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Periods in the Use of Euler-type Diagrams

Acta Baltica Historiae Et Philosophiae Scientiarum 5 (1):50-69 (2017)

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World and Logic.Jens Lemanski - 2021 - London, Vereinigtes Königreich: College Publications.details 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, (...) Download Export citation Bookmark 11 citations
Logic, Spatial Algorithms and Visual Reasoning.Andrew Schumann & Jens Lemanski - 2022 - Logica Universalis 16 (4):535-543.details 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.). (shrink) Download Export citation Bookmark 1 citation
Logic Diagrams, Sacred Geometry and Neural Networks.Jens Lemanski - 2019 - Logica Universalis 13 (4):495-513.details 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 (...) Download Export citation Bookmark 3 citations
Euler-type Diagrams and the Quantification of the Predicate.Jens Lemanski - 2020 - Journal of Philosophical Logic 49 (2):401-416.details 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 (...) Download Export citation Bookmark 6 citations
A Diagrammatic Representation of Hegel’s Science of Logic.Jens Lemanski & Valentin Pluder - 2021 - In Stapleton G. Basu A. (ed.), Diagrams 2021: Diagrammatic Representation and Inference. 93413 Cham, Deutschland: Springer. pp. 255-259.details In this paper, we interpret a 19th century diagram, which is meant to visualise G.W.F. Hegel’s entire method of the `Science of Logic' on the basis of bitwise operations. For the interpretation of the diagram we use a binary numeral system, and discuss whether the anti-Hegelian argument associated with it is valid or not. The reinterpretation is intended to make more precise rules of construction, a stricter binary code and a review of strengths and weaknesses of the critique. Download Export citation Bookmark 1 citation

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