Wolfgang Schwarz

Diamond implicature

If I say "", you would often take me to have asserted both "" and "". A quick internet search didn't come up with any useful literature on this, so I'd be grateful for pointers.

Examples:

• You may have beer or wine.
  [Implies: you may have beer and you may have wine.]
• For all I know, she might be in the pub or in the library.
  [Implies: for all I know, she might be in the pub, and for all I know, she might be in the library.]
• It is physically possible that a dropped cup goes sideways or even upwards.
  [Implies: it is physically possible that a dropped cup goes sideways and that it goes upwards.]
• If I were to drop this cup, it might go sideways or even upwards.
  [Implies: if I were to drop the cup, it might go sideways, and if I were to drop the cup, it might go upwards.]

The same happens with existential quantification instead of disjunction:

• You may have one of the drinks on the top shelf.
• She might be in one of the pubs in Civic.

Arguably, it also occurs when the antecedent in some other way leaves relevant details open:

• You're allowed to install software on your office computer.
  [Implies: you're allowed to install any (reasonable, legal) software on the computer, not just, say, Microsoft Word.]
• She might be married and have children.
  [Implies that there are several people p and numbers n and functions f from n to sexes such that I cannot rule out that she married p and has n children with sex f(1)..f(n).]

I'm currently interested in this phenomenon because I've been thinking about counterfactuals a little, and it seems that here it shows up not only in the consequent of might-counterfactuals, but also in the antecedent of counterfactuals quite generally:

• If I had arrived 5 or 10 minutes later, I would still have caught the train.
  [Implies: if I had arrived 5 minutes later, I would still have caught the train, and if I had arrived 10 minutes later, I would still have caught the train.]
• If she had drunk from one of the bottles on the top shelf, she would now be dead.
  [Implies: for any bottle on the top shelf, if she had drunk from it, she would be dead.]
• If the dart had landed on a red field or anywhere on the left-hand side of the board, I would have won.
  [Implies: I would have one in any of these cases.]
• If I had been run over by a car yesterday, I would be either dead now or severely injured.
  [Implies: on any (reasonable) way I could have been run over by a car, I would now be dead or severely injured. To see the implication, drop one of the disjuncts in the consequent and notice how it sounds false.]

(Why does the antecedent behave like a diamond context in this respect? Maybe because it is a negated compound in a box context?)

I've found an old article by Barry Loewer, "Counterfactuals with disjunctive antecedent" (JoP 1976, pp.531-537), where he attempts a Gricean explanation of cases with disjunctive antecedents. It goes as follows: suppose I assert a counterfactual "if A or B, then C". Case 1: It isn't known which of A and B is closer to actuality. Then I normally shouldn't have made the assertion unless I believed it was true in either case. So you take me to believe both. Case 2: it is known which of A and B is closer, say A. Then saying "if A then C" would have been saying something shorter and stronger, so I should rather have said that; as I didn't, you re-interpret what I said to be the conjunction of the two counterfactuals. But this doesn't sound very convincing. Why would you re-interpret me in exactly this way? And actually, strengthening the antecedent doesn't strengthen a conditional; "if A then C" is usually not stronger than "if A or B then C". So at least the most straight-forward Gricean explanation doesn't seem to work here.