Sign-design; nuevas estrategias para modelar procesos y estructuras sígnicas

En este artículo vamos a presentar los resultados parciales de un estudio que actualmente estamos desarrollando en el ámbito de la semiótica peirceana, más específicamente en el campo de las clasificaciones sígnicas de Charles S. Peirce. Creemos que la estrategia adoptada en este estudio, que llamamos Sign-Design, puede ser generalizada como un método de investigación en el campo de la semiótica. Se trata del abordaje sistemático de aspectos específicos de la teoría del signo de Peirce, que tiene como objetivo la construcción de modelos visuales de estructuras y procesos sígnicos, estableciendo conexiones entre la semiótica peirceana y los campos del diseño gráfico y del razonamiento diagramático (diagrammatic reasoning). Ella extrae del diseño gráfico una posible metodología y del campo de investigación, conocido como razonamiento diagramático, el argumento de que los diagramas son herramientas valiosas, no sólo para solucionar problemas específicos (problem solving), sino también, de una forma general, para la organización del pensamiento (cf. Chandrasekaran et al., 1995: xv-xxvII).

Operationalism: An Interpretation of the Philosophy of Ancient Greek Geometry

I present a systematic interpretation of the foundational purpose of constructions in ancient Greek geometry. I argue that Greek geometers were committed to an operationalist foundational program, according to which all of mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key foundational aspects of Greek geometry are analogous to core tenets of 20th-century operationalist/positivist/constructivist/intuitionist philosophy of science and mathematics. Operationalism provides coherent answers to a range of traditional philosophical problems regarding classical mathematics, such as the epistemic warrant and generality of diagrammatic reasoning, superposition, and the relation between constructivism and proof by contradiction. Alleged logical flaws in Euclid (implicit diagrammatic reasoning, superposition) can be interpreted as sound operationalist reasoning. Operationalism also provides a compelling philosophical motivation for the otherwise inexplicable Greek obsession with cube duplication, angle trisection, and circle quadrature. Operationalism makes coherent sense of numerous specific choices made in this tradition, and suggests new interpretations of several solutions to these problems. In particular, I argue that: Archytas’s cube duplication was originally a single-motion machine; Diocles’s cissoid was originally traced by a linkage device; Greek conic section theory was thoroughly constructive, based on the conic compass; in a few cases, string-based constructions of conic sections were used instead; pointwise constructions of curves were rejected in foundational contexts by Greek mathematicians, with good reason. Operationalism enables us to view the classical geometrical tradition as a more unified and philosophically aware enterprise than has hitherto been recognised.

Spatial diagrams and geometrical reasoning in the theater

This article offers an analysis of the cognitive role of diagrammatic movements in the theater. Based on the recognition of a theatrical work’s inherent ability to provide new insights concerning reality, the article concentrates on the way by which actors’ movements on stage create spatial diagrams that can provide new insights into the spectators’ world. The suggested model of theater’s epistemology results from a combination of Charles S. Peirce’s doctrine of diagrammatic reasoning and David Lewis’s theoretical account of the truth value of counterfactual conditionals. I argue that in several theatrical works – in particular those whose central image is dominated by movements – the relation of what Lewis names “comparative overall similarity” between the fictional and the actual world is based on diagrammatic homology. The cognitive process involved in deciphering them is, hence, based on diagrammatic reasoning. The main emphasis of the analysis is on the previously unnoticed but important cognitive role of observation in the theater: the idea that observation takes an active role in the reasoning process that enables the spectators to form new knowledge about their actual world. Samuel Beckett’s plays Quad and Come and Go serve here as case studies.

Image Schemas and Conceptual Blending in Diagrammatic Reasoning: The Case of Hasse Diagrams

In this work, we propose a formal, computational model of the sense-making of diagrams by using the theories of image schemas and conceptual blending, stemming from cognitive linguistics. We illustrate our model here for the case of a Hasse diagram, using typed first-order logic to formalise the image schemas and to represent the geometry of a diagram. The latter additionally requires the use of some qualitative spatial reasoning formalisms. We show that, by blending image schemas with the geometrical configuration of a diagram, we can formally describe the way our cognition structures the understanding of, and the reasoning with, diagrams. In addition to a theoretical interest for diagrammatic reasoning, we also briefly discuss the cognitive underpinnings of good practice in diagram design, which are important for fields such as human-computer interaction and data visualization.

Peirce’s diagrammatic reasoning and the cinema: Image, diagram, and narrative in The Shape of Water

This article aims to examine the relationship between image and narrative by means of Peirce’s first trichotomy of qualisign-sinsign-legisign or, for the purposes of the current argument, image-diagram-metaphor. It is argued that narrative, as an extended metaphor, can be examined in three modes: in the image; schematically, in the imagination; and allegorically or in a thought experiment, through hypothetic interpretation. The article outlines two kinds of diagrammatic reasoning emphasized by Peirce: corollarial deduction in which the image is ‘literally seen’ and the reasoning steps are manifest in its conclusion; and theorematic deduction where the conclusion in a diagram is subject to a hypothesis which transforms the image into something new. Demonstrating the breadth of diagrammatic reasoning with reference to the 2018 film, The Shape of Water, the article seeks to explore how allegory and diagram are mutually cooperative, based on three ontological modes: the expressive, the cognitive, and the symbolic. Its primary focus, then, is not so much on the story events of the narrative, as the way that they are visualized and characterized as the fairy story unfolds. It is suggested that the interpreting activity involved in allegory and diagram ties interpretation to metacognition, ultimately (re)recognizing the image in The Shape of Water in an attempt to ascertain the meaning of love.