Logica Universalis

, Volume 10, Issue 2–3, pp 215–231

Singular Propositions, Negation and the Square of Opposition

Article

Abstract

This paper contains two traditions of diagrammatic studies namely one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions (through a diagram system Venn-i, involving constants), their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence (taking a cue from the notion of ‘abhãva’ existing in ancient Indian knowledge system). We have also considered the changes that take place in the context of open universe.

Keywords

Square of oppositions singular propositions open universe Abhãva (absence) 

Mathematics Subject Classification

Primary 03B99 Secondary 00A66 

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References

  1. 1.
    Barwise, J., Etchemendy, J.: Visual information and valid reasoning. In: Allwein, G., Barwise, J. (eds.) Logical Reasoning with Diagrams, pp. 3–25. Oxford University Press, Oxford (1990)Google Scholar
  2. 2.
    Bernhard P.: Visualization of the square of opposition. Logica Universalis 2, 31–41 (2008)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Béziau, J.Y., Payette, G. (eds.) The square of opposition. In: A General Framework for Cognition. Peter Lang, Bern (2012)Google Scholar
  4. 4.
    Choudhury L., Chakraborty M.K.: On representing Open Universe. Stud. Logic 5(1), 96–112 (2012)Google Scholar
  5. 5.
    Choudhury, L., Chakraborty, M.K.: On extending Venn diagram by augmenting names of individuals. In: Blackwell, A., et al. (eds.) Diagrams 2004, LNAI 2980, pp. 142–146 (2004)Google Scholar
  6. 6.
    Choudhury, L., Chakraborty, M.K.: Comparison between spider diagrams and venn diagrams with individuals. In: Proceedings of the Workshop Euler Diagrams 2005. INRIA, Paris (2005)Google Scholar
  7. 7.
    Choudhury, L., Chakraborty, M.K.: Singular propositions and their negations in diagrams published in the proceedings of DLAC 2013. In: CEUR Workshop Proceedings, vol. 1132 (2013). http://ceur-ws.org/
  8. 8.
    Euler, L.: Letters a une princesse d’allemagne, Sur divers sujets de physique et de philosophie. Letters No. 102–108, vol. 2. Basel Birkhauser (1761)Google Scholar
  9. 9.
    Hammer E.: Logic and Visual Information. CSLI Pubs., USA (1995)MATHGoogle Scholar
  10. 10.
    Hopcroft J.E., Ullman J.D.: Formal Languages and Their Relations to Automata. Addison-Wesley, London (1969)MATHGoogle Scholar
  11. 11.
    Horn L.R.: A Natural History of Negation. CSLI Pub, USA (2001)Google Scholar
  12. 12.
    Khomiskii, Y.: William of Sherwood, Singular Proposition and the Hexagon of Opposition. In: Béziau, J.Y., Payette, G. (eds.) The Square of Opposition. A general Framework for Cognition, pp. 43–57. Peter Lang, Bern (2012)Google Scholar
  13. 13.
    Larkin J.H., Simon H.A.: Why a diagram is (Sometimes) Worth Ten Thousand Words. Cognit. Sci. 11, 65–99 (1987)CrossRefGoogle Scholar
  14. 14.
    Krishna M.B.: Logic, Language and Reality. Motilal Banarasidass. Pub, New Delhi (1990)Google Scholar
  15. 15.
    Peirce, C.S.: Collected Papers of C.S.Peirce. iv, HUP (1933)Google Scholar
  16. 16.
    Russell B.: Philosophy of Logical Atomism: Logic and Knowledge. Unwin Hyman, London (1988)Google Scholar
  17. 17.
    Sharma, S.S.: Interpreting square of oppositions with the help of diagrams. In: Béziau, J.Y., Payette, G. (eds.) The Square of Opposition. A general Framework for Cognition, pp. 174–192. Peter Lang, Bern (2012)Google Scholar
  18. 18.
    Shin S.J.: The Logical Status of Diagrams. CUP, Cambridge (1994)MATHGoogle Scholar
  19. 19.
    Stapleton, G.,Taylor J., Thompson S., Howse, J.: The expressiveness of spider diagrams augmented with constants. J. Vis. Lang. Comput. 20(1), 30–49 (2009)Google Scholar
  20. 20.
    Stapleton G., Howse J., Taylor J.: A decidable constraint diagram reasoning system. J. Logic Comput. 15(6), 975–1008 (2005)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Stapleton, G.: Incorporating negation into visual logics: a case study using Euler diagrams. Vis. Lang. Comput., 187–194 (2007)Google Scholar
  22. 22.
    Swoboda N., Allwein, G.: Heterogeneous reasoning with Euler/Venn diagrams containing named constants and FOL. Electron. Not. Theor. Comput. Sci. 134, 153–187 (2005)Google Scholar
  23. 23.
    Tadeusz C.: On certain peculiarities of singular propositions. Mind 64, 392–395 (1955)Google Scholar
  24. 24.
    Venn J.: On the diagrammatic and mechanical representation of propositions and reasoning. Philos. Mag. J. Sci. Ser. 5 10(59), 1–18 (1880)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Philosophy, School of Cognitive ScienceJadavpur UniversityJadavpur, KolkataIndia
  2. 2.School of Cognitive ScienceJadavpur UniversityJadavpur, KolkataIndia

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