Authors
Amirouche Moktefi
Tallinn University of Technology
Abstract
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.
Keywords Euler diagram  Venn diagram  Carroll diagram  Spider diagram  Existence  Particular proposition  Disjunctive proposition  Singular proposition  John Venn  Lewis Carroll  Charles S. Peirce  Logic notation
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DOI 10.1007/s10849-015-9228-1
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References found in this work BETA

Collected Papers.Charles S. Peirce - 1931 - Cambridge: Belknap Press of Harvard University Press.
Diagrams.Sun-Joo Shin - 2008 - Stanford Encyclopedia of Philosophy.
Logic: Part I.W. E. Johnson - 1921 - Mind 30 (120):448-455.

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