This article by Jonathan Wolff has a joke near the end that goes like this:
"The example everyone remembers is the popular song lyric "everybody loves my baby, but my baby don't love nobody but me". From this, it logically follows that "I am my baby" ... By the common consensus of logicians and philosophers everywhere, this really is very funny indeed. And the real beauty is that it is also a brilliant illustration of the semantics of the universal quantifier in standard first-order predicate calculus. But perhaps you'll have to take my word for that."
This is formally correct:
1. (p)(Lpb)
2. (p)(Lbp > p=j)
(where (p) = every person, Lxy = x loves y, j = me, b = my baby)
3. Lbb
4. Lbb > b=j
5. b=j
But something seems wrong. When I first read the article I immediately thought, "that can't be right!" and I think I figured out what was bugging me. When we say "everybody loves my baby" it seems we restrict the universal quantifier "everybody" so that it does not range over "my baby" - that is, when we normally say "everybody loves my baby" we don't imply that my baby loves him/herself.
Here's some more evidence:
A: Let's invite Jeremy to the party.
B: Are you sure?
A: Yeah, everybody loves Jeremy.
B: I don't know, he doesn't seem narcissistic to me.
A: No, I didn't say that he loves himself.
The question then arises: does this quantifier restriction occur at the level of semantics or pragmatics? Something I'll think about and then post again soon. Let me know if you buy any of this.