Jens Lemanski

From the mid-1600s to the beginning of the eighteenth century, there were two main circles of German scholars which focused extensively on diagrammatic reasoning and representation in logic. The first circle was formed around Erhard Weigel in Jena and consists primarily of Johann Christoph Sturm and Gottfried Wilhelm Leibniz; the second circle developed around Christian Weise in Zittau, with the support of his students, particularly Samuel Grosser and Johann Christian Lange. Each of these scholars developed an original form of using geometric diagrams in logic. In this paper, I will trace the historical notes of John Venn and other modern logicians back to the original works published in the Weigel and Weise circles and describe the development of using geometric figures for logical reasoning and representation in that period of time.

Extensions of traditional syllogistics have been increasingly researched in philosophy, linguistics, and areas such as artificial intelligence and computer science in recent decades. This is mainly due to the fact that syllogistics is seen as a logic that comes very close to natural language abilities. Various forms of extended syllogistics have become established. This paper deals with the question to what extent a syllogistic representation in CL diagrams can be seen as a form of extended syllogistics. It will be shown that the ontology of CL enables numerically exact assertions and inferences.

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.

In the year 1714, Johann Christian Lange published a baroque textbook about a logic machine, supposed to simulate human cognitive abilities such as perception, judgement, and reasoning. From today’s perspective, it can be argued that this blueprint is based on an inference engine applied to a strict ontology which serves as a knowledge base. In this paper, I will first introduce Lange’s approach in the period of baroque logic and then present a diagrammatic modernization of Lange’s principles, entitled Calculus CL. Finally, I would like to discuss the possibilities of how to apply CL to modern cases of concern by using an example from epidemiology.

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.

The paper distinguishes three interpretations of Kant’s so called ‘Copernican Revolution’: an epistemological, a hermeneutical and a scientific-theoretical or methodological one. It is argued that the ‘scientific-theoretical reading’ can be based on new historical evidence. Kant borrowed the metaphors ‘army of stars’ (‘Sternenheer’) and ‘spectator’ (‘Zuschauer’) from Johann Heinrich Lambert and used them in a context similar to Lambert’s. This suggests that Kant’s formula “first thoughts of Copernicus” (“den ersten Gedanken des Copernicus”) refers, again following Lambert, to the first 9 chapters of Copernicus’ De revolutionibus, which contain a change from inductive geocentrism to deductive heliocentrism. This interpretation is itself no revolution: Johann Baptist Schad claimed in 1800 that metaphysics must be regarded as a deductive rather than an inductive science. Kant explicitly agreed.

A widely debated question in current research centres on determining the precursors to G. W. F. Hegel's theory of recognition. Until now Fichte, Rousseau and Aristotle have been discussed. However, the present paper analyses a further surprising correspondence between Marsilio Ficino's theory of love and Hegel's theory of recognition. Here it is shown that Hegel studied Ficino in 1793 and that we can discover syntactical, semantical, and structural vestiges of Ficino's De amore II 8 in Hegel's early fragments on religion (1793) and love (1797), which are closely related to the general theory of recognition found in the Phenomenology of Spirit. Not only may this thesis be relevant for Hegel or Ficino scholarship, but it could also be a further indication that social theories with normative content are an integral characteristic of (early) modern self-consciousness.

In recent years the cultural pessimistic position has become known, according to which we live in an “age of post-truth.” This thesis is supported by the observation of an increasing use of argumenta ad passiones in politics. In contrast to this view, I believe that “time” and “representation” play a more decisive role in individual post-truth arguments than the appeal to passiones. By analysing typical post-truth arguments, I arrive at a much more positive view on the present age: the designation of individual arguments as “post-truth” is already an expression of a process of enlightenment.

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.).

Logicians have often suggested that the use of Euler-type diagrams has influenced the idea of the quantification of the predicate. This is mainly due to the fact that Euler-type diagrams display more information than is required in traditional syllogistics. The paper supports this argument and extends it by a further step: Euler-type diagrams not only illustrate the quantification of the predicate, but also solve problems of traditional proof theory, which prevented an overall quantification of the predicate. Thus, Euler-type diagrams can be called the natural basis of syllogistic reasoning and can even go beyond. In the paper, these arguments are presented in connection with the book Nucleus Logicae Weisaniae by Johann Christian Lange from 1712.

In early modernity, one can find many spatial logic diagrams whose geometric forms share a family resemblance with religious art and symbols. The family resemblance these diagrams bear in form is often based on a vesica piscis or on a cross: Both logic diagrams and spiritual symbols focus on the intersection or conjunction of two or more entities, e.g. subject and predicate, on the one hand, or god and man, on the other. This paper deals with the development and function of logic diagrams, their analogy to religious art and symbols, and their modern application in artificial intelligence.

Die Frage ›Warum ist überhaupt etwas und nicht vielmehr nichts?‹ gehört zu den ebenso traditionsreichen wie umstrittenen Problemen der Philosophie. Bereits mehrmals in die Mottenkiste der Philosophiegeschichte verbannt, erlebt sie doch zuverlässig ihre Renaissancen. Der vorliegende Band nimmt sich der ›Grundfrage‹ in einer ideengeschichtlichen Perspektive an. Dabei stellt sich heraus, dass die systematisch keineswegs erst mit Leibniz auftauchende Frage in ihrer Geschichte von der Antike bis zur gegenwärtigen analytischen Philosophie nicht nur jeweils unterschiedliche Antworten provoziert hat, sondern vor allem auch ganz verschieden gestellt worden ist: Formuliert Leibniz »Pourquoi il y a plus tôt quelque chose que rien?«, heißt es bei Schelling »Warum ist nicht nichts, warum ist überhaupt etwas?«, während Schopenhauer ihr eine existentielle Wendung gibt (»Lieber nichts als etwas«). Heideggers Auseinandersetzung mit dem Nihilismus führt zu der Frage: »Warum ist überhaupt Seiendes und nicht vielmehr Nichts?«, während Arendt sie ins Politische wendet (»Warum ist überhaupt jemand und nicht niemand?«). Der Band wird durch einen Überblick über die vielschichtige Diskussion der ›letzten Warum-Frage‹ in der Tradition der Analytischen Philosophie sowie einen Antwortversuch aus Sicht der aktuellen Physik und Kosmologie abgerundet.

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 question of naturalness in logic is widely discussed in today’s research literature. On the one hand, naturalness in the systems of natural deduction is intensively discussed on the basis of Aristotelian syllogistics. On the other hand, research on “natural logic” is concerned with the implicitly existing logical laws of natural language, and is therefore also interested in the naturalness of syllogistics. In both research areas, the question arises what naturalness exactly means, in logic as well as in language. We show, however, that this question is not entirely new: In his Berlin Lectures of the 1820s, Arthur Schopenhauer already discussed in depths what is natural and unnatural in logic. In particular, he anticipates two criteria for the naturalness of deduction that meet current trends in research: (1) Naturalness is what corresponds to the actual practice of argumentation in everyday language or scientific proof; (2) Naturalness of deduction is particularly evident in the form of Euler-type diagrams.

In the second preface to the Critique of Pure Reason, Kant claims that Galileo Galilei, Evangelista Torricelli and Georg Ernst Stahl caused a scientific revolution in experimental physics (B xii). In this paper, I advance the historical thesis that Kantʼs claim refers precisely to three passages from Discursus et demonstrationes mathematicae (Galilei), Lettera a Filaleti Di Timauro Antiate (Torricelli), and Beweiß von den Saltzen (Stahl). This historical thesis provides evidence for a newer systematic interpretation, which says that the topic of the second preface is not epistemological, but rather methodological.

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.

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.

›Bottom-up‹ und ›top-down‹ sind heutzutage gängige Methodenbezeichnungen in allen Bereichen der Wissenschaft. Dennoch sind beide Methoden keine Entdeckung der Moderne, sondern wurden unter Begriffen wie beispielsweise ›Auf-‹ und ›Abstieg‹, ›Induktion‹ und ›Deduktion‹ in der Wissenschaftsgeschichte häufig verwendet, um komplexe Wissensbestände vollständig aufzuarbeiten und zu strukturieren. Paradigmatisch für eine derartige Aufarbeitung stehen die mittelalterliche Summa und das neuzeitliche System. Aktuellen Studien zufolge hat aber bereits Dionysius Areopagita in der Spätantike eine derartige Summe verfasst, während in der Neuzeit erst J. G. Fichtes Wissenschaftslehre (1804) allen Systemansprüchen genügen konnte. Daher beschäftigt sich die vorliegende Studie mit den Auf- und Abstiegsmethoden bei Dionysius und Fichte, ihrer antiken Vorgeschichte und kontrastiert ihre Methoden mit der aktuellen Wissenschaftsphilosophie. Dabei zeigt sich, dass beide Autoren bei der Aufstiegs- bzw. bottom-up-Methode bislang unberücksichtigte Strategien zur Lösung des Induktionsproblems anwenden.

Beginning with a research review, the present paper shows that Hans Slugaʼs and esp. Robert Brandomʼs thesis, according to which Frege has adopted the context-principle and the priority of propositional from Kant, can solve problems in current Frege scholarship, on the one hand, but is itself fraught with further problems, on the other hand. In contrast, this paper maintains that the context-principle and the priority of the propositional are implicitly present in Fregeʼs Begriffsschrift since both have not been taken over from Kant, but rather from neo-Aristotelianism: The context-principle and the priority of the propositional were first drawn up in 1834 by O. F. Gruppe. As a consequence, A. F. Trendelenburg has published a re-arranged edition of Aristotleʼs Organon in 1836 which became one of the most influential schoolbooks on logic in the 19th century and of which Frege ought to have been aware. In the beginning of this schoolbook, using the original ancient Greek sentences of Aristotle, the priority of the propositional (De int. I 1) is deduced from the context-principle (De anima III 6).

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.

It is little known that Schopenhauer (1788–1860) made thorough use of Euler diagrams in his works. One specific diagram depicts a high number of concepts in relation to Good and Evil. It is, hence, uncharacteristic as logicians of that time seldom used diagrams for more than three terms (the number demanded by syllogisms). The objective of this paper is to make sense of this diagram by explaining its function and inquiring whether it could be viewed as an early serious attempt to construct complex diagrams.

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.