So going off the last post, but too disorganized even for it, I was thinking about when "If P or Q, then R" amounts to "If P then R and if Q then R."

It seems to me that

(1) If Alice is in France or Germany, it's France

makes sense, even though it doesn't imply "If Alice is in Germany, she's in France" (except as a material implication, which we will ignore for now). But perhaps only because "If Alice is in Germany, she's in France" would be absurd. If I believe that if Alice is having a good time in France, but would not be having a good time were she in Germany, it seems at least misleading to say

(2) If Alice is in France or Germany, she's having a good time.

Unless, perhaps, it is mutually acknowledged that she would not be having a good time in Germany, so (2) is taken to entail (1).

And I'm pretty sure it's infelicitous to say

(3) If Alice is in France, or if she's in Germany, it's France she's in.

"If P, or if Q, then R" seems practically an explicit assertion of "If P then R" or "If Q then R."

The assertion in question in my last post was actually of the form "Whether or not P, then P." Take the general form to be "Whether P or Q, R"; that seems to me more like (3) ("If P or if Q, R") than (1) ("If P or Q, R"). So this also seems infelictous:

(4) Whether Alice is in France or Germany, she's in France.

And that suggests that I was entitled (in my analysis) to move from "I believe that whether or not P, P" to "I believe that if P then P, and if not-P then P."

Posted by Matt Weiner at December 14, 2005 02:14 PMComments

Huh. Your statement (1) looks to me to have an implication (given that France and Germany are mutually exclusive) that "Alice is not in Germany." "If P or not P, then P" has satisfied the conditional, since P and not-P occupy the whole universe, right (as opposed to, say, France and Germany). So, given that P and not-P are mutually exclusive, "If P or not P, then P" basically means "If P, then P" with an implication of "not not-P", which is, of course, P.

So from one statement we get "If P, then P" and "P".

Seems like a pretty tricky way to go about making a statement while seeming like making concessions.

Posted by: silvana at December 15, 2005 06:32 AMTrue; "If P or not P, then P" sounds weird. Maybe it's because "If P or not P" is redundant, since "P or not P" is always true?

Posted by: Matt Weiner at December 15, 2005 08:06 AMDo you not think "whether or not P" to be equivalent to "If P or not P"?

Posted by: silvana at December 15, 2005 08:38 AM"If P or if not P," to be specific. The thing is that my post doesn't explain why "If P or not P, P" would be weird, since it suggests that it *doesn't* entail "If not P, P"; whereas "If P or if not P, P" does entail "If not P, P."

It follows from (1) that Alice cannot be in Germany, so from a logical point of view, "If Alice is in Germany, Alice is in France," is perfectly correct, since a false proposition implies any proposition.

It sounds odd in ordinary language since we don't normally make the observation that false things imply true things.

Note however that we *are* comfortable with observing in ordinary language that false things imply other false or impossible things. "If Alice is in Germany, I'm a pickled herring!" Which actually has pretty much the same informational content as (1).