Peeters Online Bibliographies
Peeters Publishers
this issue
  previous article in this issuenext article in this issue  

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.

download article