Disjunction mailbox

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The saga of English or (last discussed on Language Log here) continues in my e-mail, with several pointers to literature (taking us away from traditional logic) and possibly relevant data.

What started as several short postings on and/or and exclusive or has begun branching off in several different directions, as writing on the web tends to do. It's also moved into areas I don't know much about, so I'm inclined to make this my last posting on the topic of disjunction, at least for a while, and return to the hundreds of other postings I have partly prepared.

1. Disjunctive offers. Dominik Sklenar wrote to tell me about Ray Jennings's treatment of disjunctive offers, a brief account of which is available on-line in the Stanford Encyclopedia of Philosophy. Jennings observes that the disjunctive offer

(1) You can have ice cream for tea or you can have strawberries for tea.

entails both

(1a) You can have ice cream for tea. (1b) You can have strawberries for tea.

so that the meaning of (1) should be represented by a CONJUNCTION of (1a) and (1b) (perhaps with a third exclusionary conjunct meaning 'but/and you cannot have both', although Sklenar suggests that this bit of conveyed meaning is matter of conversational implicature).

Sklenar also doubts that there is ANY sentence of the form X or Y that is false if both X and Y are true. This is a subtle point, turning on the notion of the "literal meaning" of a sentence, and I won't pursue it here.

2. Multiple senses of or. Jennings's treatment of disjunctive offers (as logical conjunctions) leads us away from the position that words like or should be assigned a single meaning in all of their uses (outside of idioms). This should be no great surprise, given the multiple (but related) senses of many lexical items, but many semanticists have hoped that "logical" lexical items like or (and the and a number of others) could be assigned a single meaning via constructs of logic, without multiplying entities.

3. Linear Logic. Two correspondents, Chris Martens and Robert Furber, note that the system of Linear Logic (see the Wikipedia page here, with references) provides a number of non-truth-functional connectives, some of which can be used to translate the uses of or discussed in my recent posting. Linear Logic takes "resources" rather than "truth" to be the central concept of the logic; to get the flavor of how this idea might be applied to or, look at Martens on my breakfast-juice example (disjunctive offers again):

… the connective &, pronounced "with", is defined such that A & B intuitively means "A and B can be produced with the same set of resources", such that with a given set of resources you can make an A, or you can make a B, but you can't have both at once. This is probably the connective you'd want for the breakfast example: "orange juice & grapefruit juice & tomato juice".

I'd give you a little lecture on Linear Logic, but I don't know enough about it to say anything illuminating.

4. Forcing exclusive understandings. In my last posting, I mentioned one linguistic feature that can sometimes be used to force an exclusive understanding of or in English: the explicit exclusion but not both, to which we can now add but only one and similar expressions. But these are of limited utility, and over the years people have suggested other linguistic resources that might be pressed into service to force an exclusive understanding: either on the first disjunct, else on the second, and contrastive accent (or one of its typographical counterparts) on or. David Schwartz suggested in e-mail that some dictionaries maintain that either … or is always exclusive (I haven't found any that say this clearly) and offered some examples that are understood inclusively with or without the either:

You cannot donate blood if you have ever been diagnosed with (either) HIV or hepatitis.

Have (either) you or any member of your family done business with the defendant?

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As I pointed out in a posting a while back, the usage literature is strangely silent on the either of either … or. I would have expected Omit Needless Words enthusiasts to have fixed on the either here as usually dispensable without change of meaning, or those who tease out shades of meaning to have discerned some whiff of exclusivity in either, but neither group seems to have attended to either.

I leave it as an exercise for the reader to invent examples where the else strategy and the accent strategy fail to force an exclusive understanding (though sometimes they might favor exclusivity a bit). It looks like the only way to ensure exclusivity is to use an explicit exclusion.

[Addendum 4/22/08, from"Surely You're Joking, Mr. Feynman!" (by Richard P. Feyman, as told to Ralph Leighton, 1985), where on p. 60 Feynman is,  awkwardly, attending his first tea at Princeton's Graduate College:

I go through the door, and there are some ladies, and some girls, too. It's all very formal and I'm thinking about where to sit down and should I sit next to this girl, or not, and how should I behave, when I hear a voice behind me. "Would you like cream or lemon in your tea, Mr. Feynman?" It's Mrs. Eisenhart [the wife of the dean], pouring tea. "I'll have both, thank you," I say, still looking for where I'm going to sit, when suddenly I hear "Heh-heh-heh-heh-heh. Surely you're joking, Mr. Feynman."

(Hat tip to Nathan Myers.)]  

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