Icons for Identity: Peirce's Beta Graphs

JAVIER LEGRIS

CIUDAD AUTONOMA DE BUENOS AIRES

Congreso; Leibniz's Principle of Identity of Indescernibles and Its Repercussion in Physics and Mathemati; 2019

UNIVERSIDAD CAECE

Charles S.Peirce discussed the notion of identity and the ontological principle ofindiscernibles many times and in different respects. From a logical point ofview, Peirce examined identity in his algebra of relatives as a second-orderpredicate. In his later diagrammatic logic, the Existential Graphs, identity and Quantifiers are expressed on thebasis of the same sign: the line ofidentity of the Beta Graphs. Hence, identity is built into quantification. Theaim of this presentation is to examine the diagrammatic expression of identityand identity statements in this system, stressing its notational features anddiscussing the problems related to the principle of indiscernibles. It isargued that this diagrammatic notation is especially useful and illuminating,with potential applications to other fields.<!-- /* 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 134217746 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:-536870145 1107305727 0 0 415 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-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;}