Abstract
This paper aims to tackle some of the basic (a-)symmetries of presupposition projection in a pragmatic, bivalent, and incrementally-oriented framework. The main data point that we are trying to capture is that projection from the first conjunct of a conjunction is asymmetric, while projection from the first disjunct of a disjunction can be symmetric. We argue that a solution where there are effectively two filtering mechanisms, one symmetric and one asymmetric, [11], is not tenable given recent experimental evidence, [4, 7]. Instead, we propose a bivalent system, where at each point during the incremental interpretation of a sentence S, the comprehender is trying to compute the sets of worlds in the context where the truth value of S has already been determined. This computation plays out differently in the case of conjunction vs the case of disjunction, and coupled with appropriate definitions of the incremental interpretation process and of what it means for a presupposition to project in the current system, it leads to asymmetric conjunction, but symmetric disjunction.
Thanks to Florian Schwarz for many helpful discussions and comments on this work. Thanks also to Phillipe Schlenker, Jacopo Romoli, Julie Legate, Anna Papafragou, Ryan Budnick, Andrea Beltrama, Spencer Caplan, and to the members of the Penn Semantics Lab for helpful comments and suggestions. Thanks also to the ESSLLI reviewers for useful feedback and suggestions. All errors are my own.
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Notes
- 1.
The reason that these disjunctions are known as ‘bathroom disjunctions’ is that they resemble certain Partee sentences involving symmetric anaphora resolution:
.
- 2.
- 3.
\((p \vee q) \leftrightarrow (p \vee ((\lnot p) \wedge q))\) is a tautology.
- 4.
Throughout the rest of this paper, the \(\texttt {verbatim}\) font is used to mark partial syntactic objects.
- 5.
Note that I sometimes use the term ‘parsing’ to mean roughly ‘getting access to bits of syntactic structure during incremental interpretation’, which deviates from the common usage of the term somewhat. Nonetheless, within the presuppositions literature, approaches like that of [11] that work by manipulating partial strings of expressions, are often referred to as ‘parsing-based’ (see e.g. [6]), and it is this usage I have in mind here.
- 6.
- 7.
There are similarities here with the Strong Kleene algorithm, [2], where projection (i.e., the third truth value) results when the other sentences of a larger sentence are not enough for determining the classical truth value, given the semantics of the connective. In fact, as discussed for instance in [8], the predictions of Strong Kleene and symmetric Local Contexts are very close to one another.
- 8.
This is just the ‘for any D’ part in the definitions of local contexts.
- 9.
This leads to no loss of generality. Every time a sentence contains the same \(p_{i}'p_{j}\) symbol in two different positions, just rewrite S with one of the \(p_{i}'p_{j}\) instance changed to \(p_{k}p_{j}\), where \(i \ne k\), with the stipulation that F assigns to both \(p_i\) and \(p_k\) the same set of worlds.
- 10.
A reviewer points out that this way of thinking about presuppositions (as representationally distinct from assertions) is not necessarily compatible with triggering algorithms (e.g., [1, 12]), which view presuppositions as entailments of the overall proposition that are selected by the triggering algorithm and marked as presuppositions. Nevertheless, I think one could view the process I’m describing here as what happens once an entailment has been triggered as a presupposition, essentially taking triggering for granted and focusing on a representation where what is to be presupposed has been already marked; in effect this follows [11] in separating conceptually the triggering problem from the projection problem.
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Kalomoiros, A. (2024). Limited Symmetry. In: Pavlova, A., Pedersen, M.Y., Bernardi, R. (eds) Selected Reflections in Language, Logic, and Information. ESSLLI 2019. Lecture Notes in Computer Science, vol 14354. Springer, Cham. https://doi.org/10.1007/978-3-031-50628-4_10
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