness, heterogeneity, and finiteness. Cassirer pointed out that pure intuition must be correlated with synthetic a priori judgements. Therefore, the diversity of the forms of pure intuition should be correlated with the structure of a priori synthesis. This structure is characterized by twofold opposition. Pure synthesis includes both the synthesis of the sensory manifold and intuition. Both are united and separated moments of a priori synthesis. The present paper argues that Cassirer explained this opposition by specifying the concept of a priori synthesis as the concept of relation. The “concept of relation” is the model of concept that Cassirer has previously elaborated. The concept of relation includes moments that stay separated and are united simultaneously. This model of concept supposes double-thinking in the meaning of a concept. Cassirer explained it by the logic of non-identity. This logic confirms the characteristic of a priori synthesis which is defined as both combinations of moments in synthesis and initial unity in intuition.

_{¹ In this article, cognition (Erkenntnis) means the process of constituting objects, whereas knowledge — is an endpoint.}

_{² Verene [6] argued that the roots of Cassirer’s philosophy of symbolic forms can be found rather in Hegel’s than in Kant's philosophy. In contrast, Krois [7] argued that Cassirer's cultural philosophy was close to ideas of phenomenology (Husserl, Heidegger, Merleau-Ponty).}

_{³ On this issue, see my article [11. P. 171—172].}

_{⁴ Friedman [12. P. 30—34] assumed that the origin of Cassirer’s theory of the concept stems from Bertrand Russell’s philosophy of mathematics.}

_{⁵ See my research regarding connection between Cassirer’s mythical symbolic form and the space of visual perception, investigated by Gestalt psychology [15].}

_{⁶ The Swedish philosopher Konrad Marc-Wogau claimed that Cassirer's definition of the symbol is based on the concept of relation, which contains a contradiction. For an exposition of the discussion between Cassirer and Marc-Wogau, ref. [11. P. 173—174]}

About the authors

Ira Katsur

Author for correspondence.
Email: ira.kachur@gmail.com
ORCID iD: 0000-0002-8610-0293

PhD in Philosophy, Researcher, Center for German Studies

References