On the Diagrammatic Representation of Existential Statements with Venn Diagrams

Amirouche Moktefi*, Ahti Veikko Pietarinen

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

17 Citations (Scopus)


It is of common use in modern Venn diagrams to mark a compartment with a cross to express its non-emptiness. Modern scholars seem to derive this convention from Charles S. Peirce, with the assumption that it was unknown to John Venn. This paper demonstrates that Venn actually introduced several methods to represent existentials but felt uneasy with them. The resistance to formalize existentials was not limited to diagrammatic systems, as George Boole and his followers also failed to provide a satisfactory symbolic representation for them. This difficulty points out issues that are inherent to the very nature of existentials. This paper assesses the various methods designed for the representation of existential statements with Venn diagrams. First, Venn’s own attempts are discussed and compared with other solutions proposed by his contemporaries and successors, notably Lewis Carroll and Peirce. Since disjunctives hold an important role in an effective representation of existentials, their representation is also discussed. Finally, recent methods for the diagrammatic representation of existing individuals, rather than mere existence, are surveyed.

Original languageEnglish
Pages (from-to)361-374
Number of pages14
JournalJournal of Logic, Language and Information
Issue number4
Publication statusPublished - Dec 2015

Scopus Subject Areas

  • Computer Science (miscellaneous)
  • Philosophy
  • Linguistics and Language

User-Defined Keywords

  • Carroll diagram
  • Charles S. Peirce
  • Disjunctive proposition
  • Euler diagram
  • Existence
  • John Venn
  • Lewis Carroll
  • Logic notation
  • Particular proposition
  • Singular proposition
  • Spider diagram
  • Venn diagram


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