On the Contrary: Disjunctive Syllogism and Pragmatic Strengthening

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


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).


Contrariety Disjunctive syllogism Excluded middle Pragmatic strengthening Singular square 

Mathematics Subject Classification

03A99 03B65 03B99 



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.


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Authors and Affiliations

  1. 1.Departments of Linguistics and PhilosophyYale UniversityNew HavenUSA

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