Lifting conditionals to inquisitive semantics

Abstract

This paper describes how any theory which assigns propositions to conditional sentences can be lifted to the setting of inquisitive semantics, where antecedents and consequents may be associated with multiple propositions. We show that the lifted account improves on the original account in two ways: first, it leads to a better analysis of disjunctive antecedents, which are treated as introducing multiple assumptions; second, it extends the original account to cover two further classes of conditional constructions, namely, unconditionals and conditional questions.

Fatalism and the Logic of Unconditionals

“…See Biezma & Rawlins () for a battery of arguments that alternative questions have exhaustivity and non‐overlapping presuppositions both in root environments and when embedded under intensional attitude verbs like wonder and adjoined in unconditionals. Ciardelli () also shows how the ability of the exhaustivity presupposition to project out of the whether ‐adjuncts of unconditionals can help explain our contrasting judgments in cases like the following: (54) a.Whether the card is red or black, it might be a jack. b.?…”

“…Getting clear about this requires a proper understanding of how inference works when it initiates from interrogative premises. Ciardelli's (,b, ) support‐based account of the logic of questions will be especially helpful.…”

“…To interpret the Fatalist's premises, we still need a semantics for the conditional operator ‘→ ’. My proposal is that a decision state supports a conditional of the form or iff every way of minimally updating s to ensure that the antecedent φ 0 or holds delivers a state that supports the consequent ψ as well (this semantics is inspired by related proposals in Yalcin ; Kolodny & MacFarlane ; Ciardelli ; and others). This set of updated states is defined as follows, where is a sentence of the form φ 0 or : (51) …”

“…Under the "dynamic turn" initiated by Kamp (1981) and Heim (1982) (building on earlier work by Karttunen 1969, Stalnaker 1974, 1978, and Lewis 1979, truth conditions gave way to dynamic updates on information states and various informational notions of consequence were defined in terms of these "context change potentials" (CCPs) rather than truth preservation (see also Groenendijk & Stokhof 1991;Veltman 1996;Groenendijk, Stokhof & Veltman 1996;Beaver 2001). More recently, Ciardelli, Groenendijk & Roelofsen (2013, 2018 have proposed a new "inquisitive turn" of their own, showing how to compositionally assign "support conditions" to both declarative and interrogative sentences relative to states of information in a single unified framework. With support conditions so assigned, a general informational consequence relation can be defined over sentences of both types.…”

“…In this paper, I'm interested less in fate‐determinism and practical reason per se and more in what the new Idle Argument has to teach us about the logic of unconditionals, and more generally about the nature of logic and deduction. In the end, I hope to show that the argument is grist for the mills of logicians and philosophers pushing support‐oriented approaches to these subjects, such as Veltman (); Ciardelli, Groenendijk & Roelofsen (, ); Bledin (, ); Ciardelli (,b, ).…”