Diagrammatic reasoning An introduction Riccardo Fusaroli and Kristian Tylén
Many types of everyday and specialized reasoning depend on diagrams: we use maps to find our way, we draw graphs and sketches to communicate concepts and prove geometrical theorems, and we manipulate diagrams to explore new creative solutions to problems. While the linear and symbolic character of verbal language has long served as the predominant model of human thought, it is remarkable how — through a range of contexts — thinking and communication critically depend on manipulations of external, often non-linear, and manipulable iconic-diagrammatic vehicles. In this issue of Pragmatics and Cognition we explore such diagrammatic reasoning, that is, of individual and intersubjectively distributed cognitive processes relying on external representations (i.e. diagrams in a broad sense) as tools for thinking and communicating. The philosopher and semiotician C.S. Peirce was among the first to observe how human thought is deeply intertwined with our external representational capacities. He claimed that the chemist “think with his test tubes” and famously argued that if someone took away his inkstand, his thoughts would be just as disrupted as if a psychologist cut out a lobe of his brain (Fusaroli, 2011; Peirce, 1931; Stjernfelt, 2007). However, diagrammatic reasoning also lies at the very origins of cognitive and computer science. Early AI models of cognitive computation were inspired by the mathematician’s act of writing formulas and sketching diagrams to actively develop their demonstrations and solutions. For instance, A. Turing imagined his universal machine in the act of repeatedly writing data on a string of paper in order to be able to rely on and modify them at a later stage. H. Simon analogously widely discussed and analyzed mathematicians sketching and modifying graphical representations on their blackboard in order to formally define problem-solving procedures (for further discussion, cf. Hutchins, 1995). After these essentially diagrammatic beginnings, however, for long time thinking and cognitive representations have been assumed only within “the boundaries of skin and skull” (Clark, 2008) and problem solving has been often deemed a matter of internal mental operations (Kirsh, 2009). Pragmatics & Cognition 22:2 (2014), 183–186. doi 10.1075/pc.22.2.01fus issn 0929–0907 / e-issn 1569–9943 © John Benjamins Publishing Company
184 Riccardo Fusaroli and Kristian Tylén
The contributors to this issue of Pragmatics and Cognition bring the focus back on the crucial role of the construction and manipulation of external representations. Coming from a variety of disciplines — from cognitive psychology to experimental semiotics and philosophy of science — they highlight a number of crucial aspects of human cognition: 1) Cognition is an active process that 2) relies on a variety of different external representational supports, 3) substantially intertwined in larger social dynamics at different time scales. In “Diagrams, Jars, and Matchsticks”, Vallée-Tourangeau & Vallée-Tourangeau (2015) discuss the implications of rethinking cognition as an active engagement of external representations. Revisiting traditional experiments on hypothesis testing and problem solving (e.g. matchstick problems), the authors allow participants to manually interact with the representational objects involved. Their findings unveil rich strategies involving the manipulation of the environment, which results in new information becoming available. The findings motivate a systemic perspective to the study of cognition, conceiving of the participant as an agent deeply embedded in a context of material and cognitive affordances, much closer to how people actually think outside the cognitive psychologist’s laboratory. In “Thinking in Action”, Tversky and Hessel (2015) argue for the pervasiveness of diagrammatic reasoning and focus on the importance of the representational formats of the resources engaged. The studies reviewed show that individuals and groups spontaneously employ gestures and graphical sketches to solve problems and develop new ideas. Even more crucially, the authors articulate the impact of the active and rapidly fading nature of gesture as opposed to more stable graphical sketches. Different representational formats facilitate effective solutions in different contexts and are sometimes jointly engaged to afford for more complex problem solving. In “Scientists’ Use of Diagrams in Developing Mechanistic Explanations”, Burnston and colleagues (2015) widen the perspective to the slow evolution and distributed character of real-life complex scientific investigations. Diagrammatic representations are often produced to summarize the state-of-the-art research on a given topic (in this case the central circadian oscillator in Synechococcus elongatus), thus highlighting what is still unknown in order to motivate new hypotheses and investigations. Subsequent findings and their interpretations involves the development and integration of multiple versions of different types of diagrams, sometimes progressively refined, sometimes re-hauled to facilitate innovative insight. This process pervades not only the individual case study, but the the scientific enterprise in general, as diagrams are developed and manipulated across research groups over longer period of time. In “Iconicity” Fay and colleagues (2015) focus more specifically on the evolution of external representations to support information exchange and construction
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of cultural traditions. The authors explore diverse representational formats — graphical, gestural and verbal representations — and how a multitude of social factors and pressures impact their development and use. While in early stages, sign systems seem primarily grounded in iconic similarity to their referents, they tend to develop towards simpler, symbolic conventions. The authors discuss how these developmental trajectories reflect the interaction of different pressures: the need to maintain signs that are easily interpretable, but also easy to learn and produce in contexts of communication and cultural traditions. Furthermore, it is discussed how these types of studies and observations can potentially inform theories about language evolution. In “Diagrammatic Reasoning”, Tylén and colleagues (2015) outline a conceptual framework for the study of diagram use and manipulation, based on ethnographic, experimental and historical evidence. Diagrams can be employed to selectively profile already known information for instance for purposes of communication. However, diagrams are also often employed and manipulated to explore information and test hypotheses so to provide better solutions or gain new insights. This often entails manipulations that either generate additional information or extract information by means of abstraction. Furthermore, a particular emphasis is put on joint diagrammatic reasoning, that is cases when several individuals together explore external representational materials in order to solve problems or create new creative solution. It is suggested that beyond manual explorations of diagrams, interacting individuals can stimulate, push and poke each others’ reasoning processes for instance to better escape functional fixations and reach higher levels of abstraction. In summary, the contributions to this issue build on the growing body of approaches showing that cognition far from being only a process internal to the brain is an open multi-modal system deeply relying on bodily interactions and manipulations of the environment (Chemero, 2009; Clark, 2008; Fusaroli, Gangopadhyay, & Tylén, 2014; Hutchins, 2010). However, new important perspectives are added to the literature: i) different types of cognitive processes, task or problems afford quite different types of diagrammatic reasoning involving a heterogeneity of resources and tools, ii) diagrammatic reasoning is profoundly immersed in evolving cultural practices continuously developing and refining these resources. Beyond providing a state-of-the-art of the study of diagrammatic reasoning, the papers constituting this volume also encourage further dialogue, motivate new predictions and pave the way for novel investigations. We are thus only beginning to understand how diverse resources interact in diagrammatic reasoning processes, how different contexts and cultural traditions motivate the evolution of diverse diagrammatic resources, and how multiple agents coordinate their access and manipulation of diagrams. Enjoy the reading.
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References Burnston, D., Sheredos, B., Abrahamsen, A., & Bechtel, W. (2015). Scientists’ Use of Diagrams in Developing Mechanistic Explanations, Pragmatics and Cognition. Pragmatics and Cognition, 22(2), 224–242. Chemero, A. (2009). Radical embodied cognitive science. Cambridge, Mass.: MIT Press. Clark, A. (2008). Supersizing the mind: Embodiment, action, and cognitive extension. New York: Oxford University Press. Fay, N., Ellison, M., & Garrod, S. (2015). Iconicity: From Sign to System in Human Communication and Language. Pragmatics and Cognition, 22(2), 243–262. Fusaroli, R. (2011). The social horizon of embodied language and material symbols. Versus, 112–113, 95–120. Fusaroli, R., Gangopadhyay, N., & Tylén, K. (2014). The dialogically extended mind: Making a case for language as skilful intersubjective engagement. Cognitive Systems Research, 29-30, 31–39. DOI: 10.1016/j.cogsys.2013.06.002 Hutchins, E. (1995). Cognition in the Wild. Cambridge, Mass.: MIT Press. Hutchins, E. (2010). Cognitive Ecology. Topics in Cognitive Science, 2(4), 705–715. DOI: 10.1111/j.1756-8765.2010.01089.x Kirsh, D. (2009). Problem solving and situated cognition. The Cambridge handbook of situated cognition, 264–306. Peirce, C. S. (1931). Collected papers of Charles Sanders Peirce. Cambridge: Harvard University Press. Stjernfelt, F. (2007). Diagrammatology: An investigation on the borderlines of phenomenology, ontology, and semiotics. New York: Springer. Tversky, B., & Kessel, A. (2015). Thinking in Action. Pragmatics and Cognition, 22(2), 206–223. Tylén, K., Fusaroli, R., Bjørndahl, J. S., Rączaszek-Leonardi, J., Østergaard, S., & Stjernfelt, F. (2015). Diagrammatic Reasoning: abstraction, interaction, and insight. Pragmatics and Cognition., 22(2), 263–281 Vallée-Tourangeau, F., & Vallée-Tourangeau, G. (2015). Diagrams, Jars, and Matchsticks: A Systemicist’s Toolkit. Pragmatics and Cognition, 22(2), 187–205.
Authors’ addresses Riccardo Fusaroli Center for Semiotics Jens Chr Skous Vej 2 8000, Aarhus Denmark
Kristian Tylén Center for Semiotics Jens Chr Skous Vej 2 8000, Aarhus Denmark
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