Practically all theories of iconicity are denunciations of its subject matter (for example, those of Goodman, Bierman and the early Eco). My own theory of iconicity was developed in order to save a particular kind of iconicity, pictoriality, from such criticism. In this interest, I distinguished pure iconicity, iconic ground, and iconic sign, on one hand, and primary and secondary iconic signs, on the other hand. Since then, however, several things have happened. The conceptual tools that I created to explain (...) pictoriality have been shown by others to be relevant to linguistic iconicity. On the other hand, semioticians with points of departure different from mine have identified mimicry as it is commonly found in the animal world as a species of iconicity. In the evolutionary semiotics of Deacon, iconicity is referred to in such a general way that it seems to be emptied of all content, while in the variety invented by Donald the term mimesis is used for a particular phase in the evolution of iconic meaning. The aim of this article is to consider to what extent the extension of iconicity theory to new domains will necessitate the development of new models. (shrink)

It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is to (...) show that this branch of mathematics can furnish a natural conceptual system for Gestalt psychology, in that it provides effective tools for describing global qualitative aspects of the latter’s object of investigation. We distinguish three possible ways in which mathematics can contribute to this: explanation, explication and metaphor. We hold that all three of these can be usefully characterized as throwing light on their subject matter, and argue that in each case this contrasts with the role of explanations in physics. Mathematics itself, we argue, provides something different from such explanations when applied in the field of psychology, and this is nevertheless still cognitively fruitful. (shrink)

This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also (...) consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance. (shrink)