The paper gives a detailed reconstruction and discussion of Peirce’s doctrine of propositions, so-called Dicisigns, developed in the years around 1900. The special features different from the logical mainstream are highlighted: the functional definition not dependent upon conscious stances nor human language, the semiotic characterization extending propositions and quasi-propositions to cover prelinguistic and prehuman occurrences of signs, the relations of Dicisigns to the conception of facts, of diagrammatical reasoning, of icons and indices, of meanings, of objects, of syntax in Peirce’s (...) logic-as-semiotics. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

In this paper, we try to shed light on the ontological puzzle pertaining to models and to contribute to a better understanding of what models are. Our suggestion is that models should be regarded as a specific kind of signs according to the sign theory put forward by Charles S. Peirce, and, more precisely, as icons, i.e. as signs which are characterized by a similarity relation between sign (model) and object (original). We argue for this (1) by analyzing from a (...) semiotic point of view the representational relation which is characteristic of models. We then corroborate our hypothesis (2) by discussing the conceptual differences between icons, i.e. models, and indexical and symbolic signs and (3) by putting forward a general classification of all icons into three functional subclasses (images, diagrams, and metaphors). Subsequently, we (4) integratively refine our results by resorting to two influential and, as can be shown, complementary philosophy of science approaches to models. This yields the following result: models are determined by a semiotic structure in which a subject intentionally uses an object, i.e. the model, as a sign for another object, i.e. the original, in the context of a chosen theory or language in order to attain a specific end by instituting a representational relation in which the syntactic structure of the model, i.e. its attributes and relations, represents by way of a mapping the properties of the original, which hence are regarded as similar in a relevant manner. (shrink)

This paper investigates the notion of semiotic scaffolding in relation to mathematics by considering its influence on mathematical activities, and on the evolution of mathematics as a research field. We will do this by analyzing the role different representational forms play in mathematical cognition, and more broadly on mathematical activities. In the main part of the paper, we will present and analyze three different cases. For the first case, we investigate the semiotic scaffolding involved in pencil and paper multiplication. For (...) the second case, we investigate how the development of new representational forms influenced the development of the theory of exponentiation. For the third case, we analyze the connection between the development of commutative diagrams and the development of both algebraic topology and category theory. Our main conclusions are that semiotic scaffolding indeed plays a role in both mathematical cognition and in the development of mathematics itself, but mathematical cognition cannot itself be reduced to the use of semiotic scaffolding. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

Uma seção da Gramática Especulativa de C.S.Peirce – Dez classes de signos – recebeu, a partir de 1903, um importante tratamento diagramático. Neste artigo, são apresentados e discutidos dois diagramas desenvolvidos por Peirce para as dez classes, incluindo esboços desses modelos.

Spider diagrams are based on Euler and Venn/Peirce diagrams, forming a system which is as expressive as monadic first order logic with equality. Rather than being primarily intended for logicians, spider diagrams were developed at the end of the 1990s in the context of visual modelling and software specification. We examine the original goals of the designers, the ways in which the notation has evolved and its connection with the philosophical origins of the logical diagrams of Euler, Venn and Peirce (...) on which spider diagrams are based. Using Peirce’s concepts and classification of signs, we analyse the ways in which different sign types are exploited in the notation. Our hope is that this analysis may be of interest beyond those readers particularly interested in spider diagrams, and act as a case study in deconstructing a simple visual logic. Along the way, we discuss the need for a deeper semiotic engagement in visual modelling. (shrink)

The icon is the type of sign connected to efficient representational features, and its manipulation reveals more information about its object. The London Underground Diagram (LUD) is an iconic artifact and a well-known example of representational efficiency, having been copied by urban transportation systems worldwide. This paper investigates the efficiency of the LUD in the light of different conceptions of iconicity. We stress that a specialized representation is an icon of the formal structure of the problem for which it has (...) been specialized. By embedding such rules of action and behavior, the icon acts as a semiotic artifact distributing cognitive effort and participating in niche construction. (shrink)

In the vein of a renewed interest in diagrammatic reasoning, this paper challenges an opposition between logic diagrams and formal languages that has traditionally been the common view in philosophy of logic and linguistics. We examine, from a philosophical point of view, what we call five dogmas of logic diagrams. These are as follows: (1) diagrams are non-linguistic; (2) diagrams are visual representations; (3) diagrams are iconic, and not symbolic; (4) diagrams are non-linear; (5) diagrams are heterogenous, and not homogenous. (...) Using historical examples, we argue that none of these dogmas is an adequate criterion to distinguish logic diagrams from formal languages. Instead, we advocate that there is a common core between linguistic and diagrammatic representation and reasoning. (shrink)