•  8
    Extended Syllogistics in Calculus CL
    Journal of Applied Logics 8 (2): 557-577. 2021.
    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 syll…Read more
  •  18
    The productive ambiguity of Venn’s three circles.
    In Kristof Nyiri, András Benedek & Petra Aczel (eds.), How Images Behave: 9th Budapest Visual Learning Conference, Budapest, 26 November 2020., Hungarian Academy of Sciences. pp. 245-248. 2020.
    It is not rare to meet in scientific literature with a figure made of three circles, intersecting in such a way as to delineate all the combinations of the components that they stand for. This figure is commonly known as a ‘Venn diagram’ or ‘Venn’s three circles’. In this paper, we argue that many so-called Venn diagrams found in modern scientific literature do not truly depict intersections, and hence, are not true Venn diagrams.
  • "Christentum im Atheismus" (Christianity in Atheism) analyses the history of the development of a normative ethic of imitation, mimesis and role model that sprang from Platonism and Christianity and was transformed in the atheistic or agnostic philosophy of modernity. The first volume describes the development of this ethics from antiquity to the Enlightenment using the example of several philosophical and theological writings. It is shown that even the descriptive representation of exemplary b…Read more
  • "Christentum im Atheismus" (Christianity in Atheism) analyses the history of the development of a normative ethic of imitation, mimesis and role model that sprang from Platonism and Christianity and was transformed in the atheistic or agnostic philosophy of modernity. The first volume describes the development of this ethics from antiquity to the Enlightenment using the example of several philosophical and theological writings.
  • Fichte-Schule
    In Gerald Hartung (ed.), Philosophie im deutschsprachigen Raum 1800-1830. pp. 138-150. 2020.
    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, i…Read more
  •  79
    “Dialectic” has been a matter of growing interest in contemporary philosophy. The present article analyzes dialectical methods and positions them by reference to two paradigmatic texts of German idealism and analytic philosophy, i.e. J.G. Fichte’s Science of Knowing (1804) and J. McDowell’s Mind and World. Both dialectical approaches will be interpreted with regard to their contribution in the debate on reductionism and anti-reductionism: both Fichte and McDowell claim that philosophical positi…Read more
  •  19
    Schopenhauer Diagrams for Conceptual Analysis
    In Ahti Veikko Pietarinen, P. Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker (eds.), Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169., . 2020.
    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 giv…Read more
  •  76
    Reism, Concretism and Schopenhauer Diagrams
    Studia Humana 9 (3/4): 104-119. 2020.
    Reism or concretism are the labels for a position in ontology and semantics that is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan Woleński have shown, there are two dimensions with which the abstract expression of reism can be made concrete: The ontological dimension of reism says that only things exist; the semantic dimension of reism says that all concepts must be reduced to concrete terms in order to be meaningful. In this paper we argue for the following two theses: (…Read more
  •  20
    Calculus CL - From Baroque Logic to Artificial Intelligence
    Logique Et Analyse 249 111-129. 2020.
    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, e…Read more
  •  10
    This paper is an introduction to the volume Language, Logic and Mathematics in Schopenhauer. It shows the basic interpretations discussed in Schopenhauer’s research, explains the aims and tasks of Schopenhauer’s philosophy and shows the importance of language, logic and mathematics in Schopenhauer’s system.
  •  5
    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 a…Read more
  •  21
    Calculus CL as a Formal System
    In Ahti Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker (eds.), Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169. 2020., . pp. 445-460. 2020.
    In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.
  • 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 Schopenh…Read more
  •  17
    Language, Logic, and Mathematics in Schopenhauer. (edited book)
    Birkhäuser. 2020.
    The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demo…Read more
  •  20
    The Cretan Square
    Logica Universalis 14 (1): 1-5. 2020.
    This special issue is related to the 6th World Congress on the Square of Opposition which took place at the Orthodox Academy of Crete in November 2018. In this introductory paper we explain the context of the event and the topics discussed.
  •  17
    Logic Diagrams, Sacred Geometry and Neural Networks
    Logica Universalis 13 (4): 495-513. 2019.
    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…Read more
  •  56
    ショーペンハウアーにおける意味の使用理論と文脈原理 : ヴィトゲンシュタイン
    ショーペンハウアー研究 = Schopenhauer-Studien 22 150-190. 2017.
    Japanese translation of ""Schopenhauers Gebrauchstheorie der Bedeutung und das Kontextprinzip. Eine Parallele zu Wittgensteins Philosophischen Untersuchungen". In: 97. Schopenhauer-Jahrbuch (2016), S. 29–51" by Tadahiro Oota (太田 匡洋 [訳])
  •  25
    Post-Truth as a Procrastination of Enlightenment
    Studia Philosophica Estonica 11 (1): 117-127. 2018.
    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 designati…Read more
  •  71
    Logikdiagramme und Logikmaschinen aus der Zittauer Schule um Christian Weise
    Neues Lausitzische Magazin 141 (1): 39-57. 2019.
    A particularly promising trail on the search for forgotten logic diagrams leads to Upper Lusatia in the 17th century, more precisely to Christian Weise and his students. Samuel Grosser, who later became rector in Görlitz, and Johann Christian Lange, who later became professor of logic at the University of Gießen, are the most prominent to have published remarkable logic diagrams. Even more remarkable, however, is the fact that Lange's interest in these diagrams ultimately gave rise to the idea o…Read more
  •  26
    Oppositional Geometry in the Diagrammatic Calculus CL
    South American Journal of Logic 3 (2): 517-531. 2017.
    The paper presents the diagrammatic calculus CL, which combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. In its basic form, `CL' (= Cubus Logicus) organizes terms in the form of a square or cube. By applying the arrows of the square of opposition to CL, judgments and inferences can be displayed. Thus CL offers on the one hand an intuitive method to display ontologies and on the other hand a diagrammatic tool to check inferences. The paper focuses mainly on the …Read more
  •  21
    Euler-type Diagrams and the Quantification of the Predicate
    Journal of Philosophical Logic 49 (2): 401-416. 2020.
    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 …Read more
  •  38
    Problems and interpretations of Schopenhauer’s World as Will and Representation
    with Daniel Schubbe
    Voluntas: Revista Internacional de Filosofia 10 (1): 199-211. 2019.
    In this paper we present an overview of the current interpretations of the first volume of Arthur Schopenhauer’s main work The World as Will and Representation (W I) and discuss their problems. We discuss four issues, which in our opinion must clarify a current interpretation implicitly or explicitly, if it claims to be an interpretation of the whole book: (1) What does Schopenhauer mean by the fact that his work shares only one (single) thought? (2) How are the individual books of W I related? …Read more
  •  20
    An analogy between Hegel's theory of recognition and Ficino's theory of love
    British Journal for the History of Philosophy 27 (1): 95-113. 2019.
    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 e…Read more
  •  95
    Schopenhauer's World. The System of The World as Will and Presentation I
    Schopenhaueriana. Revista Española de Estudios Sobre Schopenhauer 2. 2017.
    in recent years, the research on Schopenhauer has shown a change in the interpretation of his main work, «The World as Will and Presentation», from (1) a normative and linear instruction which guides the reader from idealism to mysticism, pessimism and nothingness to (2) value-free and independent descriptions of the world with all phenomena (like idealism, mysticism, nothingness etc.) in it. thus Schopenhauer’s main work has become an empirical or baconian approach—something like a «philosophic…Read more
  •  14
    Warum ist überhaupt etwas und nicht nichts? Wandel und Variationen einer Frage
    with Daniel Schubbe and Rico Hauswald
    Meiner. 2013.
    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 …Read more
  • ›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 Syste…Read more
  •  64
    Inspired by various research results on the history of philosophy that have not yet been compiled, the paper pursues the thesis that the question "Why is there something rather than nothing" was formulated long before Leibniz. In reviewing this thesis, the 'fundamental question' is differentiated into two individual questions: "Why is there something at all" and 'Why isn't rather nothing?". On the basis of this systematic distinction, the paper examines the history of philosophy from early histo…Read more
  • This article compares the research literature published by Goethe and Schopenhauer on the subject of evolutionary theory. The metatheoretical thesis is supported that the results of any comparison between Schopenhauer or Goethe and a concrete theory of evolution always depend on three dimensions: 1. the scientific point of view of the comparative, 2. the meaning and definition of the central terms and 3. the selection of the analyzed primary literature. It is also argued that no previously publi…Read more
  •  18
    Logik und Eristische Dialektik
    In Daniel Schubbe & Matthias Koßler (eds.), Schopenhauer-Handbuch: Leben – Werk – Wirkung, Springer. pp. 160-165. 2018.
    The paper examines Schopenhauer's logic lectures and the eristic dialectics of the manuscript remains in particular. The content of the logic lectures is briefly presented, then the characteristics are highlighted and finally Schopenhauer’s Euler diagrams are examined. The section on eristic dialectics summarizes the history of the text and its origin and reflects the content and order of the document.