Dynamic semantics versus dynamic propositionalism

ABSTRACT

Una Stojnić's Context and Coherence: The Logic and Grammar of Prominence offers a series of interesting criticisms of the classical dynamic paradigm in natural language semantics and offers a sophisticated alternative outlook, one that does recognize a dynamic, context change inducing dimension of meaning but at the same preserves the idea that (declarative) utterances express propositions in context. The purpose of this note is to set the record straight: existing dynamic analyses of modals and conditionals compare favorably with Stojnić's dynamic propositionalism.

KEYWORDS:

• Dynamic semantics
• dynamic propositionalism
• conditionals
• modals

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The analyses to be discussed here stand in the Update Semantics tradition (starting with Veltman 1985, 1996); other prominent dynamic semantic analyses include Discourse Representation Theory (Kamp 1982; Kamp and Reyle 1993), Dynamic Predicate Logic (Groenendijk and Stokhof 1991), and File Change Semantics (Heim 1982).

2 An alternative proposal, frequently mentioned in the literature just to be dismissed, is that modus tollens does not even license the problematic inference in question here since the modal must takes wide scope in (2). Problems abound for wide-scoping strategies, one of them being that they have a tendency to generate false readings. For instance, in ‘If it was done before midnight, then the butler might have an alibi but the gardener does not’ the modal might does not take wide scope over the whole conditional: we are not just saying that the conditional ‘If it was done before midnight, then the butler has an alibi but the gardener does not’ is possibly true, but rather that the gardener for sure doesn’t have an alibi if it was done before midnight (and that the butler might have one if it was). See, for instance, Yalcin 2012 for discussion.

3 Stojnić says that modus tollens failures are a source of motivation for “non-propositionalist” analyses of modals and conditionals (ch. 10). It is worth noting that one does not have to stray far away from the semantic mainstream to see modus tollens get the boot. Lewis’s (1973, ch. 5) truth-conditional analysis of deontic conditionals, to wit, rejects modus tollens by dropping the centering constraint. Kratzer’s analysis of conditionals (see Kratzer 2012 and references therein) also rejects modus tollens, insofar as it makes sense to talk about such inference rules in her framework in the first place. But as stressed by e.g. Willer (2012) moving beyond the mainstream into dynamic territory does have something special to offer, insofar as it allows us to reject modus tollens while also preserving desirable inference rules such as modus ponens.

4 Veltman’s (1996) discussion is the classical source of inspiration, though its analysis of conjunction and conditionals differs at important moments of detail that need not detain us here. The critical ideas can be articulated in a variety of ways, including a Yalcin-style domain semantics (see Yalcin 2007, 2012).

5 We do not need to worry about the intricacies of disjunctions here; for current purposes they can be defined in the usual way as negated conjunctions.

6 Hence might and must are duals so that $s+\text{□}\phi =s+\mathrm{\neg }\diamond \mathrm{\neg }\phi$.

7 Veltman (1996) discusses various alternatives (see also van Benthem 1986); an “update-to-test” conception of validity is especially popular in the literature: ${\phi }_1,\dots ,{\phi }_n\models \psi$ just in case for all $s,s+{\phi }_1+\dots +{\phi }_n$⊩ψ. Update-to-test requires that every state accepts the conclusion once updated with the premises. Such a view of validity would serve our purposes just as well but introduces a few additional complexities that need not detain us here.

8 An implicit assumption here is that will is a modal rather than a temporal operator. Klecha (2014) offers an influential defense of this assumption.

9 Zvolenszky’s (2002) discussion is specifically concerned with a Kratzer-style analysis of if-clauses as restrictors; part of the point here is that the key concern is of a general nature.

10 Klecha (2011) draws attention to the empirical fact that cross-sentential modal subordination is optional for some modal expressions (including going to, might, and bound to) and obligatory for others (such as will, would, and could). Building on Frank (1997), Klecha accounts for this fact in a dynamic framework that distinguishes between definite modals (which come with a familiarity presupposition and obligatorily undergo modal subordination) and indefinite modals (which lack a familiarity presupposition and optionally undergo modal subordination).

11 I focus here on deontic ought but submit that the strategy to be outlined generalizes to other modal expressions.

12 To see this, recall that mights test whether the prejacent is compatible with the input state. But once we have updated with ‘It is not raining’ (the first conjunct), we can no longer consistently update with ‘It is raining’ and so an update with ‘It might be raining’ (the second conjunct) is guaranteed to result in the absurd state.

13 To see this, if s affords both worlds at which it is raining and worlds at which it is not, it of course passes the test imposed by the second conjunct. So, now an update with (14a) just amounts to adding the proposition that it is raining, which is perfectly consistent.