The Role of Abduction in Self-Similarity : On the Peircean Concept of the Map of the Map

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Pareyon , G 2010 , The Role of Abduction in Self-Similarity : On the Peircean Concept of the Map of the Map . in E Tarasti (ed.) , Abstracts of the International Summer School for Semiotic and Structural Studies : 25 Years Semiotics in Imatra . International Summer School for Semiotic and Structural Studies , Imatra , pp. 35-36 , 25 Years Semiotics in Imatra , Imatra , Finland , 11/06/2010 .

Title: The Role of Abduction in Self-Similarity : On the Peircean Concept of the Map of the Map
Author: Pareyon, Gabriel
Editor: Tarasti, Eero
Contributor: University of Helsinki, Department of Philosophy, History, Culture and Art Studies 2010-2017
Publisher: International Summer School for Semiotic and Structural Studies
Date: 2010-06-07
Language: eng
Number of pages: 2
Belongs to series: Abstracts of the International Summer School for Semiotic and Structural Studies 25 Years Semiotics in Imatra
URI: http://hdl.handle.net/10138/24799
Abstract: Based on the Aristotelian criterion referred to as 'abductio', Peirce suggests a method of hypothetical inference, which operates in a different way than the deductive and inductive methods. “Abduction is nothing but guessing” (Peirce, 7.219). This principle is of extreme value for the study of our understanding of mathematical self-similarity in both of its typical presentations: relative or absolute. For the first case, abduction incarnates the quantitative/qualitative relationships of a self-similar object or process; for the second case, abduction makes understandable the statistical treatment of self-similarity, 'guessing' the continuity of geometric features to the infinity through the use of a systematic stereotype (for instance, the assumption that the general shape of the Sierpiński triangle continuates identically into its particular shapes). The metaphor coined by Peirce, of an exact map containig itself the same exact map (a map of itself), is not only the most important precedent of Mandelbrot’s problem of measuring the boundaries of a continuous irregular surface with a logarithmic ruler, but also still being a useful abstraction for the conceptualisation of relative and absolute self-similarity, and its mechanisms of implementation. It is useful, also, for explaining some of the most basic geometric ontologies as mental constructions: in the notion of infinite convergence of points in the corners of a triangle, or the intuition for defining two parallel straight lines as two lines in a plane that 'never' intersect.
Subject: 611 Philosophy
abduction
self-similarity
stereotype
synecdoche
metaphor
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