Polarity Reversal and Scalarity in Counterfactuals
Cleo Condoravdi, Stanford University
Positive polarity items (PPIs) can exceptionally appear with
clause-mate negation in the antecedent of counterfactual
conditionals. This is an instance of a phenomenon termed 'polarity
reversal' by Baker (1970) and is exemplified with the PPIs
"already" and "pretty" in (1) and (2).
(1) If she had not arrived already, we would have postponed the
(2) If she weren't pretty smart, she wouldn't have dealt with the
situation so well.
Baker's generalization, reflected in his licensing principle, was that
PPIs can be in the scope of negation in the antecedent of a
conditional if and only if the conditional presupposes the prejacent
of the negation, e.g., in (1) that she had already arrived. Taking
this generalization for granted, more recent work has attributed the
phenomenon to a special kind of negation, either 'light negation',
presupposing its prejacent (Schwarz & Bhatt 2006, Ippolito & Su 2014),
or high negation, denoting FALSUM and conveying a speaker bias toward
the truth of its prejacent (Romero 2015).
In this talk, I argue that the phenomenon is the result of the lexical
semantics of PPIs and the interpretation of counterfactuals, with
negation being regular truth-functional negation. Taking PPIs to be
associated with alternatives and to give rise to scalar assertions, I
show that polarity reversal results in scalar assertions, because in
making a counterfactual assumption any contextual entailments are
given up once the information that gives rise to them is revised.
This alternative analysis derives the connection between polarity
reversal and counterfactuality on the basis of how asserting the
conditional in a context which is compatible with its antecedent
influences the relation between the ordinary content of the
conditional and the content of the alternatives. The analysis also
yields better empirical predictions: a conditional with polarity
reversal in the antecedent is acceptable when the negated clause is
compatible with the context, or even presupposed, as long as the
entire antecedent is counterfactual.