Abstract
This paper develops a semantic solution to the puzzle of Free Choice permission. The paper begins with a battery of impossibility results showing that Free Choice is in tension with a variety of classical principles, including Disjunction Introduction and the Law of Excluded Middle. Most interestingly, Free Choice appears incompatible with a principle concerning the behavior of Free Choice under negation, Double Prohibition, which says that Mary can’t have soup or salad implies Mary can’t have soup and Mary can’t have salad. Alonso-Ovalle 2006 and others have appealed to Double Prohibition to motivate pragmatic accounts of Free Choice. Aher 2012, Aloni 2018, and others have developed semantic accounts of Free Choice that also explain Double Prohibition. This paper offers a new semantic analysis of Free Choice designed to handle the full range of impossibility results involved in Free Choice. The paper develops the hypothesis that Free Choice is a homogeneity effect. The claim possibly A or B is defined only when A and B are homogenous with respect to their modal status, either both possible or both impossible. Paired with a notion of entailment that is sensitive to definedness conditions, this theory validates Free Choice while retaining a wide variety of classical principles except for the transitivity of entailment. The homogeneity hypothesis is implemented in two different ways, homogeneous alternative semantics and homogeneous dynamic semantics, with interestingly different consequences. EARLY ACCESS
Highlights
In the last few decades there has been a flurry of research into the apparent validity of the ‘Free Choice’ inference, where sentences like (1) and (3) appear to imply sentences like (2) and (4).1(1) You may have soup or salad.Simon Goldstein (2) You may have soup and you may have salad. (3) Mary might be in New York or Los Angeles. (4) Mary might be in New York and Mary might be in Los Angeles.FREE CHOICE ♦(A ∨ B) |= ♦A ∧ ♦BFree Choice is a surprising inference from the perspective of a classical possible worlds semantics for modals, and a Boolean semantics for disjunction
We develop a new semantics for Free Choice by integrating homogeneity effects into alternative semantics
It takes less for an inference to be valid in homogeneous alternative semantics, since we can restrict our attention to the worlds where the conclusion is defined
Summary
In the last few decades there has been a flurry of research into the apparent validity of the ‘Free Choice’ inference, where sentences like (1) and (3) appear to imply sentences like (2) and (4).. These two principles can be accepted independently of Disjunction Introduction They appear incompatible with the validity of Free Choice and Double Prohibition. Previous attempts to validate Free Choice have given up a variety of classical principles, including Disjunction Introduction, Upwards Monotonicity, Contraposition, Double Prohibition, LEM, and Constructive Dilemma. Like Barker 2010, have offered the reverse diagnosis, validating Free Choice while offering a pragmatic account of Double Prohibition Any such attempt, though, still gives some of the classical assumptions 1. The upshot is that homogeneity effects offer an attractive tool for a wide variety of defenders of the semantic validity of Free Choice: many such theories can go on to validate Double Prohibition and preserve much of classical logic by using a single idea. The semantic accounts in Aher 2012 and Aloni 2018 differ from our own by departing further from classical logic, giving up instances of the Law of Excluded Middle, Law of Non-Contradiction, and Explosion. (Along the way, we’ll consider the accounts in Starr 2016 and Willer 2017a.)
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