[FOM] back to disjunctions

Jeremy Avigad avigad at cmu.edu
Tue Jan 23 17:28:20 EST 2007

I didn't follow the discussion of disjunctions closely, but I forwarded 
the initial query to my colleague, Mandy Simons, who is a linguist and 
philosopher of language. She offers the following response.

Jeremy Avigad

 > Can anyone provide a principled reason for why logicians choose to
 >   interpret "or" as inclusive disjunction?

I can't speak for logicians; but I thought readers of the list might be 
interested in some references to material in linguistic semantics, where 
it is more or less standard to assume that natural language "or" is 
truth conditionally equivalent to logical inclusive disjunction, as 
opposed to logical exclusive disjunction.

One reason is the behavior of "or" under negation, as in: "I didn't sing 
or dance". This sentence means that I didn't sing and I didn't dance, as 
predicted if "or" is semantically equivalent to V (and assuming an 
extension to allow for disjunction of predicates rather than clauses). 
The interpretation is incompatible with an analysis of "or" as 
equivalent to logical exclusive disjunction, as the sentence is NOT true 
if in fact I engaged in both activities.

A similar argument against treating "or" as exclusive disjunction is 
provided by sentences with multiple disjuncts: in fact, with any odd 
number of disjuncts. If "or" were equivalent to exclusive disjunction, 
then, for example, "Bill sang or danced or juggled" would be predicted 
to be false if any two of its disjuncts were true, but true if all of 
its disjuncts were true, an entirely counter-intuitive result.

Nonetheless, there is a robust implication that a speaker of a 
disjunction believes that at most one of the disjuncts is true 
(regardless of how many disjuncts there are). Gazdar 1979 offered an 
account of this implication along Gricean lines, and this account is 
still assumed by many linguists. However, Gazdar's account has been 
critiqued as making stronger predictions than are actually licensed by 
the Gricean assumptions. There is a competing view that has been 
proposed by a number of different linguists that the exclusiveness 
implication is a consequence of a tendency to interpret disjuncts as 
exhaustive (i.e. complete) answers to a question under discussion, in 
the same way that we tend to interpret independent assertions. The most 
developed version of this account appears in:
Robert van Rooij and Katrin Schulz (2004): Exhaustive interpretation of
complex sentences, Journal of Logic, Language, and Information, 2004,
13: 491-519.

There is quite a bit of relatively recent work on the semantics and 
pragmatics of natural language "or", much of which offers quite 
different accounts of the semantics of "or". For anyone who is 
interested, a good place to get an overview would be a recent 
dissertation by Luis Alonso-Ovalle (2006) from the Dept. of Linguistics 
at UMass Amherst. His dissertation can be downloaded from his website:

Mandy Simons

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