Advertisement

On the Contrary: Disjunctive Syllogism and Pragmatic Strengthening

  • Laurence Horn
Part of the Studies in Universal Logic book series (SUL)

Abstract

Bosanquet’s dictum that “The essence of formal negation is to invest the contrary with the character of the contradictory” (Bosanquet in Logic, vol. 1. Clarendon, Oxford, 1888) describes the tendency for contradictory (apparent wide-scope) negation to be semantically or pragmatically strengthened to contrary readings whenever possible. Strengthening to a contrary instantiates the inference schema of disjunctive syllogism or modus tollendo ponens: from ϕφ and ¬ϕ, infer φ. The role of disjunctive syllogism is instantiated in a variety of strengthening shifts in natural language where a disjunctive excluded-middle premise is pragmatically presupposed in relevant contexts. In a range of apparently quite diverse phenomena—negative strengthening in lexical and clausal contexts (e.g. “neg-raising”), apparent scope adjustments with negated plural definites and bare plurals, epistemic strengthening of weak implicature in both main and embedded contexts, and children’s word learning strategies, among others—can be collected under the umbrella the general preference for strengthening to contrariety via disjunctive syllogism. This can be modelled using the Square of Opposition Aristotle describes in Chap. 46 of the Prior Analytics I, which I dub the Singular Square, to formalise his analysis of the interrelations among singular expressions (it’s good/it isn’t good/it’s not-good/it isn’t not-good).

Keywords

Contrariety Disjunctive syllogism Excluded middle Pragmatic strengthening Singular square 

Mathematics Subject Classification

03A99 03B65 03B99 

Notes

Acknowledgements

Some of this material was presented in other forms at previous occasions, including the first World Congress on the Square of Opposition in Montreux (June 2007), LNAT (Logic Now and Then) in Brussels (November 2008), and especially in the versions delivered at ESSLLI in Ljubljana (August 2011), SCLP in Santa Cruz (November 2011), CRISSP in Brussels (December 2011), and the Workshop on Logical Words at CIL 19 (Geneva 2013). I am grateful to Barbara Abbott, Donka Farkas, Bart Geurts, Susanne Grassmann, Elena Herburger, Dany Jaspers, Jacques Moeschler, Ben Russell, and Uli Sauerland for helpful discussions, with the usual disclaimers of responsibility.

References

  1. 1.
    Aberdein, A.: Logic for dogs. In: Hales, S. (ed.) What Philosophy Can Tell You About Your Dog, pp. 167–181. Open Court, Chicago (2008) Google Scholar
  2. 2.
    Ackrill, J.L. (ed. and trans.): Aristotle: Categories and De Interpretatione Clarendon, Oxford (1963) Google Scholar
  3. 3.
    Amis, K.: Jake’s Thing. Viking, New York (1979) Google Scholar
  4. 4.
    Aust, U., Range, F., Steurer, M., Huber, L.: Inferential reasoning by exclusion in pigeons, dogs, and humans. Anim. Cogn. 11, 587–597 (2008) CrossRefGoogle Scholar
  5. 5.
    Bartsch, R.: ‘Negative transportation’ gibt es nicht. Linguist. Ber. 27, 1–7 (1973) Google Scholar
  6. 6.
    Béziau, J.-Y., Payette, G. (eds.): The Square of Opposition: A General Framework for Cognition. Peter Lang, Bern (2012) Google Scholar
  7. 7.
    Blanché, R.: Structures Intellectuelles, 2nd edn. Vrin, Paris (1969) Google Scholar
  8. 8.
    Bloom, P.: How Children Learn the Meanings of Words. MIT Press, Cambridge (2000) Google Scholar
  9. 9.
    Bloom, P.: Can a dog learn a word? Science 304, 1605–1606 (2004) CrossRefGoogle Scholar
  10. 10.
    Bogen, J.: Aristotelian contraries. Topoi 10, 53–66 (1991) MathSciNetCrossRefGoogle Scholar
  11. 11.
    Bosanquet, B.: Logic, vol. 1. Clarendon, Oxford (1888) Google Scholar
  12. 12.
    Call, J.: Inferences by exclusion in the great apes: the effect of age and species. Anim. Cogn. 9, 393–403 (2006) CrossRefGoogle Scholar
  13. 13.
    Chierchia, G.: Scalar implicatures, polarity phenomena and the syntax/pragmatics interface. In: Belletti, A. (ed.) Structures and Beyond, pp. 39–103. Oxford U. Press, Oxford (2004) Google Scholar
  14. 14.
    Chierchia, G.: Broaden your views: implicatures of domain widening and the “locality” of language. Linguist. Inq. 37, 535–590 (2006) MathSciNetCrossRefGoogle Scholar
  15. 15.
    Clark, E.V.: The principle of contrast: a constraint on language acquisition. In: MacWhinney, B. (ed.) Mechanisms of Language Acquisition, pp. 1–33. Erlbaum, Hillsdale (1987) Google Scholar
  16. 16.
    Collins, C., Postal, P.: Classical NEG-Raising: An Essay in the Syntax of Negation. MIT Press, Cambridge (2014) Google Scholar
  17. 17.
    Deutscher, M.: A note on saying and believing. Analysis 105, 53–57 (1965) CrossRefGoogle Scholar
  18. 18.
    Erdöhegyi, Á., Topál, J., Virányi, Zs., Miklósi, Á.: Dog-logic: inferential reasoning in a two-way choice task and its restricted use. Anim. Behav. 74, 725–737 (2008) CrossRefGoogle Scholar
  19. 19.
    Fillmore, C.: The position of embedding transformations in a grammar. Word 19, 208–231 (1963) Google Scholar
  20. 20.
    Fodor, J.D.: The linguistic description of opaque contexts. PhD dissertation, MIT (1970) Google Scholar
  21. 21.
    Gajewski, J.: Neg-raising and polarity. Linguist. Philos. 30, 289–328 (2007) CrossRefGoogle Scholar
  22. 22.
    Geach, P.T.: Logic Matters. University of California Press, Berkeley (1972) Google Scholar
  23. 23.
    Geurts, B.: Scalar implicature and local pragmatics. Mind Lang. 24, 51–79 (2009) CrossRefGoogle Scholar
  24. 24.
    Geurts, B.: Quantity Implicatures. Cambridge U. Press, Cambridge (2010) CrossRefGoogle Scholar
  25. 25.
    Grassmann, S., Stracke, M., Tomasello, M.: Two-year-olds exclude novel objects as potential referents of novel words based on pragmatics. Cognition 112, 488–493 (2009) CrossRefGoogle Scholar
  26. 26.
    Grice, H.P.: Studies in the Way of Words. Harvard U. Press, Cambridge (1989) Google Scholar
  27. 27.
    Hamilton, W.: Lectures on Logic, vol. I. Blackwood, Edinburgh (1860) Google Scholar
  28. 28.
    Henry, D.P.: The Logic of St. Anselm. Clarendon, Oxford (1967) Google Scholar
  29. 29.
    Hintikka, J.: Knowledge and Belief. Cornell U. Press, Ithaca (1962) Google Scholar
  30. 30.
    Hirschberg, J.: A Theory of Scalar Implicature. Garland, New York (1991) Google Scholar
  31. 31.
    Hopkins, J.: A Companion to the Study of St. Anselm. U. of Minnesota Press, Minneapolis (1972) Google Scholar
  32. 32.
    Horn, L.R.: The semantic properties of logical operators in English. PhD dissertation, UCLA (1972) Google Scholar
  33. 33.
    Horn, L.R.: Remarks on neg-raising. In: Cole, P. (ed.) Syntax and Semantics 9: Pragmatics, pp. 129–220. Academic Press, New York (1978) Google Scholar
  34. 34.
    Horn, L.R.: Toward a new taxonomy for pragmatic inference: Q-based and R-based implicature. In: Schiffrin, D. (ed.) Meaning, Form, and Use in Context (GURT ‘84), pp. 11–42. Georgetown University Press, Washington (1984) Google Scholar
  35. 35.
    Horn, L.R.: A Natural History of Negation. U. of Chicago Press, Chicago (1989). Reissue edition, Stanford: CSLI, 2001 Google Scholar
  36. 36.
    Horn, L.R.: Hamburgers and truth: why Gricean inference is Gricean. In: Parasession on the Legacy of Grice. Proceedings of the Annual Meeting of the Berkeley Linguistics Society, vol. 16, pp. 454–471 (1990) Google Scholar
  37. 37.
    Horn, L.R.: Duplex negatio affirmat…: the economy of double negation. In: Papers from the Parasession on Negation, vol. 27, pp. 78–106. CLS, Chicago (1991) Google Scholar
  38. 38.
    Horn, L.R.: All John’s children are as bald as the King of France: existential import and the geometry of opposition. In: Proceedings of the Thirty-Third Regional Meetings of the Chicago Linguistic Society, vol. 33, pp. 155–179 (1997) Google Scholar
  39. 39.
    Horn, L.R.: Contradiction. Revised entry. In: Zalta, E. (ed.) Stanford Encyclopedia of Philosophy (2010). http://plato.stanford.edu/entries/contradiction/ Google Scholar
  40. 40.
    Horn, L.R.: Histoire d’*O: lexical pragmatics and the geometry of opposition. In: Béziau, J.-Y., Payette, G. (eds.) The Square of Opposition: A General Framework for Cognition, pp. 393–426 Peter Lang, Bern (2012) Google Scholar
  41. 41.
    Horn, L.R.: The singular square: contrariety and double negation from Aristotle to Homer. In: Blochowiak, J., et al. (eds.) (2014). http://www.unige.ch/lettres/linguistique/moeschler/Festschrift/Festschrift.php
  42. 42.
    Horn, L.R., Bayer, S.: Short-circuited implicature: a negative contribution. Linguist. Philos. 7, 397–414 (2004) CrossRefGoogle Scholar
  43. 43.
    Humberstone, L.: Extensionality in sentence position. J. Philos. Log. 15, 27–54 (1986) MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Jackendoff, R.: On some questionable arguments about quantifiers and negation. Language 47, 282–297 (1971) CrossRefGoogle Scholar
  45. 45.
    Jacoby, P.: A triangle of opposites in Aristotelian logic. New Scholast. XXIV, 32–56 (1950) CrossRefGoogle Scholar
  46. 46.
    Jaspers, D.: Operators in the lexicon: on the negative logic of natural language. Universiteit Leiden dissertation. Utrecht: LOT (2005) Google Scholar
  47. 47.
    Jespersen, O.: Negation in English and Other Languages. A. F Høst, Copenhagen (1917) Google Scholar
  48. 48.
    Kaminski, J., Call, J., Fischer, J.: Word learning in a domestic dog: evidence for ‘fast mapping’. Science 304, 1682–1683 (2004) CrossRefGoogle Scholar
  49. 49.
    Katzir, R.: Structurally defined alternatives. Linguist. Philos. 30, 669–690 (2007) CrossRefGoogle Scholar
  50. 50.
    Katzir, R., Singh, R.: Constraints on the lexicalization of logical operators. Linguist. Philos. 36, 1–29 (2013) CrossRefGoogle Scholar
  51. 51.
    Klooster, W.: Negative raising revisited. In: Koster, J., van Riemsdijk, H. (eds.) Germania et Alia: A Linguistic Festschrift for Hans den Besten (2003). Available at http://odur.let.rug.nl/~koster/DenBesten/contents.htm Google Scholar
  52. 52.
    Krifka, M.: Pragmatic strengthening in plural predications and donkey sentences. In: Proceedings of SALT, vol. 6 (1996) Google Scholar
  53. 53.
    Leslie, S.-J.: Generics: cognition and acquisition. Philos. Rev. 117, 1–47 (2008) CrossRefGoogle Scholar
  54. 54.
    Levinson, S.C.: Presumptive Meanings. MIT Press, Cambridge (2000) Google Scholar
  55. 55.
    Löbner, S.: Definites. J. Semant. 4, 279–325 (1985) CrossRefGoogle Scholar
  56. 56.
    Löbner, S.: Quantification as a major module of natural language semantics. In: Groenendijk, J., et al. (eds.) Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers, pp. 53–85. Foris, Dordrecht (1987) Google Scholar
  57. 57.
    Löbner, S.: Polarity and natural language: predication, quantification, and negation in particularizing and characterising sentences. Linguist. Philos. 23, 213–308 (2000) CrossRefGoogle Scholar
  58. 58.
    Markman, E., Abelev, M.: Word learning in dogs? Trends Cogn. Sci. 8, 489–491 (2004) CrossRefGoogle Scholar
  59. 59.
    Markman, E., Wachtel, G.: Children’s use of mutual exclusivity to constrain the meanings of words. Cogn. Psychol. 20, 121–157 (1988) CrossRefGoogle Scholar
  60. 60.
    Mates, B.: Stoic Logic. University of California Press, Berkeley (1953) Google Scholar
  61. 61.
    Mates, B. (ed. and trans.): The Skeptic Way: Sextus Empiricus’s Outlines of Pyrrhonism. Oxford U. Press, New York (1996) Google Scholar
  62. 62.
    McCall, S.: Contrariety. Notre Dame J. Form. Log. 8, 121–138 (1967) CrossRefzbMATHGoogle Scholar
  63. 63.
    Mill, J.S.: An Examination of Sir William Hamilton’s Philosophy, 2nd edn. Longman, Green, London (1865) Google Scholar
  64. 64.
    Oesterle, J. (ed. and trans.): Aristotle: On Interpretation. Commentary by St. Thomas and Cajetan. Marquette University Press, Milwaukee (1962) Google Scholar
  65. 65.
    Pilley, J., Reid, A.: Border collie comprehends object names as verbal referents. Behav. Process. 86, 184–195 (2011) CrossRefGoogle Scholar
  66. 66.
    Poutsma, H.: A Grammar of Late Modern English. Noordhoff, Groningen (1928) Google Scholar
  67. 67.
    Prince, E.F.: The syntax and semantics of neg-raising, with evidence from French. Language 52, 404–426 (1976) CrossRefGoogle Scholar
  68. 68.
    Quine, W.V.O.: Word and Object. MIT Press, Cambridge (1960) zbMATHGoogle Scholar
  69. 69.
    Richter, F.K.: Hitler and words. Etc. 1, 256–258 (1944) Google Scholar
  70. 70.
    Russell, B.: Against grammatical computation of scalar implicatures. J. Semant. 23, 361–382 (2006) CrossRefGoogle Scholar
  71. 71.
    Russell, B.: Topics in the computation of scalar implicatures. PhD dissertation, Brown University (2011) Google Scholar
  72. 72.
    Sapir, E.: Grading: a study in semantics (1944). Reprinted in P. Swiggers et al. (eds.), The Collected Works of Edward Sapir, I, 447–470. Berlin: de Gruyter, 2008 Google Scholar
  73. 73.
    Sauerland, U.: Scalar implicatures in complex sentences. Linguist. Philos. 27, 367–391 (2004) CrossRefGoogle Scholar
  74. 74.
    Sesmat, A.: Logique II. Hermann, Paris (1951) Google Scholar
  75. 75.
    Sharvit, Y., Gajewski, J.: On the calculation of local implicatures. WCCFL 26, 411–419 (2008) Google Scholar
  76. 76.
    Sigwart, Ch.: Logic, vol. I. (1885). H. Dendy, trans. New York: Macmillan, 1895 Google Scholar
  77. 77.
    Stalnaker, R.: A defense of conditional excluded middle. In: Harper, W.L., et al. (eds.) Ifs, pp. 87–104. Reidel, Dordrecht (1981) Google Scholar
  78. 78.
    Stalnaker, R.: Context and Content. Oxford University Press, Oxford (1999) CrossRefGoogle Scholar
  79. 79.
    Thomas Aquinas: The Summa Theologica, vol. I. Benzinger Brothers, New York (1947). Literally translated by Fathers of the English Dominican Province Google Scholar
  80. 80.
    van der Auwera, J.: Why languages prefer prohibitives. Wai Guo Yu, 1–25 (2006) Google Scholar
  81. 81.
    van der Auwera, J.: Prohibition: constructions and markers. In: Shu, D., et al. (eds.) Contrasting Meaning in Languages of the East and the West, pp. 443–475. Peter Lang, Bern (2010) Google Scholar
  82. 82.
    van Rooij, R., Schulz, K.: Exhaustive interpretation of complex sentences. J. Log. Lang. Inf. 13, 491–513 (2006) CrossRefGoogle Scholar
  83. 83.
    Vincent-Smith, L., Bricker, D., Bricker, W.: Acquisition of receptive vocabulary in the toddler-age child. Child Dev. 45, 189–193 (1974) CrossRefGoogle Scholar
  84. 84.
    Vizitelly, F.: A Desk-Book of Errors in English. Funk & Wagnalls, New York (1910) Google Scholar
  85. 85.
    von Fintel, K.: Bare plurals, bare conditionals, and only. J. Semant. 14, 1–56 (2007) CrossRefGoogle Scholar
  86. 86.
    Williams, C.J.F.: Saint Anselm and his biographers. Downside Rev. 82, 124–140 (1964) Google Scholar
  87. 87.
    Williams, J.R.G.: Defending conditional excluded middle. Noûs 44, 650–668 (2010) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Departments of Linguistics and PhilosophyYale UniversityNew HavenUSA

Personalised recommendations