Jens Lemanski

Over the past few years, CL diagrams have gained popularity in diagrammatic reasoning, drawing inspiration from Lange’s Cubus Logicus. The intuitive understanding of CL diagrams is based on simple structures that are straightforward both to draw and to comprehend. This structure supports embedding of information and inferencing. Furthermore, these diagrams are more than just heuristic tools; CL diagrams can actually be extended to full blown formal systems. The present paper shows that a formal system for CL diagrams can have an expressivity similar to standard Boolean algebra of propositions or propositional logic without losing their intuitive properties. It is also possible to combine this interpretation of CL with elements from the class calculus. The syntax and semantics are presented separately, and the system’s soundness and completeness are proven using a variant of bitstring semantics.

Usually, a sharp break in the history of philosophy is assumed, separating continental or post-Kantian philosophy from analytic philosophy and the new logic from the old. In research, this division is typically dated to the year 1879, when Gottlob Frege's Begriffsschrift was published. In recent decades, however, research has repeatedly sought out Frege's predecessors and speculated on the path by which the mathematician Frege acquired his philosophical knowledge. The following paper presents a new source: Gottlob Frege's father Alexander studied with a philosopher from the broad circle of German idealism and tried in several writings to apply and continue his philosophy himself. This new source not only elucidates Gottlob Frege's familiarity with post-Kantian philosophy, but also has the potential to explain logical influences, such as that of Leibniz.

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 article examines the origins and development of the so-called Schlussmaß (or Logometrum), a diagrammatic method for representing logical inferences developed by the mathematician and philosopher Erhard Weigel in the 17th century. The starting point is Weigel's critique of scholastic and Aristotelian logic, which he sought to reform by combining logic and geometry. The article shows how Weigel first formulated the idea of illustrating logical relationships by means of geometric diagrams and proportions in his 'Analysis Aristotelica ex Euclide restituta', and how his students, in particular Johann Christoph Sturm, further developed these approaches in the 'Universalia Euclidea'. Using examples, it reconstructs how the Schlussmaß was conceived as a geometric test procedure for the validity of inferences and subsequently influenced Leibniz, Euler and Kant. The historical arc ranges from the early modern period to the diagram tradition of the Enlightenment to the rediscovery of diagrammatic methods in modern logic and artificial intelligence. It is argued that Weigel's Schlussmaß can be regarded not only as a precursor to Euler's diagram, but also as a paradigmatic example of the long-term interaction between logical and geometric modes of thought – a connection that is gaining new relevance in the digital age.

Over the past few years, _CL_ diagrams have gained popularity in diagrammatic reasoning, drawing inspiration from Lange’s _C_ubus _L_ogicus. The intuitive understanding of _CL_ diagrams is based on simple structures that are straightforward both to draw and to comprehend. This structure supports embedding of information and inferencing. Furthermore, these diagrams are more than just heuristic tools; _CL_ diagrams can actually be extended to full blown formal systems. The present paper shows that a formal system for _CL_ diagrams can have an expressivity similar to standard Boolean algebra of propositions or propositional logic without losing their intuitive properties. It is also possible to combine this interpretation of _CL_ with elements from the class calculus. The syntax and semantics are presented separately, and the system’s soundness and completeness are proven using a variant of bitstring semantics.

Gestures are usually regarded as a casual element of communication processes between logicians. By contrast, we aim to show that gestures have played a significant role in logic. We argue that the development of communication techniques and their standardization have led to the rise of formal notation systems commonly used in logic today. In order to substantiate this claim, the historical development of the use of gestures in (early) modern logic is investigated. This investigation uncovers exemplary communication and proof techniques that illustrate the efficacy of gestures as representational media in formal logic. Revisiting the tradition of gestures in logic offers promising paths and insights for today’s logic as a communication practice in the digital age.

Euler diagrams often require several figures to adequately represent propositions and syllogisms. Euler’s followers, notably Friedrich Ueberweg, endeavored to overcome this difficulty with the use of dotted lines to express uncertainty about the relation between the terms of a proposition. Subsequently, Venn regarded such attempts as ineffectual and went to construct his own celebrated scheme. In this paper, we argue that Ueberweg’s method could be expanded to meet Venn’s expectations, and hence, produce alternative Venn-like diagrams.

‘Byzantine logic diagrams’ have been used since at least late antiquity, and became popular in Europe in the 16th century. However, since the criticism of W. Hamilton and J. Venn in the 19th century, Byzantine diagrams have been largely dismissed as obsolete. This paper challenges this prevailing view. Initially, we provide a comprehensive overview of the current state of research pertaining to these diagrams, illustrating their applicability in analyzing assertoric syllogisms. Subsequently, we propose that the expressive capacity of these diagrams extends far beyond their traditional use. In particular, we demonstrate that the expressivity of these diagrams is not limited to checking the validity of syllogisms. Rather, we show that there are various extensions of Byzantine diagrams, including opposition relations, modal logic, particular instances, n-term diagrams and logical connectives. These extensions are compositional and can therefore be combined to create very complex Byzantine diagrams that go far beyond what has been commonly believed since Hamilton and Venn.

This article examines the evolution of the concept of existence in modern visual representation and reasoning, highlighting important milestones. In the late eighteenth century, during the so-called golden age of visual reasoning, nominalism reigned supreme and there was limited scope for existential import or individuals in logic diagrams. By the late nineteenth century, a form of realism had taken hold, whose existential commitments continue to dominate many areas in logic and visual reasoning to this day. Physical, metaphysical, epistemological, and linguistic positions underlie both nominalist and realist views. Since the paradigmatic works on visual reasoning in the 1990s, formal diagram systems have been developed that revive either the nominalist or realist perspectives. Unlike in the nineteenth century, these are not motivated by philosophical views. Nevertheless, they may still have an impact on many areas of philosophy and science outside logic.

This book constitutes the refereed proceedings of the 14th International Conference on the Theory and Application of Diagrams, Diagrams 2024, held in Münster, Germany, during September 27–October 1, 2024. The 17 full papers, 19 short papers and 11 papers of other types included in this book were carefully reviewed and selected from 69 submissions. They were organized in topical sections as follows: Keynote Talks; Analysis of Diagrams; Euler and Venn Diagrams; Diagrams in Logic; Diagrams and Applications; Diagram Tools; Historical Aspects of Diagrams; and Posters.

The criticism of Immanuel Kant’s logic commenced with the advent of the so-called ‘new logic’ in the 20th century. One particular passage from the second preface to the Critique of Pure Reason has been a source of contention, where Kant asserted that logic has not taken a step forward or backward since Aristotle (B VIII). In Kant scholarship, one current strategy to avoid this criticism is to relocate Kant within the domain of philosophy of logic or by segregating his general logic from modern formal systems. In this paper, it will be contended that this strategy is too weak, given that the B-preface has currently been analyzed in a markedly divergent manner by the so-called ‘methodological interpretation’. In his methodology and history of science of the B-preface, Kant means something different by progress and regression than what his 20th-century critics assume he meant. By examining what Kant and his critics considered to be progress and regress in science and logic, good reasons can be put forward for the argument that Kant was correct in his assertion that logic has not gone a step forward or backward.

What is the primacy of logic? Concepts, judgments, or inferences? Whereas representationalists traditionally argue for a primacy of the conceptual, rationalists, referring to the context principle and the use theory of meaning, consider judgments and inferences to be primary. This dispute also seems to be applicable to logic diagrams: Whereas “Euler-type diagrams” are actually only for judgments and inferences, “concept diagrams” represent ontologies by using concepts. With reference to Schopenhauer, the paper develops a position called “rational representationalism.” According to this point of view, the question of primacy is decided by analyzing the functions of the logic principles: For the explanation of logic and language, concepts are primary, but for understanding it is judgments. The mediation between intuitive representation and logical rationality is ensured by concept diagrams.

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.

In the rapidly evolving landscape of multimodal communication research, this paper explores the transformative role of machine learning (ML), particularly using multimodal large language models, in tracking, augmenting, annotating, and analyzing multimodal data. Building upon the foundations laid in our previous work, we explore the capabilities that have emerged over the past years. The integration of ML allows researchers to gain richer insights from multimodal data, enabling a deeper understanding of human (and non-human) communication across modalities. In particular, augmentation methods have become indispensable because they facilitate the synthesis of multimodal data and further increase the diversity and richness of training datasets. In addition, ML-based tools have accelerated annotation processes, reducing human effort while improving accuracy. Continued advances in ML and the proliferation of more powerful models suggest even more sophisticated analyses of multimodal communication, e.g., through models like ChatGPT, which can now “understand” images. This makes it all the more important to assess what these models can achieve now or in the near future, and what will remain unattainable beyond that. We also acknowledge the ethical and practical challenges associated with these advancements, emphasizing the importance of responsible AI and data privacy. We must be careful to ensure that benefits are shared equitably and that technology respects individual rights. In this paper, we highlight advances in ML-based multimodal research and discuss what the near future holds. Our goal is to provide insights into this research stream for both the multimodal research community, especially in linguistics, and the broader ML community. In this way, we hope to foster collaboration in an area that is likely to shape the future of technologically mediated human communication.

Im Folgenden stellen wir drei aktuelle Forschungsbereiche zur formalen Logik bei Kant allgemeinverständlich dar und greifen dabei auf die trans zendentale Logik nur dann zurück, wenn sie ein besseres Verständnis der formalen Logik ermöglicht: Zunächst wird Kants Beitrag zur Rezeption und Weiterentwicklung von Euler-artigen Diagrammen dargestellt. Diese Diagramme wurden in den 1990er Jahren wiederentdeckt, als formales System interpretiert und werden heute insbes. in der Didaktik, in den Kognitionswissenschaften, in der Linguistik, in KI-Bereichen wie der (Logik-basierten) Wissensrepräsentation eingesetzt, und auch in der Philosophie verwendet (Kapitel 2). Mehrere Studien haben in den letzten Jahren gezeigt, dass Kant in weiten Teilen seines Systems Oppositionsverhältnisse verwendet, die der Struktur des logischen Quadrats entsprechen. Das logische Quadrat ist heute Gegenstand intensiver Forschung, da es neben der klassischen, auch die paravollständige und parakonsistente Negation abbildet (Kap. 3). Jüngst wurde zudem die Implementierbarkeit der kantischen Logik in ein formalisiertes deduktives System bewiesen. Die Bedeutung dieses Ergebnisses wird insbesondere im Hinblick auf die formalisierte Umsetzung der Sätze vom Widerspruch, vom zureichenden Grund und der Ausschließung des Mittleren erläutert (Kap. 4). Abschließend möchten wir ein paar Perspektiven für die Forschung zur formalen Logik bei Kant nennen (Kap. 5). -- Note: No financial support acknowledged by the second autor (S. Kovač).

The paper gives an overview of Arthur Schopenhauer's theory of rationality. For Schopenhauer, rationality is a human faculty based on language, which, in addition to language, is primarily concerned with knowledge or philosophy of science and practical action. For Schopenhauer, language is the umbrella term under which he subsumes logic and eristics. This paper will first introduce Schopenhauer's logic and clarify its connection to the philosophy of language. This is followed by eristic dialectics, which reflects on how one can protect oneself from people who argue irrationally in a goal-oriented way. Schopenhauer's philosophy of mathematics belongs to the field of philosophy of science. Unlike many other authors of his time, Schopenhauer does not advocate a rationalist but a representationalist approach, which, however, includes a theory of rationality. Therefore, Schopenhauer's representationalist approach will finally be discussed, emphasizing its relationship to his theory of rationality.

Logic diagrams have seen a resurgence in their application in a range of fields, including logic, biology, media science, computer science and philosophy. Consequently, understanding the history and philosophy of these diagrams has become crucial. As many current diagrammatic systems in logic are based on ideas that originated in the 18th and 19th centuries, it is important to consider what motivated the use of logic diagrams in the past and whether these reasons are still valid today. This paper proposes that transcendental philosophy was a key inspiration for the development of logic diagrams and that such diagrams can be employed in transcendental arguments, even after the linguistic turn.

This paper presents an analysis of Seneca's 58th letter to Lucilius and Porphyry's Isagoge, which were the origin of the tree diagrams that became popular in philosophy and logic from the early Middle Ages onwards. These diagrams visualise the extent to which a concept can be understood as a category, genus, species or individual and what the method of dihairesis (division) means. The paper explores the dissimilarities between Seneca's and Porphyry's tree structures, scrutinising them through the perspective of modern graph theory. Although traditional trees can be interpreted in a modern way, their terms and definitions defy modern standardisation. These distinctions are not only useful for differentiating between Seneca's and Porphyry's trees, but also for comprehending the evolution of this philosophical tradition. Thus the paper highlights the continued significance of these tree diagrams in analysing concepts and categories in philosophy and structuring objects and information in modern fields such as artificial intelligence, computer science, bioinformatics, graph theory, and many more.

To believe that logic has no history might at first seem peculiar today. But since the early 20th century, this position has been repeatedly conflated with logical monism of Kantian provenance. This logical monism asserts that only one logic is authoritative, thereby rendering all other research in the field marginal and negating the possibility of acknowledging a history of logic. In this paper, I will show how this and many related issues have developed, and that they are founded on only one prominent statement by Kant. I will argue, however, that this statement takes on a very different meaning in a broader context of the history and philosophy of science, and that Kant and his supporters never advocated the logical monism that they are still said to hold today.

The essay review examines three current editions of Arthur Schopenhauer's early works. These editions reveal a departure from his more academically-oriented early work towards the more popular late work. The extent to which these new editions accommodate current Schopenhauer research is discussed, with a focus on moving beyond the biased interpretations of the 19th and 20th centuries. Furthermore, the essay argues that Schopenhauer's early work is still valuable today for several reasons. Stylistically, the early works prevent one-dimensional readings that reduce Schopenhauer to stereotypical positions and roles such as irrationalism, pessimism, and negation of life. This can be seen in the emphasis on logic, philosophy of science, philosophy of law, ethics and others. Additionally, the review argues that Schopenhauer's holistic and organic system provides readers with considerable freedom in making judgments, while also revealing connections between theoretical, practical philosophy, and aesthetics that are often overlooked by mere subject-specific philosophising.

Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial role in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics.

Multimodal communication research focuses on how different means of signalling coordinate to communicate effectively. This line of research is traditionally influenced by fields such as cognitive and neuroscience, human-computer interaction, and linguistics. With new technologies becoming available in fields such as natural language processing and computer vision, the field can increasingly avail itself of new ways of analyzing and understanding multimodal communication. As a result, there is a general hope that multimodal research may be at the “precipice of greatness” due to technological advances in computer science and resulting extended empirical coverage. However, for this to come about there must be sufficient guidance on key (theoretical) needs of innovation in the field of multimodal communication. Absent such guidance, the research focus of computer scientists might increasingly diverge from crucial issues in multimodal communication. With this paper, we want to further promote interaction between these fields, which may enormously benefit both communities. The multimodal research community (represented here by a consortium of researchers from the Visual Communication [ViCom] Priority Programme) can engage in the innovation by clearly stating which technological tools are needed to make progress in the field of multimodal communication. In this article, we try to facilitate the establishment of a much needed common ground on feasible expectations (e.g., in terms of terminology and measures to be able to train machine learning algorithms) and to critically reflect possibly idle hopes for technical advances, informed by recent successes and challenges in computer science, social signal processing, and related domains.

Das folgende Essay erläutert, warum der Tod Gottes sowohl in einem konsequent theistischen System als auch bei atheistischen Denkern unausweichlich ist. Zur Beantwortung der Frage, wie Gott gestorben ist, werden hauptsächlich Autoren wie Friedrich W. Schelling , Friedrich Nietzsche und Peter Sloterdijk herangezogen. Da die Rede vom Tod Gottes den Verdacht erweckt, metaphorisch zu sein, werden wir mit Apoptose und Nekrose auch zwei unterschiedliche Metaphern anwenden, um den vorliegenden Sachverhalt zu beschreiben . Das letzte Kapitel fragt dann nach den Konsequenzen von Gottes Tod für die heutige Ethik.The following essay describes the death of god as unavoidable in a consequent theistic as well as in an atheistic system. To answer the question: how god died, philosophers like Friedrich W. Schelling , Friedrich Nietzsche und Peter Sloterdijk were taken into consideration. For the matter of god’s death is suggestive of being metaphorical, we use two different metaphors to discuss the issue – apoptosis and necrosis . Finally the last chapter asks for the consequences of god’s death concerning nowadays ethics

Fichte’s Foundations of the Entire Wissenschaftslehre 1794 is one of the most fundamental books in classical German philosophy. The use of laws of thought to establish foundational principles of transcendental philosophy was groundbreaking in the late eighteenth and early nineteenth century and is still crucial for many areas of theoretical philosophy and logic in general today. Nevertheless, contemporaries have already noted that Fichte’s derivation of foundational principles from the law of identity is problematic, since Fichte lacked the tools to correctly present the formal parts of Foundations. In this paper, however, we argue that Fichte’s approach intuitively offers an important contribution to transcendental philosophy, and especially to philosophy of logic. We first point out the difficulties of Fichte’s logic in the Foundations and improve it in a second part on the basis of a formal system in which both propositional logic and syllogistic are combined.

Emily Thomas's seminal book The Meaning of Travel has brought the philosophy of travel back into the public eye in recent years. Thomas has shown that the topic of travel can be approached from numerous different perspectives, ranging from the historical to the conceptual‐analytical, to the political or even social‐philosophical perspectives. This article introduces another perspective, which Thomas only indirectly addresses, namely the argumentation‐theoretical perspective. It is notable that contemporary philosophy of travel lacks the nineteenth‐century approach of using diagrams and maps to examine arguments for and against travel. Since this approach starts with Schopenhauer, we first introduce his argument maps, discuss their advantages and disadvantages, and argue that a modified version is suitable to visualize and analyze arguments for and against traveling as presented in Thomas's work.