Disjunction and Symmetry

This paper concerns what might be called the variably bad behavior of the word or. As is well known, there are a variety of environments in which the word or misbehaves – misbehaves, in the sense that it gives rise to interpretations which are not expected given the standard analysis of this word as, roughly, set union. One of these environments is the scope of a modal. This case has received a lot of attention recently in the literature, and a number of researchers, including myself, have proposed accounts of or which explain its behavior in this environment. But here is where the problem arises: When we embed or under both a modal and negation, it stops misbehaving and starts acting again like a well behaved Boolean operator. This is problematic for those of us who have gone to some lengths to argue, on the basis of the affirmative cases, that or isn’t a Boolean operator at all. In this paper, I will offer an explanation for this variable misbehavior. I will propose that or is, after all, more or less a Boolean operator, although one which works in a somewhat special way. In addition, I will argue that or coordinations are subject to a special constraint, called Symmetry; and that it is the requirement to satisfy Symmetry which sometimes forces or to display apparently non-Boolean behavior.