Benjamin Spector (Institut Jean Nicod, ENS Paris)
Anaphora without dynamic semantics - A static trivalent semantics for pronouns and indefinites
Current theories of presupposition projection fall, by and large, into three categories: - dynamic theories (Heim 1983, and much subsequent work)- static trivalent approaches (Peters 1997, Beaver & Krahmer 2001, a.o)
- static bivalent approach supplemented with the Transparency Principle, according to which presupposed content must be redundant in the syntactic environment in which the presupposition trigger appears (Schlenker 2007, 2008), or Chemla's Similarity Principle (Chemla 2008).
It has been recognized long ago that the phenomenology of presupposition projection is closely related to that of the licensing of anaphora. That is, the conditions under which a non-referential pronoun can be anaphoric to a previously introduced indefinite (as in `Ada bought a pen and she used it to write a letter' ) are very similar to those under which the presupposition triggered by some expression can be `filtered out' by previously introduced content (as in `Ada bought a pen and John knows that she bought a pen').
This striking resemblance is well accounted for in dynamic theories of anaphora (Kamp 1981, Heim 1982, Groenedijk & Stokhof 1991 and much subsequent work) which are conceptually related to dynamic theories of presupposition, or even unified with them (van der Sandt & Geurts 1991, van der Sandt 1992) . But, with the exception of Rothschid 2017, nobody has yet proposed a non-dynamic theory of anaphora which would use the conceptual ingredients of non-dynamic theories of presupposition, based on either trivalent semantics or the Transparency Principle. Rothschild's own approach incorporates some non-trivial syntactic copying operation, a move which, everything else being equal, would be better to dispense with on parsimony grounds.
In my talk, I will propose a non-dynamic, static approach to anaphora which combines a trivalent approach with Schlenker's principle of Transparency. I will make use of a key idea recently introduced by Matt Mandelkern (in his manuscript `Witnesses'), according to which an existential statement such as 'Someone_x came' introduces a variable (notated x here), and, relative to a world w and and assignment function g, is undefined, rather than true or false, if it is classically true in w (i.e. if someone came in w) but g(x) does not denote an individual who came in w. Furthermore, I will assume that a sentence such as `She_x came' comes with the presupposition that the variable x is "valued* by the assignment function (which can be partial), a presupposition which is subject to the Transparency principle.
While related to Mandelkern's approach, my proposal, unlike his, is fully static at the level of compositional semantics.
Consideration of sentences with nested quantifier-variable dependencies will show this system to be inadequate. I will then (time permitting) present a version of this system in which I use plural assigments (cf. works Van den Berg, Nouwen, Brasoveanu, Kuhn among others) instead of simple assignments. This will solve this problem and will furthermore provide an added benefit: the system will now account for quantificational subordination/paycheck sentences.
For convenience, I will present the core ideas applied to the language of predicate logic (into which the relevant English sentences will be translated).