"Everybody Loves My Baby"

R. Warner in his intro to Grice 2001, uses this example to illustrate Grice's theory of implicit reasoning.

For Grice, reasoners implicitly reason.

Suppose I say

Everybody loves my baby
But:
My baby don't love nobody -- but me

This, Warner, argues, is possibly valid provided we bring in the implicit clauses:

The conclusion, Warner, argues is
that I am my baby.

For,

Everybody loves my baby.
Since my baby falls in the class of everybody, it follows
from the above that
My baby loves my baby.

Now, since
My baby don't love nobody but me.

It turns out that the only
universe of discourse consistent with
the premises is
I am my baby.

Warner finds that paradoxical. I don't.

I suppose he's thinking that the singer is hidind something when he is not saying that he is his baby. But I find that, perhaps out of self-modesty, or something he keeps it to his-self?