Abstract
The key to an adequate account of presupposition projection is to accommodate the fact that the presuppositions of a sentence cannot always be read off the sentence but can often be identified only on the basis of prior utterances in the conversation in which the sentence is uttered. In addition, an account of presupposition requires a three-valued semantics of assertibility and deniability in a context. Presuppositions can be explicated as sentences that belong to the conversation and the assertibility of which ensures that the remaining assertibility and deniability conditions of the presupposition-bearing sentence are dual to one another. The prevailing approach to presuppositions, grounded in Heim’s context-change semantics, can be criticized both on philosophical grounds and for failing to accommodate the phenomena.
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Notes
The fact that a presupposition cannot be read off the sentence containing the presupposition trigger and somehow depends on an “active context” was especially emphasized by Kripke in his 1990 lecture, which circulated unpublished for many years, until an enhanced version was published in 2009. Kartunnen’s 1974 account of “too” seems clearly designed to allow that the presuppositions must be in some sense given by the context and not wholly generated by the sentence containing “too”, but Kartunnen does not particularly emphasize the point.
Deniability conditions are dual to assertibility conditions and conversely when they can be obtained by subsituting “deniable” for “assertible” and conversely, disjunction for conjunction and conversely, and existential quantification for universal quantification and conversely.
Proof Suppose (7P) is not true of Γ. Then (7) is neither assertible nor deniable in Γ, not even if (7A′) is fulfilled and not even if (7D′) is fulfilled. Suppose (7P) is true of Γ. Then the fulfillment of (7A′) is necessary and sufficient for the assertibility of (7) in Γ, and the fulfillment of (7D′) is necessary and sufficient for the deniability of (7) in Γ.
Another leading paradigm is the theory of van der Sandt (1992), elaborated by Geurts (1999). Van der Sandt and Geurts, like me, advertise their theory as treating presuppositions as anaphoric. What they mean by this is that where the presupposed material resides in the discourse representation for a sentence is determined by where it is anaphorically bound. What I mean by comparing presuppositions to anaphors is entirely different. I have criticized the van der Sandt and Geurts theory in my 2008. For lack of space, I will not reiterate that critique here.
The first disjunct in clause (ii) provides for the case in which [DP f VP aff too] is not a member of the sequence σ.
Inasmuch as clause (iv) concerns a quantifier, we will need to supplement the account of assertibility and deniability conditions with an account of the assertibility and deniability conditions for quantified sentences. I will not take the space to do that here. For indications of how to do it, see Gauker (2003, 2005).
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Gauker, C. Presuppositions as Anaphoric Duality Enablers. Topoi 35, 133–144 (2016). https://doi.org/10.1007/s11245-014-9282-3
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DOI: https://doi.org/10.1007/s11245-014-9282-3