On the Diagram (and a Practice of Diagrammatics)

Visual Reasoning with Diagrams, 2013

In this article, I propose an operational framework for diagrams. According to this framework, diagrams do not work like sentences, because we do not apply a set of explicit and linguistic rules in order to use them. Rather, we become able to manipulate diagrams in meaningful ways once we are familiar with some specific practice, and therefore we engage ourselves in a form of reasoning that is stable because it is shared. This reasoning constitutes at the same time discovery and justification for this discovery. I will make three claims, based on the consideration of diagrams in the practice of logic and mathematics. First, I will claim that diagrams are tools, following some of Peirce's suggestions. Secondly, I will give reasons to drop a sharp distinction between vision and language and consider by contrast how the two are integrated in a specific manipulation practice, by means of a kind of manipulative imagination. Thirdly, I will defend the idea that an inherent feature of diagrams, given by their nature as images, is their ambiguity: when diagrams are 'tamed' by the reference to some system of explicit rules that fix their meaning and make their message univocal, they end up in being less powerful.

Atlas, 2024

bsrlm.org.uk

Journal of Visual Art Practice

Exploratory diagrams can be distinguished from statistical and explanatory diagrams in that they do not merely communicate what already exists, but provide a method of discovery, experiment and creative invention. As such, they are recommended as productive modes which can be utilized for art, education and philosophy. This paper seeks to draw out a number of key concepts and approaches to exploratory diagramming by examining three powerful diagram theories. First, A.J. Greimas' invention of the 'semiotic square'; second, C.S. Peirce's semiotic account of the diagram as icon; and third, Gilles Châtelet's retelling of scientific and mathematical discovery through diagrammatic devices. Respectively, these theories can each be identified according to a primary operative principle: opposition, relation and gesture.

arXiv (Cornell University), 2020

As the use and diversity of diagrams across many disciplines grows, there is an increasing interest in the diagrams research community concerning how such diversity might be documented and explained. In this article, we argue that one way of achieving increased reliability, coverage, and utility for a general classification of diagrams is to draw on recently developed semiotic principles developed within the field of multimodality. To this end, we sketch out the internal details of what may tentatively be termed the diagrammatic semiotic mode. This provides a natural account of how diagrammatic representations may integrate natural language, various forms of graphics, diagrammatic elements such as arrows, lines and other expressive resources into coherent organisations, while still respecting the crucial diagrammatic contributions of visual organisation. We illustrate the proposed approach using two recent diagram corpora and show how a multimodal approach supports the empirical analysis of diagrammatic representations, especially in identifying diagrammatic constituents and describing their interrelations in a manner that may be generalised across diagram types and be used to characterise distinct kinds of functionality.

Diagrammatic Reasoning, 2015

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. The active involvement and manipulation of representational artifacts for purposes of thinking and communicating is discussed in relation to C.S. Peirce’s notion of diagrammatical reasoning. We propose to extend Peirce’s original ideas and sketch a conceptual framework that delineates different kinds of diagram manipulation: Sometimes diagrams are manipulated in order to profile known information in an optimal fashion. At other times diagrams are explored in order to gain new insights, solve problems or discover hidden meaning potentials. The latter cases often entail manipulations that either generate additional information or extract information by means of abstraction. Ideas are substantiated by reference to ethnographic, experi...

The use of diagrams as external aids to facilitate cognitive abilities is not new. This paper looks into cognitive studies for insight into when, why and how diagrams are effective in problem solving. A case study examines the use of diagrammatic representations as thinking tools and tools for communicating information. The purpose is to examine whether diagramming could be used as a design method, as part of the designer's creative process.

Proceedings, 2017

The article aims to demonstrate the importance of the diagrammatic image as an essential element of the inferential process: a necessary tool for us to interpret and to communicate the intelligible. Accordingly, it will be discussed how diagrams privilege and display pertinences of the object they stand for, consequently affecting our interpretation and what we can fathom. As a fundamental graphic-sign for reasoning and discovery, the diagram will be described in accordance with a theoretical model, to provide the visual designer with a useful instrument to monitor and probe their designs. In this view it will also emerge how the designer's work resembles that of the scientist, both with the intention to innovate models to describe an object.

This paper offers an overview of our recent pedagogic action-research that explores Art and Design students' use of diagramming, to develop their contextual and critical understanding. In so doing it considers the often difficult relationship between 'theory' and 'practice' as experienced by students. We argue that student diagramming can provide a productive bridge between theory and practice and between 'read/write' and visually orientated modes of learning. We conclude that our students' frequent misapplication of certain key forms of diagramming often provide a productive 'first gesture' into their developing insights. Hence such notional 'mistakes' should be actively encouraged rather than corrected.

ArXiv, 2020

In this article, we propose a multimodal perspective to diagrammatic representations by sketching a description of what may be tentatively termed the diagrammatic mode. We consider diagrammatic representations in the light of contemporary multimodality theory and explicate what enables diagrammatic representations to integrate natural language, various forms of graphics, diagrammatic elements such as arrows, lines and other expressive resources into coherent organisations. We illustrate the proposed approach using two recent diagram corpora and show how a multimodal approach supports the empirical analysis of diagrammatic representations, especially in identifying diagrammatic constituents and describing their interrelations.