Skip to main content
SpringerLink
Log in

Is ‘No’ a Force-Indicator? Yes, Sooner or Later!

  • Published:
Logica Universalis Aims and scope Submit manuscript

Abstract

This paper discusses the philosophical and logical motivations for rejectivism, primarily by considering a dialogical approach to logic, which is formalized in a Question–Answer Semantics. We develop a generalised account of rejectivism through close consideration of Mark Textor’s arguments against rejectivism that the negative expression ‘No’ is never used as an act of rejection and is equivalent with a negative sentence. In doing so, we also shed light upon well-known issues regarding the supposed non-embeddability and non-iterability of force indicators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Belnap, N.: A useful four-valued logic. In: Dunn, M. (ed.) Modern Uses of Multiple-Valued Logic, pp. 8–37. Reidel, Boston (1977)

    Google Scholar 

  2. Béziau, J.-Y.: A new four-valued approach to modal logic. Log. Anal. 54(213), 109–121 (2011)

    MathSciNet  MATH  Google Scholar 

  3. Chiffi, D., Schang, F.: The logical burdens of proof: assertion and hypothesis. Log. Log. Philos. (2017). doi:10.12775/LLP.2017.006

    Google Scholar 

  4. Dummett, M.A.E.: The Logical Basis of Metaphysics. Harvard University Press, Cambridge (1991)

    Google Scholar 

  5. Dummett, M.A.E.: Elements of Intuitionism. Oxford University Press, Oxford (2000)

    MATH  Google Scholar 

  6. Dunn, M., Restall, G.: Relevance logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic. Kluwer, Dordrecht (2002)

    Google Scholar 

  7. Edgington, D.: Conditionals, truth and assertion. In: Ravenscroft, I. (ed.) Minds, Ethics, and Conditionals: Themes From the Philosophy of Frank Jackson. OUP Oxford, Oxford (2009)

    Google Scholar 

  8. Font, J.M., Hájek, P.: On Lukasiewicz’s four-valued modal logic. Stud. Log. 70(2), 157–182 (2002)

    Article  MATH  Google Scholar 

  9. Frankowski, S.: Formalization of a plausible inference. Bull. Sect. Log. 33(1), 41–52 (2004)

    MathSciNet  MATH  Google Scholar 

  10. Geach, P., Black, M.: Translations From the Philosophical Writings of Gottlob Frege, vol. 4. Philosophical Library, New York (1952)

    Google Scholar 

  11. Ginsberg, M.: Multivalued logics: a uniform approach to reasoning in AI. Comput. Intell. 4, 256–316 (1988)

    Google Scholar 

  12. Humberstone, L.: The Connectives. MIT Press, Cambridge (2011)

    MATH  Google Scholar 

  13. Incurvati, L., Smith, P.: Is "no" a force-indicator? sometimes, possibly. Analysis 72(2), 225–231 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Keiff, L.: Dialogical logic. Stanford Encyclopedia of Philosophy, Stanford (2010)

    Google Scholar 

  15. Lambek, J., Scott, P.J.: Introduction to higher-order categorical logic, vol. 7. Cambridge University Press, Cambridge (1988)

    MATH  Google Scholar 

  16. Malinowski, G.: Q-consequence operation. Rep. Math. Log. 24(1), 49–59 (1990)

    Google Scholar 

  17. Murzi, J., Carrara, M.: Denial and disagreement. Topoi 1, 1–11 (2014)

    Google Scholar 

  18. Parsons, T.: Assertion, denial, and the liar paradox. J. Philos. Log. 13(2), 137–152 (1984)

    Article  MathSciNet  Google Scholar 

  19. Pavlov, S.: The logic with truth and falsehood operators from a point of view of universal logic. Log. Univ. 5(2), 319–325 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Prawitz, D.: Meaning approached via proofs. Synthese 148(3), 507–524 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Price, H.: “Not” again (Unpublished)

  22. Priest, G.: Doubt Truth to Be a Liar. Oxford University Press, Oxford (2006)

    MATH  Google Scholar 

  23. Ramsey, F.: General propositions and causality. In: Mellor, D.H. (ed.) Philosophical Papers, pp. 145–163. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  24. Restall, G.: Multiple conclusions. In: Hajek, V.-V.L.P., Westerstahl, D. (eds.) Logic, Methodology, and Philosophy of Science: Proceedings of the Twelfth International Congress, pp. 189–205. Kings College Publications (2005)

  25. Restall, G.: Assertion, denial and non-classical theories. In: Berto, F., Mares, E., Tanaka, K., Paoli, F. (eds.) Paraconsistency: Logic and Applications, pp. 81–99. Springer, Berlin (2013)

    Chapter  Google Scholar 

  26. Ripley, D.: Embedding denial. In: Caret, C., Hjortland, O. (eds.) Foundations of Logical Consequence, pp. 289–309. Oxford University Press (2015)

  27. Rumfitt, I.: Yes and no. Mind 109(436), 781–823 (2000)

    Article  MathSciNet  Google Scholar 

  28. Schang, F.: Beyond the fregean myth: the value of logical values. In: Stalmaszczyk, P. (ed.) Philosophy of Language and Linguistics, p. 245. Ontos Verlag, Paris (2010)

  29. Schang, F.: The football of logic. Studia Humana (2017) (forthcoming)

  30. Skura, T.: On pure refutation formulations of sentential logics. Bull. Sect. Log. 19(3), 102–107 (1990)

    MathSciNet  MATH  Google Scholar 

  31. Słupecki, J., Bryll, G., Wybraniec-Skardowska, U.: Theory of rejected propositions. I. Stud. Log. 29(1), 75–123 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  32. Słupecki, J., Bryll, G., Wybraniec-Skardowska, U.: The theory of rejected propositions. II. Stud. Log. 30(1), 97–145 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  33. Smiley, T.: Rejection. Analysis 56(1), 1–9 (1996)

    Article  MathSciNet  Google Scholar 

  34. Tappenden, J.: Negation, denial and language change in philosophical logic. In: Gabbay, D., Wansing, H. (eds.) What is Negation?, pp. 261–298. Springer, Berlin (1999)

    Chapter  Google Scholar 

  35. Textor, M.: Is "no" a force-indicator? no!. Analysis 71(3), 448–456 (2011)

    Article  Google Scholar 

  36. Trafford, J.: Structuring co-constructive logic for proofs and refutations. Logica Universalis, Berlin (2016)

    MATH  Google Scholar 

  37. van der Schaar, M.: The assertion-candidate and the meaning of mood. Synthese 159(1), 61–82 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  38. Wansing, H.: Falsification, natural deduction and bi-intuitionistic logic. J. Log. Comput. 26(1), 425–450 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  39. Willard van Orman, Q.: Methods of Logic. Harvard University Press, Cambridge (1982)

  40. Wright, G.H.V.: Truth-logics. Log. Anal. 30(120), 311–334 (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidade Estadual de Maringá, Avenida Colombo, 5.790, Câmpus Universitário, Maringá, CEP 87.020-900, Brazil

    Fabien Schang

  2. UCA Epsom, Ashley Road, Epsom, KT18 5BE, UK

    James Trafford

Authors
  1. Fabien Schang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James Trafford
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to James Trafford.

Additional information

The order of author’s names is arbitrary.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Schang, F., Trafford, J. Is ‘No’ a Force-Indicator? Yes, Sooner or Later!. Log. Univers. 11, 225–251 (2017). https://doi.org/10.1007/s11787-017-0170-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11787-017-0170-7

Mathematics Subject Classification

Keywords

Search

Navigation