Operational iconicity as a necessary condition for diagrammatic reasoning

JAVIER LEGRIS

CIUDAD AUTONOMA DE BUENOS AIRES

Congreso; 14th World Congress of Semiotics; 2019

International Association for Semiotics Studies / Association Internationale de Sémiotique (IASS/AIS) organized by the Asociación Argentina de Semiótica ? AAS and the Universidad Nacional de las Artes ? UNA, Buenos Aires

Charles S. Peirce formulated his ultimate conceptionof logic in the context of his theory of signs and his pragmaticist philosophy.For him, deduction was a process accomplished by means of diagrams, and diagrammatic reasoning is the accurate method forrepresenting the ?course of thinking?. Peirce?s approach to logic followeddirectly from his conception of mathematics: mathematical thought was for himessentially diagrammatic: algebraic equations were as diagrammatic as geometricfigures. Now, diagrams are icons.  The notion of iconicity is not always a neatone. Peirce provided different characterization in his writings, originating adiscussion among scholars. The idea of analogy, similarity (or resemblance)plays an important role. For example, in 1885 Peirce considered an icon as a ?signwhich stands for something because it resembles it (CW 5.163; CP 3.362)?, andaround 1890 he wrote: ?The first [kind of sign] is the diagrammatic sign or icon,which exhibits a similarity or analogy to the subject of discourse? (CP1.369; CW 5.243). The aim ofthis paper consists in showing that Frederik Stjernfelt?s idea of an operational iconicity provides thesemiotic basis for the analysis of the relation of deduction underlying logicalreasoning. According to Frederik Stjernfelt, ?Here,similarity as well as its utilization in sign reference are necessaryprerequisites for the Icon, but only taken together do they become sufficientprerequisites.? (Stjernfelt 2007, p. 49) ?An Icon is a sign which refers to the Objectthat it denotes merely by virtue of characters of its own, and which itpossesses, just the same, whether any such Object actually exists or not. It istrue that unless there really is such an object, the Icon does not act as asign; but this has nothing to do with its character as a sign. Anythingwhatever, be it quality, existent, individual, or law, is an Icon of anything,in so far it is like that thing and used as a sign of it.? (?Syllabus?, 1903,EPII, 291; 2.247) It is important to stress that ?similarity?shared between a sign and an object is not enough for having a semioticrelation, because semiotic relations are always asymmetric, but similarity issymmetric. Peirce introduces the asymmetry through the pragmatic notion of ?useas a sign?. Hence, an icon a must signify through its similarity to its object(and not because of it). Now,diagrams are icons. In a diagram the analytical role of icons turns to beessential. Peirce referred to an ?icon [or analytic picture]? (Peirce CP 1.275).  Anicon provides knowledge through its decomposition in basic elements. There isfurther evidence from unpublished manuscripts that Peirce conceived his systemof the Existential Graphs not only as a diagrammatic proof procedure fordeductive logic, but also (and mainly) as a tool for logical analysis. Clearly, this analysis is not of linguistic butof semiotic nature. Moreover, Peirce regarded his systems of Existential Graphsas the best diagrammatic method fordeductive logic. Hence, they should provide the best (an the most accurate)analysis of logical concepts.  This paperaddresses the notion of analysis underlying the Existential Graphs. In linewith this aim, the notion analysis. Moreover, the claim of Francesco Bellucciand Ahti-Veikko Pietarinen that uniquedecomposition is the essential feature of Peirce?s notion of analysis willbe brought into discussion and will be illustrated by the case of the ?scroll?in the Alpha system of Existential Graphs. Finally, for the sake of a better understanding,Peirce?s perspective will be briefly compared with Gottlob Frege?s conceptionof analysis in Begriffsschrift, andsome relevant differences between them will be pointed out.  <!-- /* Font Definitions */ @font-face{font-family:"MS Mincho";panose-1:2 2 6 9 4 2 5 8 3 4;mso-font-alt:"ＭＳ 明朝";mso-font-charset:128;mso-generic-font-family:modern;mso-font-pitch:fixed;mso-font-signature:-536870145 1791491579 18 0 131231 0;}@font-face{font-family:"Cambria Math";panose-1:2 4 5 3 5 4 6 3 2 4;mso-font-charset:0;mso-generic-font-family:roman;mso-font-pitch:variable;mso-font-signature:3 0 0 0 1 0;}@font-face{font-family:Cambria;panose-1:2 4 5 3 5 4 6 3 2 4;mso-font-charset:0;mso-generic-font-family:roman;mso-font-pitch:variable;mso-font-signature:-536870145 1073743103 0 0 415 0;}@font-face{font-family:"\@MS Mincho";panose-1:2 2 6 9 4 2 5 8 3 4;mso-font-charset:128;mso-generic-font-family:modern;mso-font-format:other;mso-font-pitch:fixed;mso-font-signature:-536870145 1791491579 134217746 0 131231 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal{mso-style-unhide:no;mso-style-qformat:yes;mso-style-parent:"";margin:0cm;margin-bottom:.0001pt;mso-pagination:widow-orphan;font-size:12.0pt;font-family:"Cambria",serif;mso-ascii-font-family:Cambria;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:"MS Mincho";mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Cambria;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;mso-ansi-language:ES-TRAD;mso-fareast-language:ES;}.MsoChpDefault{mso-style-type:export-only;mso-default-props:yes;font-family:"Cambria",serif;mso-ascii-font-family:Cambria;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:"MS Mincho";mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Cambria;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;mso-ansi-language:ES-TRAD;mso-fareast-language:ES;}size:595.0pt 842.0pt;margin:70.85pt 3.0cm 70.85pt 3.0cm;mso-header-margin:35.4pt;mso-footer-margin:35.4pt;mso-paper-source:0;}div.WordSection1{page:WordSection1;}