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Operational constraints in diagrammatic reasoning

In Gerard Allwein & Jon Barwise (eds.), Logical reasoning with diagrams. New York: Oxford University Press (1996)

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  1. Explicaciones Geométrico-Diagramáticas en Física desde una Perspectiva Inferencial.Javier Anta - 2019 - Revista Colombiana de Filosofía de la Ciencia 38 (19).
    El primer objetivo de este artículo es mostrar que explicaciones genuinamente geométricas/matemáticas e intrínsecamente diagramáticas de fenómenos físicos no solo son posibles en la práctica científica, sino que además comportan un potencial epistémico que sus contrapartes simbólico-verbales carecen. Como ejemplo representativo utilizaremos la metodología geométrica de John Wheeler (1963) para calcular cantidades físicas en una reacción nuclear. Como segundo objetivo pretendemos analizar, desde un marco inferencial, la garantía epistémica de este tipo de explicaciones en términos de dependencia sintáctica y semántica (...)
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  • Modeling Mental Spatial Reasoning About Cardinal Directions.Holger Schultheis, Sven Bertel & Thomas Barkowsky - 2014 - Cognitive Science 38 (8):1521-1561.
    This article presents research into human mental spatial reasoning with orientation knowledge. In particular, we look at reasoning problems about cardinal directions that possess multiple valid solutions , at human preferences for some of these solutions, and at representational and procedural factors that lead to such preferences. The article presents, first, a discussion of existing, related conceptual and computational approaches; second, results of empirical research into the solution preferences that human reasoners actually have; and, third, a novel computational model that (...)
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  • Diagrams.Sun-Joo Shin - 2008 - Stanford Encyclopedia of Philosophy.
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  • Thinking with maps.Elizabeth Camp - 2007 - Philosophical Perspectives 21 (1):145–182.
    Most of us create and use a panoply of non-sentential representations throughout our ordinary lives: we regularly use maps to navigate, charts to keep track of complex patterns of data, and diagrams to visualize logical and causal relations among states of affairs. But philosophers typically pay little attention to such representations, focusing almost exclusively on language instead. In particular, when theorizing about the mind, many philosophers assume that there is a very tight mapping between language and thought. Some analyze utterances (...)
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  • Meditating and Inquiring with Imagination: Leibniz, Lambert, and Kant on the Cognitive Value of Diagrams.Lucia Oliveri - 2024 - History and Philosophy of Logic 45:1-19.
    Reasoning with diagrams is considered to be a peculiar form of reasoning. Diagrams are often associated with imagistic representations conveyed by spatial arrangements of lines, points, figures, or letters that can be manipulated to obtain knowledge on a subject matter. Reasoning with diagrams is not just ‘peculiar’ because reasoners use spatially arranged characters to obtain knowledge – diagrams apparently have cognitive surplus: they enable a quasi-intuitive form of knowledge. The present paper analyses the issue of diagrams’ cognitive value by enquiring (...)
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  • (1 other version)Visual Metaphors in the Sciences: The Case of Epigenetic Landscape Images.Jan Baedke & Tobias Schöttler - 2016 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie:1-22.
    Recent philosophical analyses of the epistemic dimension of images in the sciences show a certain trend in acknowledging potential roles of these images beyond their merely decorative or pedagogical functions. We argue, however, that this new debate has yet paid little attention to a special type of pictures, we call ‘visual metaphor’, and its versatile heuristic potential in organizing data, supporting communication, and guiding research, modeling, and theory formation. Based on a case study of Conrad Hal Waddington’s epigenetic landscape images (...)
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  • Existential graphs as an instrument of logical analysis: Part I. alpha.Francesco Bellucci & Ahti-Veikko Pietarinen - 2016 - Review of Symbolic Logic 9 (2):209-237.
    Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...)
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  • What Makes an Effective Representation of Information: A Formal Account of Observational Advantages.Gem Stapleton, Mateja Jamnik & Atsushi Shimojima - 2017 - Journal of Logic, Language and Information 26 (2):143-177.
    In order to effectively communicate information, the choice of representation is important. Ideally, a chosen representation will aid readers in making desired inferences. In this paper, we develop the theory of observation: what it means for one statement to be observable from another. Using observability, we give a formal characterization of the observational advantages of one representation of information over another. By considering observational advantages, people will be able to make better informed choices of representations of information. To demonstrate the (...)
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  • Proofs, pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
    Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid's reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the generality of the theory. How can inferences made from a particular diagrams license general mathematical results? After surveying the history behind the received (...)
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  • Theories of diagrammatic reasoning: Distinguishing component problems. [REVIEW]Corin Gurr, John Lee & Keith Stenning - 1998 - Minds and Machines 8 (4):533-557.
    Theories of diagrams and diagrammatic reasoning typically seek to account for either the formal semantics of diagrams, or for the advantages which diagrammatic representations hold for the reasoner over other forms of representation. Regrettably, almost no theory exists which accounts for both of these issues together, nor how they affect one another. We do not attempt to provide such an account here. We do, however, seek to lay out larger context than is generally used for examining the processes of using (...)
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  • The forgotten individual: diagrammatic reasoning in mathematics.Sun-Joo Shin - 2012 - Synthese 186 (1):149-168.
    Parallelism has been drawn between modes of representation and problem-sloving processes: Diagrams are more useful for brainstorming while symbolic representation is more welcomed in a formal proof. The paper gets to the root of this clear-cut dualistic picture and argues that the strength of diagrammatic reasoning in the brainstorming process does not have to be abandoned at the stage of proof, but instead should be appreciated and could be preserved in mathematical proofs.
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  • Redescubriendo la lógica diagramática de Leibniz.J. Martín Castro Manzano - 2016 - Tópicos: Revista de Filosofía 52:89-116.
    En este artículo recuperamos la lógica diagramática lineal de Leibniz para la silogística y descubrimos sus propiedades lógicas y computacionales a través de una aproximación formal en términos metalógicos, lo cual es algo que, hasta donde sabemos, aún falta por hacerse. Así, en esta contribución buscamos, respectivamente, dos metas, una histórica y una lógica: i) prestar más atención a los aspectos algorítmicos del sistema diagramático lineal de Leibniz para la silogística, de los cuales creemos que han sido desdeñados por un (...)
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  • (1 other version)Visual Metaphors in the Sciences: The Case of Epigenetic Landscape Images.Jan Baedke & Tobias Schöttler - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (2):173-194.
    Recent philosophical analyses of the epistemic dimension of images in the sciences show a certain trend in acknowledging potential roles of these images beyond their merely decorative or pedagogical functions. We argue, however, that this new debate has yet paid little attention to a special type of pictures, we call ‘visual metaphor’, and its versatile heuristic potential in organizing data, supporting communication, and guiding research, modeling, and theory formation. Based on a case study of Conrad Hal Waddington’s epigenetic landscape images (...)
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  • Inferential and expressive capacities of graphical representations: Survey and some generalizations.Atsushi Shimojima - 2004 - In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. pp. 18--21.
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