# Arthur Schopenhauer: Logic and Dialectic

Arthur Schopenhauer: Logic and Dialectic

For Arthur Schopenhauer (1788-1860), logic as a discipline belongs to the human faculty of reason, more precisely to the faculty of language. This discipline of logic breaks down into two areas. Logic or analytics is one side of the coin; dialectic or the art of persuasion is the other. The former investigates rule-oriented and monological language. The latter investigates result-oriented language and persuasive language.

Analytics or logic, in the proper sense, is a science that emerged from the self-observation of reason and the abstraction of all content. It deals with formal truth and investigates rule-governed thinking. The uniqueness of Schopenhauer’s logic emerges from its reference to intuition, which leads him to use numerous geometric forms in logic that are understood today as logic diagrams, combined with his aim of achieving the highest possible degree of naturalness, so that logic resembles mathematical proofs and, especially, the intentions of everyday thinking.

It follows from both logic and dialectic that Schopenhauer did not actively work to develop a logical calculus because axiomatisation contradicts natural thinking and also mathematics in that the foundations of mathematics should rely upon intuition rather than upon the rigor that algebraic characters are supposed to possess. However, the visualization of logic through diagrams and of geometry through figures is not intended to be empirical; rather, it is about the imaginability of logical or mathematical forms. Schopenhauer is guided primarily by Aristotle with regard to naturalness, by Euler with regard to intuition, and by Kant with regard to the structure of logic.

Schopenhauer called dialectic ‘eristics’, and the ‘art of persuasion’ and the ‘art of being right’. It has a practical dimension. Dialectic examines the forms of dialogue, especially arguments, in which speakers frequently violate logical and ethical rules in order to achieve their goal of argumentation. In pursuing this, Schopenhauer starts from the premise that reason is neutral and can, therefore, be used as a basis for valid reasoning, although it can also be misused. In the case of abuse, speakers instrumentalize reason in order to appear right and prevail against one or more opponents. Even if some texts on dialectic contain normative formulations, Schopenhauer’s goal is not to motivate invalid reasoning, but to protect against it. As such, scientific dialectic is not an ironic or sarcastic discipline, but a protective tool in the service of Enlightenment philosophy.

Schopenhauer’s dialectic is far better known than his analytics, although in direct comparison it makes up the smaller part of his writings on logic in general. For this reason, and because most texts on dialectic build on analytics, the following article is not structured around the two sub-disciplines, but around Schopenhauer’s very different texts on logic in general. First, logic is positioned as a discipline within the philosophical system. Then, the Berlin Lectures, his main text on analytics and dialectic, is introduced and followed, in chronological order, by his shorter texts on analytics and dialectic. The final section outlines research topics.

Logic and System
Schopenhauer’s Philosophical System
Normativism or Descriptivism
Logic within the System
Schopenhauer’s Treatises on Logic and Dialectics
Schopenhauer’s Logica Maior (the Berlin Lectures)
Doctrine of Concepts and Philosophy of Language
Translation, Use-Theory, and Contextuality
Abstraction, Concretion, and Graphs
Doctrine of Judgments
Relational Diagrams
Stoic Logic and Oppositional Geometry
Conversion and Metalogic
Analytic-Synthetic Distinction and the Metaphor of the Concept
Doctrine of Inferences
Foundations of Logic
Logical Aristotelianism and Stoicism
Naturalness in Logic
Further Topics of Analytic
Schopenhauer’s History of Logic
Logic and Mathematics
Hermeneutics
Dialectic or Art of Persuasion
Schopenhauer’s Logica Minor
Fourfold Root
World as Will and Representation I (Chapter 9)
Eristic Dialectics
World as Will and Representation II (Chapters 9 and 10)
Parerga and Paralipomena II
Research Topics
Schopenhauer’s Works
Other Works
1. Logic and System
a. Schopenhauer’s Philosophical System

Schopenhauer’s main work is The World as Will and Representation (W I). This work represents the foundation and overview of his entire philosophical system (and also includes a minor treatise on logic). It was first published in 1819 and was accepted as a habilitation thesis at the University of Berlin shortly thereafter. W I was also the basis for the revised and elaborated version—the Berlin Lectures (BL), written in the early 1820s. It also appeared in a slightly revised version in a second and third edition (1844, 1859) accompanied by a second volume (W II) that functioned as a supplement or commentary. However, none of these later editions were as rich in content as the revision in the BL. All other writings—On the Fourfold Root of the Principle of Sufficient Reason (1813 as a dissertation, 1847), On the Will in Nature (1836, 1854), The Two Fundamental Problems of Ethics (1841, 1860), and Parerga and Paralipomena (1851)—can also be regarded as supplements to the W I or the BL.

Schopenhauer’s claim, made in the W I (and also the BL), follows (early) modern and especially Kantian system criteria. He claimed that philosophy aims to depict, in one single system, the interrelationships between all the components that need to be examined. In Kant’s succession, a good or perfect system is determined by the criterion of whether the system can describe all components of nature and mind without leaving any gaps or whether all categories, principles, and topics have been listed in order to describe all components of nature and mind. This claim to completeness becomes clear in Schopenhauer’s system, more precisely, in W I or BL, each of which is divided into four books. The first book deals mainly with those topics that would, in contemporary philosophy, be assigned to epistemology, philosophy of mind, philosophy of science, and philosophy of language. The second book is usually understood as covering metaphysics and the philosophy of nature. The third book presents his aesthetics and the fourth book practical philosophy, including topics such as ethics, theory of action, philosophy of law, political philosophy, social philosophy, philosophy of religion, and so forth.

b. Normativism or Descriptivism

Schopenhauer’s system, as described above (Sect. 1.a), has not been uniformly interpreted in its 200-year history of reception, a factor that has also played a significant role in the reception of his logic. The differences between the individual schools of interpretation have become increasingly obvious since the 1990s and are a significant subject of discussion in research (Schubbe and Lemanski 2019). Generally speaking, one can differentiate between two extreme schools of interpretation (although not every contemporary study on Schopenhauer can be explicitly and unambiguously assigned to one of the following positions):

Normativists understand Schopenhauer’s system as the expression of one single thought that is marked by irrationality, pessimism, obscurantism, and denial of life. The starting point of Schopenhauer’s system is Kant’s epistemology, which provides the foundation for traversing the various subject areas of the system (metaphysics, aesthetics, ethics). However, all topics presented in the system are only introductions (“Vorschulen”) to the philosophy of religion, which Schopenhauer proclaims is the goal of his philosophy, that is, salvation through knowledge (“Erlösung durch Erkenntnis”). Normativists are above all influenced by various philosophical schools or periods of philosophy such as late idealism (Spätidealismus), the pessimism controversy, Lebensphilosophie, and Existentialism.
Descriptivists understand Schopenhauer’s philosophy as a logically ordered representation of all components of the world in one single system, without one side being valued more than the other. Depending on the subject, Schopenhauer’s view alternates between rationalism and irrationalism, between optimism and pessimism, between affirmation and denial of life, and so forth. Thus, there is no intended priority for a particular component of the system (although, particularly in later years, Schopenhauer’s statements became more and more emphatic). This school is particularly influenced by those researchers who have studied Schopenhauer’s intense relationship with empiricism, logic, hermeneutics, and neo-Kantianism.
c. Logic within the System

The structure of logic is determined by three sub-disciplines: the doctrines of concepts, judgments, and inferences. However, the main focus of Schopenhauerian logic is not the doctrine of inferences in the sense of logical reasoning and proving but rather in the sense that his logic corresponds with his philosophy of mathematics. According to Schopenhauer, logical reasoning in particular is overrated as people rarely put forward invalid inferences, although they often put forward false judgments. However, the intentional use of fallacies is an exception to this that is therefore studied by dialectics.

The evaluation of Schopenhauer’s logic depends strongly on the school of interpretation. Normativists have either ignored Schopenhauer’s logic or identified it with (eristic) dialectic, which in turn has been reduced to a normative “Art of Being Right” or “of Winning an Argument” (see below, Sect. 2.e, 3.c). A relevant contribution to Schopenhauer’s analytics from the school of normativists is, therefore, not known, although there were definitely intriguing approaches to dialectics. As normativism was the more dominant school of interpretation until late in the 20th century, it shaped the public image of Schopenhauer as an enemy of logical and mathematical reasoning, and so forth.

Descriptivists emphasize logic as both the medium of the system and the subject of a particular topic within the W I-BL system. The first book of W I-BL deals with representation and is divided into two sections (Janaway 2014): 1. Cognition (W I §§3–7, BL chap. 1, 2), 2. Reason (W I §§8–16, BL 3–5). Cognition refers to the intuitive and concrete, reason to the discursive and abstract representation. In the paragraphs on cognition, Schopenhauer examines the intuitive representation and its conditions, that is, space, time, and causality, while reason is built on cognition and is, therefore, the ‘representation of representation’. Schopenhauer examines three faculties of reason, which form the three sections of these paragraphs: 1. language, 2. knowledge, and 3. practical reason. Language, in turn, is then broken down into three parts: general philosophy of language, logic, and dialectics. (Schopenhauer defines rhetoric as, primarily, the speech of one person to many, and he rarely dealt with it in any substantial detail.) Following the traditional structure, Schopenhauer then divides logic into sections on concepts, judgments, and inferences. Logic thus fulfills a double role in Schopenhauer’s system: it is a topic within the entire system and it is the focus through which the system is organized and communicated. Fig. 1 shows this classification using W I as an example.
Figure 1: The first part of Schopenhauer’s system focusing on logic

However, this excellent role of logic only becomes obvious when Schopenhauer presents the aim of his philosophy. The task of his system is “a complete recapitulation, a reflection, as it were, of the world, in abstract concepts”, whereby the discursive system becomes a finite “collection [Summe] of very universal judgments” (W I, 109, BL, 551). As in Schopenhauer’s system, logic alone clarifies what concepts and judgments are: it is a very important component for understanding his entire philosophy. Schopenhauer, however, vehemently resists an axiomatic approach because in logic, mathematics and, above all, philosophy, nothing can be assumed as certain; rather, every judgment may represent a problem. Philosophy itself must be such that it is allowed to be skeptical about tautologies or laws (such as the laws of thought). This distinguishes it from other sciences. Logic and language cannot, therefore, be the foundation of science and philosophy, but are instead their means and instrument (see below, Sect. 2.c.i).

Through this understanding of the role of logic within the system, the difference between the two schools of interpretation can now also be determined: Normativists deny the excellent role attributed to logic as they regard the linguistic-logical representation as a mere introduction (“Vorschule”) to philosophical salvation at the end of the fourth book of W I or BL. This state of salvation is no longer to be described using concepts and judgments. In contrast, descriptivists stress that Schopenhauer’s entire system aims to describe the world and man’s attitude to the world with the help of logic and language. This also applies to the philosophy of religion and the treatises on salvation at the end of W I and BL. As emphasized by Wittgensteinians in particular, Schopenhauer also shows, ultimately, what can still be logically expressed and what can no longer be grasped by language (Glock 1999, 439ff.).

d. Schopenhauer’s Treatises on Logic and Dialectics

Schopenhauer’s whole oeuvre is thought to contain a total of six longer texts on logic. In chronological order, this includes the following seven texts:

(1) In the summer semester of 1811, Schopenhauer attended Gottlob Ernst (“Aenesidemus”) Schulze’s lectures on logic and wrote several notes on Schulze’s textbook (d’Alfonso 2018). As these comments do not represent work by Schopenhauer himself, they are not discussed in this article. The same applies to Schopenhauer’s comments on other books on logic, such as those of Johann Gebhard Ehrenreich Maass, Johann Christoph Hoffbauer, Ernst Platner, Johann Gottfried Kiesewetter, Salomon Maimon et al. (Heinemann 2020), as well as his shorter manuscript notes published in the Manuscript Remains. (Schopenhauer made several references to his manuscripts in BL.)

(2) Schopenhauer’s first discussion of logic occurred in his dissertation of 1813 which presented a purely discursive reflection on some components of logic (concepts, truth, and so on). In particular, his reflections on the laws of thought were emphasized.

(3) For the first time in 1819, in § 9 of W I, Schopenhauer distinguished between analytics and dialectics in more detail. In the section on analytics, he specified a doctrine of concepts with the help of a few logic diagrams. However, he wrote in § 9 that this doctrine had already been fairly well explained in several textbooks and that it was, therefore, not necessary to load the memory of the ‘normal reader’ with these rules. In the section on dialectic, he sketches a large argument map for the first time. § 9 was only lightly revised in later editions; however, his last notes in preparation for a fourth edition indicate that he had planned a few more interesting changes and additions.

(4) During the 1820s, Schopenhauer took the W I system as a basis, supplemented the missing information from his previously published writings, and developed a system that eliminated some of the shortcomings and ambiguities of W I. The system within these manuscripts then served as a source for his lectures in Berlin in the early 1820s, that is, the BL. In the first book of the BL, there is a treatise on logic the size of a textbook.

(5) Eristic Dialectics is the title of a longer manuscript that Schopenhauer worked on in the late 1820s and early 1830s. This manuscript is one of Schopenhauer’s best-known texts, although it is unfinished. It takes many earlier approaches further, but the context to analytics (and to logic diagrams) is missing in this small fragment on dialectics. With the end of his university career in the early 1830s, Schopenhauer’s intensive engagement with logic came to an end.

(6) It was not until 1844, in W II, that Schopenhauer supplemented the doctrine of concepts given in W I with a 20-page doctrine of judgment and inference. This, however, is no longer compatible with the earlier logic treatises written before 1830, as Schopenhauer repeatedly suggests new diagrammatic logics, which he does not illustrate. Given these changes, the published texts on logic look inconsistent.

(7) In 1851, Schopenhauer once again published a short treatise entitled “Logic and Dialectics” in the second volume of Parerga and Paralipomena. This treatise, however, only deals with some topics from the philosophy of logic in aphoristic style and, otherwise, focuses more strongly on dialectic. Few new insights are found here.

Since the rediscovery of the Berlin Lectures by descriptivists, a distinction has been made—in the sense of scholastic subdivision—between Logica Maior (Great Logic) and Logica Minor (Small Logic): Treatises (2), (3), (4), (5) and (6) belong to the Logica Minor and are discussed briefly in Section 3. (For more information see Lemanski 2021b, chap. 1.) The only known treatise on logic written by Schopenhauer that deserves to be called a Logica Maior is a manuscript from the Berlin Lectures written in the 1820s. This book-length text is the most profitable reading of all the texts mentioned. Thus, it is discussed in more detail in Section 2.

2. Schopenhauer’s Logica Maior (the Berlin Lectures)

Until the early 21st century, due to the dominance of the normativists in Schopenhauer scholarship, the BL were considered just a didactic version of W I and were, therefore, almost completely ignored by researchers until intensive research on Schopenhauer’s logic began in the middle of the 2010s. These lectures are not only interesting from a historical perspective, they also propose a lot of innovations and topics that are still worth discussing today, especially in the area of diagrammatic reasoning and logic diagrams. As Albert Menne, former head of the working group ‘Mathematical Logic’ at the Ruhr-Universität in Bochum stated: “Schopenhauer has an excellent command of the rules of formal logic (much better than Kant, for example). In the manuscript of his Berlin Lectures, syllogistics, in particular, is thoroughly analyzed and explained using striking examples” (Menne 2002, 201–2).

The BL are a revised and extended version of W I made for the students and guests who attended his lectures in Berlin. The belief that such an elaboration only has minor value is, however, not reasonable. Moreover, the extent, the content, and also the above-mentioned distinction between the exoteric-popular-philosophical and the esoteric-academic part of Schopenhauer’s work suggest a different evaluation. In W I, Schopenhauer deals only casually with difficult academic topics such as logic or philosophy of law; at the beginning of the BL, however, he states that these topics are the most important topics to teach prospective academics. Indeed, he repeatedly pointed out that he will also focus on logic in the title of his announcement for the Berlin Lectures. Thus, the lecture given in the winter semester of 1821-22 is titled “Dianologie und Logik” (BL, XII; Regehly 2018). Therefore, suspicion arises that research has hitherto ignored Schopenhauer’s most important textual version of his philosophical system, as the Berlin Lectures contain his complete system including some of the parts missing from W I, which are very important for the academic interpretation of the system such as logic and philosophy of law.

The first edition of the BL was published by Franz Mockrauer in 1913, reprinted by Volker Spierling in 1986, and a new edition was published in four volumes between 2017 and 2022 by Daniel Schubbe, Daniel Elon, and Judith Werntgen-Schmidt. An English translation is not available. The manuscript of the BL is deposited in the Staatsbibliothek zu Berlin Preussischer Kulturbesitz and can be viewed online at http://sammlungen.ub.uni-frankfurt.de/schopenhauer/content/titleinfo/7187127.

The Logica Maior is found in chapter III of the Berlin Lectures (book I). Here, Schopenhauer begins with (a) a treatise on the philosophy of language that announces essential elements of the subsequent theory of concepts. Then, (b) based on the diagrammatic representation of concepts, he develops a doctrine of judgment. (c) The majority of the work then deals with inferences, in which syllogistic, Stoic logic (propositional logic), modal logic, and the foundation and naturalness of logic are discussed. Together with (d) the appendix, these are the topics that belong to analytics or logic in the proper sense. (e) Finally, he addresses several topics related to dialectics.

a. Doctrine of Concepts and Philosophy of Language

This section mainly deals with BL, 234–260. Schopenhauer begins his discussion of logic with a treatise on language, which is foundational to the subsequent treatise. Several aspects of this part of the Logica Maior have been investigated and discussed to date—namely (i.) translation, use-theory, and contextuality as well as (ii.) abstraction, concretion, and graphs—which are outlined in the following subsections.

i. Translation, Use-Theory, and Contextuality

Schopenhauer distinguishes between words and concepts: he considers words to be signs for concepts, and concepts abstract representations that rest on other concepts or concrete representations (of something, that is, intuition). In order to make this difference explicit, Schopenhauer reflects on translation, as learning a foreign language and translating are the only ways to rationally understand how individuals learn abstract representations and how concepts develop and change over many generations within a particular language community.

In his translation theory, Schopenhauer defines three possible situations:

(1) The concept of the source language corresponds exactly to the concept of the target language (1:1 relation).

(2) The concept of the source language does not correspond to any concept of the target language (1:0 relation).