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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