Jens Lemanski

Eristic has been studied more and more intensively in recent years in philosophy, law, communication theory, logic, proof theory, and A.I. Nevertheless, the modern origins of eristic, which almost all current researchers see in the philosopher Arthur Schopenhauer, are considered to be a theory of the illegitimate use of logical and rhetorical devices. Thus, eristic seems to violate the norms of discourse ethics. In this paper, I argue that this interpretation of eristic is based on prejudices that contradict the original intention of modern eristic. Eristic is not an art of being right or winning an argument, but an art of protecting oneself from the one who deliberately violates norms of discourse ethics to gain argumentative acceptance. For this reason, eristic must be seen as a discipline of Enlightenment philosophy and a correlate of discourse ethics. Especially in the age of alternative facts and post-factual politics, this makes eristic a valuable discipline.

Schopenhauers handschriftlicher Nachlass im weiteren Sinne umfasst alle von ihm stammenden aber zu seinen Lebzeiten nicht im Druck veröffentlichten Aufzeichnungen und Dokumente jeglicher Art aus all seinen Lebensphasen. Im üblichen und engeren Sinne beschränkt sich die Bezeichnung ›Schopenhauers handschriftlicher Nachlass‹ meist auf die Manuskripte mit philosophischen bzw. wissenschaftlichen Themen. Reisetagebücher, Briefe sowie geschäftliche, amtliche, biographische und ähnliche Dokumente wurden in der Regel getrennt behandelt, ausgewertet und veröffentlicht. Sie geben allerdings oft wichtige Auskünfte über die Entstehungsgeschichte der Schopenhauerschen Philosophie.

Charles Darwin gilt allgemein als der ›Erfinder‹ der Evolutionstheorie. Dennoch sehen viele Wissenschaftshistoriker bereits in der Antike Anfänge und einzelne Vorwegnahmen der heutigen Entwicklungsbiologie. Die Tatsache, dass der im Titel genannte Ausdruck ›Evolutionstheorie‹ in Anführungszeichen gesetzt wurde, ist somit kein Hinweis auf die Vorzeitigkeit Schopenhauers zu Darwin, sondern betrifft die kritische Frage, ob man Schopenhauer überhaupt in diese Geschichte der Evolutionstheorie mit aufnehmen sollte oder nicht.

Schopenhauers Auseinandersetzungen mit dem Christentum und der Mystik werden im Folgenden unter drei Aspekten betrachtet: Methodologie und Definitionen, Doxographie der Dogmatik, Mystologie und Hagiologie. In ersten Abschnitt werden Schopenhauers Herangehensweisen und Meinungen im Umgang mit dem Christentum beschrieben. Im zweiten Abschnitt werden einschlägige Belegstellen aus Schopenhauers Werk zu christlich-dogmatischen Themen zusammengestellt und systematisiert. Im dritten Abschnitt wird nach der Funktion und Bedeutung der christlichen Mystiker und Heiligen für Schopenhauers Leben und Werk gefragt.

Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der Mathematik und der Logik Schopenhauers vorgestellt. Es wird gezeigt, dass Schopenhauers Logikdiagramme auf Ideen der Mathematiker Leonhard Euler (1707–1783), Bernhard Friedrich Thibaut (1775–1832) und Franz Ferdinand Schweins (1780–1856) zurückgehen und dass Schopenhauer diese Logikdiagramme auch bereits zur Analyse mathematischer Begriffe verwendet. Kapitel 4 beschäftigt sich mit der Schopenhauer-Rezeption Diesterwegs. Es wird die Frage behandelt, inwieweit Diesterweg in der Mathematik von Schopenhauer beeinflusst war und welche Rolle dieser Einfluss auf sein Verständnis von Logik und Mathematik hatte. In Kapitel 5 wird schließlich gezeigt, dass Diesterweg die schopenhauersche Begriffsanalyse der Mathematik mit Hilfe von Logikdiagrammen aufgreift und weiterführt. Da Diesterweg einer der einflussreichsten Pädagogen und Mathematikdidaktiker des 20. Jahrhunderts war, ist anzunehmen, dass sich Spuren dieser Methode noch heute finden lassen. Inwiefern dies wahrscheinlich ist, wird in der Zusammenfassung (Kapitel 6) thematisiert.

The paper addresses the question of why there is no treatise on Japanese gardens in Arthur Schopenhauer's system. First, it is explained that the system philosophy of the 18th and 19th centuries aimed at completeness in conceptual representation. Schopenhauer therefore treats the national characteristics of the garden arts in Europe and Asia, among many other arts, and conceptually determines their similarities and differences. Due to the isolation of Japan, however, Schopenhauer had no knowledge of Japanese gardens. The last part of the paper argues that Japanese gardens would have fitted well into Schopenhauer's system, as the Rock Garden, Pond Garden, Moss Garden etc. correspond well with the ideas that ground Schopenhauer's aesthetics. ###Extended and translated version of the paper "Der japanische Garten im System Schopenhauers" (2021).###

This book marks the inauguration of the Historia Logicae book series, which seeks to publish high-quality monographs, dissertations, textbooks, proceedings, and anthologies on the history of logic in either German or English. Serving as the inaugural volume in this series, the book explores the contemporary interpretation of logic across many centuries and cultures. The first section of the volume comprises a compilation of papers dedicated to ancient and medieval logic, examining prominent thinkers such as Plato, Aristotle, Seneca, Porphyry, Proclus, Boethius, Buridan, and Kilwardby. The second section shifts focus towards early-modern and contemporary logics, including the works of Caramuel, Kant, Drobisch, Husserl, and Jaskowski. Topics of discussion encompass the relationship between mathematics and logic, natural deduction, intuitionism, graph theory, categorical judgments, theories of truth, modal logic, opposition relations, logic diagrams, definitions of formal logic, many-sorted logic, model theory, and paraconsistent logic.

In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, however, came from a completely different area of logic: instead of orienting to syllogistic like Euler diagrams, Venn applied Boolean algebra to improve visual reasoning. Venn’s contribution to solving the problem of elimination also played an important role. The result of this development is still known today as the ‘Venn Diagram’.

This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in a dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue.

In the vein of a renewed interest in diagrammatic reasoning, this paper challenges an opposition between logic diagrams and formal languages that has traditionally been the common view in philosophy of logic and linguistics. We examine, from a philosophical point of view, what we call five dogmas of logic diagrams. These are as follows: (1) diagrams are non-linguistic; (2) diagrams are visual representations; (3) diagrams are iconic, and not symbolic; (4) diagrams are non-linear; (5) diagrams are heterogenous, and not homogenous. Using historical examples, we argue that none of these dogmas is an adequate criterion to distinguish logic diagrams from formal languages. Instead, we advocate that there is a common core between linguistic and diagrammatic representation and reasoning.

In this paper, we analyze and discuss Schopenhauer’s n-term diagrams for eristic dialectics from a graph-theoretical perspective. Unlike logic, eristic dialectics does not examine the validity of an isolated argument, but the progression and persuasiveness of an argument in the context of a dialogue or even controversy. To represent these dialogue situations, Schopenhauer created large maps with concepts and Euler-type diagrams, which from today’s perspective are a specific form of graphs. We first present the original method with Euler-type diagrams, then give the most important graph-theoretical definitions, then discuss Schopenhauer’s diagrams graph-theoretically and finally give an example of how the graphs or diagrams can be used to analyze dialogues.

Spatial and diagrammatic reasoning is a significant part not only of logical abilities, but also of logical studies. The authors of this paper consider some novel trends in studying this type of reasoning. They show that there are the following two main trends in spatial logic: (i) logical studies of the distribution of various objects in space (logic of geometry, logic of colors, etc.); (ii) logical studies of the space algorithms applied by nature itself (logic of swarms, logic of fungi colonies, etc.).

The aim of this chapter is to develop a semantics for Calculus CL. CL is a diagrammatic calculus based on a logic machine presented by Johann Christian Lange in 1714, which combines features of Euler-, Venn-type, tree diagrams, squares of oppositions etc. In this chapter, it is argued that a Boolean account of formal ontology in CL helps to deal with logical oppositions and inferences of extended syllogistics. The result is a combination of Lange’s diagrams with an algebraic semantics of terms: Bit-CL, in which any ordered objects are identified by characteristic bitstrings. Then, a number of objections to Bit-CL are answered to, and the process of inference is explained in this new logical framework.

Leibniz is often cited as an authority when it comes to the formulation and answer strategy of the question “Why is there something rather than nothing?” Yet much current research assumes that Leibniz advocates an unambiguous question and strategy for the answer. In this respect, one repeatedly finds the argument in the literature that alternative explanatory approaches to this question violate Leibniz’s intention, since he derives the question from the principle of sufficient reason and also demands a causal explanation to the question. In particular, the new research on non-causal explanatory strategies to the Leibniz question seems to concern this counter-argument. In this paper, however, I will argue that while Leibniz raises the question by means of the principle of sufficient reason, he even favours a non-causal explanatory strategy to the question. Thus, a more accurate Leibniz interpretation seems not only to legitimise but also to support non-causal explanations to the Leibniz question.

+++Englisch Translation in "Proceedings of Schopenhauer Congresses 2018-2020 (JSPS)"+++ Der Beitrag geht der Frage nach, warum es in Arthur Schopenhauers System keine Abhandlung über japanische Gärten gibt. Zunächst wird erläutert, dass die Systemphilosophie des 18. und 19. Jahrhunderts auf Vollständigkeit in der begrifflichen Darstellung abzielte. Schopenhauer behandelt daher neben vielen anderen Künsten auch die nationalen Besonderheiten der Gartenkunst in Europa und Asien und bestimmt begrifflich deren Gemeinsamkeiten und Unterschiede. Aufgrund der Isolation Japans hatte Schopenhauer jedoch keine Kenntnis von japanischen Gärten. Im letzten Teil des Aufsatzes wird argumentiert, dass japanische Gärten gut in Schopenhauers System gepasst hätten, da der Steingarten, der Teichgarten, der Moosgarten usw. gut mit den Ideen korrespondieren, die Schopenhauers Ästhetik begründen.

Arthur Schopenhauer’s system, as elaborated in The World as Will and Representation (1st ed.: 1819) and in the Berlin Lectures (1820s), is divided into four parts: 1. the so-called ‘epistemology’, 2. metaphysics (of nature), 3. metaphysics of the beautiful or aesthetics, 4. metaphysics of morals or ethics. The part on ‘epistemology’ is divided into two parts: the doctrine of cognition and the doctrine of reason. Whereas the doctrine of cognition discusses the three conditions for the possibility of cognition, i.e., space, time, and causality, the doctrine of reason is divided into three faculties: language, (science of) knowing, and practical reason. This paper gives an informal overview of the research on the doctrine of reason, especially on logic, that has been conducted in recent years.

Die Unterscheidung zwischen einer großen und kleinen Logik geht auf den scholastischen Unterricht zurück, in dem Bakkalaren eine grundlegende parva logicalia und Magistranden eine auf Vollständigkeit zielende logica magna zu absolvieren hatten. Erst im Laufe des 19. Jh.s wurde die begriffliche Unterscheidung weniger auf die Studiengangszuordnung, als vielmehr auf den Umfang von logischen Texten angewandt: Fand man von Autoren sowohl ausschweifende als auch knappe Darstellungen der Logik, so wurden diese salopp als ›große‹ und als ›kleine Logik‹ bezeichnet. In diesem Sinn muss man auch die begriffliche Unterscheidung zwischen einer großen und mehreren kleineren Logiken in der Schopenhauer-Forschung verstehen.

The paper examines the definitions of the concept ›philosophy‹ resp. ›the philosopher‹ in Florentine renaissance Platonism, namely Marsilio Ficino and his scholar Francesco di Zanobi Cattani da Diacceto. Following Socrates and Pythagoras, Ficino distinguishes between mundane philosophy and divine sapientia. In contrast to his teacher, Diacceto's Aristotelism rejects the Pythagoreanism and connects philosophy with sapientia. In order to show how the differences between Ficino and Diacceto emerge, three more contemporaries are taken into consideration: Christoforo Landino, Angelo Poliziano and Giovanni Pico della Mirandola. As a result of this examination, it can be said that the definition of ›philosophy‹ in Florentine renaissance Platonism tends either to Pythagoreism or to Aristotelism or to both. Closely connected with the debate on philosophy are topics and maxims such as meditatio mortis, theologia negativa, docta ignorantia, scio ne scio, nosce te ipsum, ne quid nimis et al.

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us.

Around 1800, Johann Gottlieb Fichte's primary circle of recipients consisted not only of philosophers, but above all of theologians, religiously engaged laymen, educators, writers and caricaturists, medical practitioner, civil servants and lawyers. The entire reception in post-Kantian philosophy is limited to the years between 1792 and 1810. This period can be divided into two phases: namely the phase up to 1799, in which Fichte acquired students and followers, and the phase from 1799 onwards, in which Fichte's reception was related to the atheism controversy. The discussion about Fichte began to wane in 1810, so that Beneke even claimed in 1833 that Fichte's philosophy "must be regarded as completely lost". Among others, the paper reports on Fichte's disciples such as August Ludwig Hülsen, Johann Gottfried Immanuel Berger, Johann Baptist Schad and sympathisers of Fichte such as Johann Christian Gottlieb Schaumann, Friedrich Immanuel Niethammer, Gottlieb Ernst Mehmel, and Johann Neeb.

In his Berlin Lectures of the 1820s, the German philosopher Arthur Schopenhauer (1788–1860) used spatial logic diagrams for philosophy of language. These logic diagrams were applied to many areas of semantics and pragmatics, such as theories of concept formation, concept development, translation theory, clarification of conceptual disputes, etc. In this paper we first introduce the basic principles of Schopenhauer’s philosophy of language and his diagrammatic method. Since Schopenhauer often gives little information about how the individual diagrams are to be understood, we then make the attempt to reconstruct, specify and further develop one diagram type for the field of conceptual analysis.

The paper entitled "Knowledge, Science, and Science of Knowledge" uses two relevant texts from German idealism to ask whether philosophy is a science. It is first argued that science presupposes knowledge, but that the concept of knowledge has long been subject to strong scepticism due to Fitch's paradox of knowability and especially the Gettier problem. Only in recent years have historians of philosophy made it clear that the so-called standard analysis of knowledge was not even advocated by many classical authors. This is also the case with the texts under investigation: Fichte's early Wissenschaftslehre and Schopenhauer's Berlin Lectures. Both texts argue for a very different concept of knowledge, which then also determines the concept of science and philosophy. Fichte argues that philosophy must be founded from axioms and is therefore a subordinating science. Schopenhauer argues against this and points out that philosophy can only be a coordinating science. The last part of the paper argues that Fichte's and Schopenhauer's definitions of philosophy as a coordinating or subordinating science can still be applied today.