Skip to main content
SpringerLink
Log in

On the Contrary: Disjunctive Syllogism and Pragmatic Strengthening

  • Chapter
The Road to Universal Logic

Part of the book series: Studies in Universal Logic ((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 ϕ∨φ 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).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    What of existential import? Which of the four statement forms entail or presuppose that the set over which the quantifier ranges is non-null and how does this affect the subaltern and other relations? In particular, if all is import-free while some is not, doesn’t this vitiate the Square? The fact that other operators (binary connectives, adverbs, modals, deontics) for which existential import is irrelevant can be mapped onto the Square makes such a step as unappealing as it is unnecessary. This leaves a number of options for dealing with questions of import and quantification and their relation to the Square; see Horn [38] for discussion.

  2. 2.

    Another natural extension of MaxContrary is to Conditional Excluded Middle (cf. [77, 85, 87] for discussion and references), based on the plausibility of the assumed disjunction: [if A then C] ∨ [if A then ¬C]). Given this disjunction, the denial of A>C amounts to the assertion of A>¬C.

  3. 3.

    If a child knows the label for a given object, an unfamiliar label must pick out an unfamiliar object or a subpart (trachea) or property (pewter) of a familiar one. Bloom [8, pp. 65–87] provides an excellent survey of late 20th century research on word learning, mutual exclusivity, and the role of Gricean pragmatics and “theory of mind.”

  4. 4.

    Rico’s “fast mapping” can be seen in action at http://www.youtube.com/watch?v=kW27XF21ORs#t=12, while Chaser performs with co-authors Pilley and Reid at http://www.youtube.com/watch?v=Hi8HFdPMsiM.

References

  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. Ackrill, J.L. (ed. and trans.): Aristotle: Categories and De Interpretatione Clarendon, Oxford (1963)

    Google Scholar 

  3. Amis, K.: Jake’s Thing. Viking, New York (1979)

    Google Scholar 

  4. Aust, U., Range, F., Steurer, M., Huber, L.: Inferential reasoning by exclusion in pigeons, dogs, and humans. Anim. Cogn. 11, 587–597 (2008)

    Article  Google Scholar 

  5. Bartsch, R.: ‘Negative transportation’ gibt es nicht. Linguist. Ber. 27, 1–7 (1973)

    Google Scholar 

  6. Béziau, J.-Y., Payette, G. (eds.): The Square of Opposition: A General Framework for Cognition. Peter Lang, Bern (2012)

    Google Scholar 

  7. Blanché, R.: Structures Intellectuelles, 2nd edn. Vrin, Paris (1969)

    Google Scholar 

  8. Bloom, P.: How Children Learn the Meanings of Words. MIT Press, Cambridge (2000)

    Google Scholar 

  9. Bloom, P.: Can a dog learn a word? Science 304, 1605–1606 (2004)

    Article  Google Scholar 

  10. Bogen, J.: Aristotelian contraries. Topoi 10, 53–66 (1991)

    Article  MathSciNet  Google Scholar 

  11. Bosanquet, B.: Logic, vol. 1. Clarendon, Oxford (1888)

    Google Scholar 

  12. Call, J.: Inferences by exclusion in the great apes: the effect of age and species. Anim. Cogn. 9, 393–403 (2006)

    Article  Google Scholar 

  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. Chierchia, G.: Broaden your views: implicatures of domain widening and the “locality” of language. Linguist. Inq. 37, 535–590 (2006)

    Article  MathSciNet  Google Scholar 

  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. Collins, C., Postal, P.: Classical NEG-Raising: An Essay in the Syntax of Negation. MIT Press, Cambridge (2014)

    Google Scholar 

  17. Deutscher, M.: A note on saying and believing. Analysis 105, 53–57 (1965)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  19. Fillmore, C.: The position of embedding transformations in a grammar. Word 19, 208–231 (1963)

    Google Scholar 

  20. Fodor, J.D.: The linguistic description of opaque contexts. PhD dissertation, MIT (1970)

    Google Scholar 

  21. Gajewski, J.: Neg-raising and polarity. Linguist. Philos. 30, 289–328 (2007)

    Article  Google Scholar 

  22. Geach, P.T.: Logic Matters. University of California Press, Berkeley (1972)

    Google Scholar 

  23. Geurts, B.: Scalar implicature and local pragmatics. Mind Lang. 24, 51–79 (2009)

    Article  Google Scholar 

  24. Geurts, B.: Quantity Implicatures. Cambridge U. Press, Cambridge (2010)

    Book  Google Scholar 

  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)

    Article  Google Scholar 

  26. Grice, H.P.: Studies in the Way of Words. Harvard U. Press, Cambridge (1989)

    Google Scholar 

  27. Hamilton, W.: Lectures on Logic, vol. I. Blackwood, Edinburgh (1860)

    Google Scholar 

  28. Henry, D.P.: The Logic of St. Anselm. Clarendon, Oxford (1967)

    Google Scholar 

  29. Hintikka, J.: Knowledge and Belief. Cornell U. Press, Ithaca (1962)

    Google Scholar 

  30. Hirschberg, J.: A Theory of Scalar Implicature. Garland, New York (1991)

    Google Scholar 

  31. Hopkins, J.: A Companion to the Study of St. Anselm. U. of Minnesota Press, Minneapolis (1972)

    Google Scholar 

  32. Horn, L.R.: The semantic properties of logical operators in English. PhD dissertation, UCLA (1972)

    Google Scholar 

  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. 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. Horn, L.R.: A Natural History of Negation. U. of Chicago Press, Chicago (1989). Reissue edition, Stanford: CSLI, 2001

    Google Scholar 

  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. 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. 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. Horn, L.R.: Contradiction. Revised entry. In: Zalta, E. (ed.) Stanford Encyclopedia of Philosophy (2010). http://plato.stanford.edu/entries/contradiction/

    Google Scholar 

  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. 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. Horn, L.R., Bayer, S.: Short-circuited implicature: a negative contribution. Linguist. Philos. 7, 397–414 (2004)

    Article  Google Scholar 

  43. Humberstone, L.: Extensionality in sentence position. J. Philos. Log. 15, 27–54 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  44. Jackendoff, R.: On some questionable arguments about quantifiers and negation. Language 47, 282–297 (1971)

    Article  Google Scholar 

  45. Jacoby, P.: A triangle of opposites in Aristotelian logic. New Scholast. XXIV, 32–56 (1950)

    Article  Google Scholar 

  46. Jaspers, D.: Operators in the lexicon: on the negative logic of natural language. Universiteit Leiden dissertation. Utrecht: LOT (2005)

    Google Scholar 

  47. Jespersen, O.: Negation in English and Other Languages. A. F Høst, Copenhagen (1917)

    Google Scholar 

  48. Kaminski, J., Call, J., Fischer, J.: Word learning in a domestic dog: evidence for ‘fast mapping’. Science 304, 1682–1683 (2004)

    Article  Google Scholar 

  49. Katzir, R.: Structurally defined alternatives. Linguist. Philos. 30, 669–690 (2007)

    Article  Google Scholar 

  50. Katzir, R., Singh, R.: Constraints on the lexicalization of logical operators. Linguist. Philos. 36, 1–29 (2013)

    Article  Google Scholar 

  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. Krifka, M.: Pragmatic strengthening in plural predications and donkey sentences. In: Proceedings of SALT, vol. 6 (1996)

    Google Scholar 

  53. Leslie, S.-J.: Generics: cognition and acquisition. Philos. Rev. 117, 1–47 (2008)

    Article  Google Scholar 

  54. Levinson, S.C.: Presumptive Meanings. MIT Press, Cambridge (2000)

    Google Scholar 

  55. Löbner, S.: Definites. J. Semant. 4, 279–325 (1985)

    Article  Google Scholar 

  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. Löbner, S.: Polarity and natural language: predication, quantification, and negation in particularizing and characterising sentences. Linguist. Philos. 23, 213–308 (2000)

    Article  Google Scholar 

  58. Markman, E., Abelev, M.: Word learning in dogs? Trends Cogn. Sci. 8, 489–491 (2004)

    Article  Google Scholar 

  59. Markman, E., Wachtel, G.: Children’s use of mutual exclusivity to constrain the meanings of words. Cogn. Psychol. 20, 121–157 (1988)

    Article  Google Scholar 

  60. Mates, B.: Stoic Logic. University of California Press, Berkeley (1953)

    Google Scholar 

  61. Mates, B. (ed. and trans.): The Skeptic Way: Sextus Empiricus’s Outlines of Pyrrhonism. Oxford U. Press, New York (1996)

    Google Scholar 

  62. McCall, S.: Contrariety. Notre Dame J. Form. Log. 8, 121–138 (1967)

    Article  MATH  Google Scholar 

  63. Mill, J.S.: An Examination of Sir William Hamilton’s Philosophy, 2nd edn. Longman, Green, London (1865)

    Google Scholar 

  64. Oesterle, J. (ed. and trans.): Aristotle: On Interpretation. Commentary by St. Thomas and Cajetan. Marquette University Press, Milwaukee (1962)

    Google Scholar 

  65. Pilley, J., Reid, A.: Border collie comprehends object names as verbal referents. Behav. Process. 86, 184–195 (2011)

    Article  Google Scholar 

  66. Poutsma, H.: A Grammar of Late Modern English. Noordhoff, Groningen (1928)

    Google Scholar 

  67. Prince, E.F.: The syntax and semantics of neg-raising, with evidence from French. Language 52, 404–426 (1976)

    Article  Google Scholar 

  68. Quine, W.V.O.: Word and Object. MIT Press, Cambridge (1960)

    MATH  Google Scholar 

  69. Richter, F.K.: Hitler and words. Etc. 1, 256–258 (1944)

    Google Scholar 

  70. Russell, B.: Against grammatical computation of scalar implicatures. J. Semant. 23, 361–382 (2006)

    Article  Google Scholar 

  71. Russell, B.: Topics in the computation of scalar implicatures. PhD dissertation, Brown University (2011)

    Google Scholar 

  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. Sauerland, U.: Scalar implicatures in complex sentences. Linguist. Philos. 27, 367–391 (2004)

    Article  Google Scholar 

  74. Sesmat, A.: Logique II. Hermann, Paris (1951)

    Google Scholar 

  75. Sharvit, Y., Gajewski, J.: On the calculation of local implicatures. WCCFL 26, 411–419 (2008)

    Google Scholar 

  76. Sigwart, Ch.: Logic, vol. I. (1885). H. Dendy, trans. New York: Macmillan, 1895

    Google Scholar 

  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. Stalnaker, R.: Context and Content. Oxford University Press, Oxford (1999)

    Book  Google Scholar 

  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. van der Auwera, J.: Why languages prefer prohibitives. Wai Guo Yu, 1–25 (2006)

    Google Scholar 

  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. van Rooij, R., Schulz, K.: Exhaustive interpretation of complex sentences. J. Log. Lang. Inf. 13, 491–513 (2006)

    Article  Google Scholar 

  83. Vincent-Smith, L., Bricker, D., Bricker, W.: Acquisition of receptive vocabulary in the toddler-age child. Child Dev. 45, 189–193 (1974)

    Article  Google Scholar 

  84. Vizitelly, F.: A Desk-Book of Errors in English. Funk & Wagnalls, New York (1910)

    Google Scholar 

  85. von Fintel, K.: Bare plurals, bare conditionals, and only. J. Semant. 14, 1–56 (2007)

    Article  Google Scholar 

  86. Williams, C.J.F.: Saint Anselm and his biographers. Downside Rev. 82, 124–140 (1964)

    Google Scholar 

  87. Williams, J.R.G.: Defending conditional excluded middle. Noûs 44, 650–668 (2010)

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Departments of Linguistics and Philosophy, Yale University, New Haven, USA

    Laurence Horn

Authors
  1. Laurence Horn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laurence Horn .

Editor information

Editors and Affiliations

  1. City University of New York, New York, New York, USA

    Arnold Koslow

  2. Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Arthur Buchsbaum

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Horn, L. (2015). On the Contrary: Disjunctive Syllogism and Pragmatic Strengthening. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10193-4_10

Download citation

Publish with us

Policies and ethics

Search

Navigation