An influential objection to the epistemic power of the imagination holds that it is uninformative. You cannot get more out of the imagination than you put into it, and therefore learning from the imagination is impossible. This paper argues, against this view, that the imagination is robustly informative. Moreover, it defends a novel account of how the imagination informs, according to which the imagination is informative in virtue of its analog representational format. The core idea is that analog representations represent (...) relations ‘for free,’ and this explains how the imagination can contain more information than is put into it. This account makes important contributions to both philosophy of mind, by showing how the imagination can generate new content that is not represented by a subject’s antecedent mental states, and epistemology, by showing how the imagination can generate new justification that is not conferred by a subject’s antecedent evidence. (shrink)

Free rides and observational advantages occur in visualizations when they reveal facts that must be inferred from an alternative representation. Understanding whether these concepts correspond to cognitive advantages is important: do they facilitate information extraction, saving the ‘deductive cost’ of making inferences? This paper presents the first evaluations of free rides and observational advantages in visualizations of sets compared to text. We found that, for Euler and linear diagrams, free rides and observational advantages yielded significant improvements in task performance. For (...) Venn diagrams, whilst their observational advantages yielded significant performance benefits over text, this was not universally true for free rides. The consequences are two-fold: more research is needed to establish when free rides are beneficial, and the results suggest that observational advantages better explain the cognitive advantages of diagrams over text. A take-away message is that visualizations with observational advantages are likely to be cognitively advantageous over competing representations. (shrink)

Truth diagrams are introduced as a novel graphical representation for propositional logic. To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege’s conceptual notation, diagrams from Wittgenstein’s Tractatus, Pierce’s alpha graphs and Gardner’s shuttle diagrams. The comparison (...) of the representations succeeds in distinguishing ideas that are fundamental to PL from features of common PL representations that are somewhat arbitrary. (shrink)

In the year 1714, Johann Christian Lange published a baroque textbook about a logic machine, supposed to simulate human cognitive abilities such as perception, judgement, and reasoning. From today’s perspective, it can be argued that this blueprint is based on an inference engine applied to a strict ontology which serves as a knowledge base. In this paper, I will first introduce Lange’s approach in the period of baroque logic and then present a diagrammatic modernization of Lange’s principles, entitled Calculus CL. (...) Finally, I would like to discuss the possibilities of how to apply CL to modern cases of concern by using an example from epidemiology. (shrink)

We argue that formal linguistic theory, properly extended, can provide a unifying framework for diverse phenomena beyond traditional linguistic objects. We display applications to pictorial meanings, visual narratives, music, dance, animal communication, and, more abstractly, to logical and non-logical concepts in the ‘language of thought’ and reasoning. In many of these cases, a careful analysis reveals that classic linguistic notions are pervasive across these domains, such as for instance the constituency (or grouping) core principle of syntax, the use of logical (...) variables (for object tracking), or the variety of inference types investigated in semantics/pragmatics. The aim of this overview is to show how the application of formal linguistic concepts and methodology to non-linguistic objects yields non-trivial insights, thus opening the possibility of a general, precise theory of signs. (An appendix, found in the online supplements to this article, surveys applications of Super Linguistics to animal communication.). (shrink)

Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima, is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima’s framework as a tool to analyse the occurrence and properties of them. I consider (...) a number of different examples from mathematical practice that illustrate a variety of uses of free rides in mathematics. Analysing these examples I find that mathematical free rides are sometimes based on syntactic and semantic properties of diagrams. (shrink)

This paper outlines a method to assess the effectiveness of diagrams, from semiotic foundations. In doing so, we explore the Peircian notion of signification, as applied to diagrammatic representations. We review a history of diagrams, with particular emphasis on schematics used for representing systems, and uncover the neglect of semiotic analysis of diagrammatic representations. Through application of category theory to the Peircian triadic model, we propose a set of quantitative quality measures for diagrams, and a framework for their assessment, based (...) on the properties of their encoding, pragmatic and perceptual morphisms. These measures include diagram complexity, utility, aesthetics and expert assessment of semiotic content, together with qualitative feedback. We consider the diagrams as an aid to cognitive processes, rather than a purely communication media. This utility-focused perspective on diagram quality dimensions allows for fresh insights into the creation of effective diagrams. (shrink)

We extend natural deduction for first-order logic (FOL) by introducing diagrams as components of formal proofs. From the viewpoint of FOL, we regard a diagram as a deductively closed conjunction of certain FOL formulas. On the basis of this observation, we first investigate basic heterogeneous logic (HL) wherein heterogeneous inference rules are defined in the styles of conjunction introduction and elimination rules of FOL. By examining what is a detour in our heterogeneous proofs, we discuss that an elimination-introduction pair of (...) rules constitutes a redex in our HL, which is opposite the usual redex in FOL. In terms of the notion of a redex, we prove the normalization theorem for HL, and we give a characterization of the structure of heterogeneous proofs. Every normal proof in our HL consists of applications of introduction rules followed by applications of elimination rules, which is also opposite the usual form of normal proofs in FOL. Thereafter, we extend the basic HL by extending the heterogeneous rule in the style of general elimination rules to include a wider range of heterogeneous systems. (shrink)