Meaning and use are two sides of the same linguistic coin (Ariel, 2008). Meaning enables and restricts use, and use reinforces old meanings and motivates new ones. It's a vibrant circle. Yet, the two remain apart. Semanticists and pragmatists tend to focus on meaning, ignoring or remaining naive about use. Ignoring use in natural conversation has led pragmatists to imagine how natural use "must be", based on "armchair" functional explanations (Horn, 1972 and onwards, Levinson, 2000). Functionalists, on the other hand, tend to privilege use over meaning. They have too often been seduced by the frequent discourse pattern, ignoring infrequent uses. But speakers don't ignore the infrequent.

Linguists (of all stripes) have taken the most salient feature of disjunctions to be the distinct alternatives they seem to present. Here's an example of a classical case:

1. STEPHANIE: it was either Funniest Home Videos,
           or they were filming a fi- a movie, (SBC: 035).

Note that each disjunct here presents a distinct alternative, the reading is exclusive (the alternatives are incompatible with each other), no other relevant alternatives are entertained by the speaker, and so, exactly one of the alternatives must be true. Note also that each disjunct contains a complete, indicative sentence, and the fact that () contains not just or but also either is considered irrelevant. Alas, such "well-behaved" disjunctions and interpretations are extremely rare in conversation, as evidenced in the Santa Barbara Corpus of Spoken American English.

I will argue that natural discourse shows a whole variety of interpretations associated with disjunctive constructions, and that what form the disjunction takes matters to its interpretation. Either X or Y; X or rather/instead Y; X or contra realis Y (X or I'm a monkey's uncle); X or undesired Y (do or die); X or X (Am I right, or am I right?); X or not X (to be or not to be); and X or something must each receive a separate constructional analysis. Intonation contour, Intonation Unit boundaries, and sentential versus phrasal disjunctions are all relevant to how we use and interpret disjunctions.

But the most dramatic finding is that the basic X or Y construction is not all that different from the X or something (like that) construction, in that very often, only one general concept is proposed by the speaker, despite the fact that two (or more) alternatives are mentioned explicitly. Consider:

2. NORA: Wonder who was the ruler.
           in nineteen ten.
    DIANE: Who was the king or queen? (SBC: 023)

Diane does not think that Nora is interested in finding out 'either who the king was, or else who the queen (who could be the king's wife) was'. Rather, the king or queen are intended as instances of a larger concept, that of 'the primary monarch', which the addressee needs to construct. I will argue that this is the basic function of X or Y constructions in discourse. Although the meaning of the disjunction specifies two (or more) alternatives (each disjunct describing an objectively distinct state of affairs in the world), discoursally, many disjunctions serve to introduce only one concept, and to support a single discourse point. The semantic meaning commonly assumed, namely, that at least one disjunct must be intended by the speaker, will be questioned too. In sum, my analysis revises both the semantic meaning and the pragmatic functions in discourse that are to be attributed to or.

References

Ariel, Mira. 2008. Pragmatics and grammar. Cambridge: Cambridge University Press.
Horn, Laurence R. 1972. On the semantic properties of the logical operators in English. Mimeo, Indiana University Linguistics Club.
Levinson, Stephen C. 2000. Presumptive meanings: The theory of generalized conversational implicature. Cambridge, Mass.: MIT Press.