The Representation of Negative Terms with Euler Diagrams

Reetu Bhattacharjee*, Amirouche Moktefi, Ahti Veikko Pietarinen

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingChapterpeer-review

1 Citation (Scopus)


In the common use of logic diagrams, the positive term is conveniently located inside the circle while its negative counterpart is left outside. This practice, already found in Euler’s original scheme, leads to trouble when one wishes to express the non-existence of the outer region or to tackle logic problems involving negative terms. In this chapter, we discuss various techniques introduced by Euler’s followers to overcome this difficulty: some logicians modified the data of the problem at hand, others amended the diagrams, and another group changed the mode of representation. We also consider how modern diagrammatic systems represent negation.

Original languageEnglish
Title of host publicationLogic in Question
Subtitle of host publicationTalks from the Annual Sorbonne Logic Workshop (2011- 2019)
EditorsJean-Yves Béziau, Jean-Pierre Desclés, Amirouche Moktefi, Anca Christine Pascu
PublisherSpringer - Birkhäuser Cham
Number of pages16
ISBN (Electronic)9783030944520
ISBN (Print)9783030944513, 9783030944544
Publication statusPublished - 12 Jan 2023

Publication series

NameStudies in Universal Logic
ISSN (Print)2297-0282
ISSN (Electronic)2297-0290

Scopus Subject Areas

  • Philosophy
  • Logic

User-Defined Keywords

  • Euler diagram
  • Negation
  • Syllogism
  • Venn diagram


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