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Document Details : Title: On Linear Existential Graphs Author(s): BELLUCCI, Francesco , LIU, Xinwen , PIETARINEN, Ahti-Veikko Journal: Logique et Analyse Volume: 251 Date: 2020 Pages: 261-296 DOI: 10.2143/LEA.251.0.3288641 Abstract : Peirce’s linear versions of the language of his Existential Graphs (EGs), presented in 1902, are examined. Differences between linear and non-linear languages are explained by permutational invariance and type- vs. occurrence-referentiality: Standard EGs are permutationally invariant with respect to linear EGs, while the Beta part of the system, which corresponds to first-order quantificational theory with identity, is occurrence-referential. However, occurrence-referentiality of Beta graphs constitutes a defect of expressivity: since the meaning of a quantifier is inextricably connected to the meaning of the sign of identity, certain complex assertions cannot be expressed in the language of Beta graphs without a new extension of its standard notation. |
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