On Linear Existential Graphs

Francesco Bellucci, Xinwen Liu, Ahti Veikko Pietarinen

Research output: Contribution to journalReview articlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)261-296
Number of pages36
JournalLogique et Analyse
Publication statusPublished - May 2020
Externally publishedYes

Scopus Subject Areas

  • Philosophy

User-Defined Keywords

  • Existential Graphs
  • Linear Notations
  • Quantification and Identity
  • Type vs. Occurrence-Referentiality


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