Only one vs. One and only one

Question

Suppose that someone proposes "only Jenny can eat this cookie".
Is this proposition saying that Jenny can indeed eat this cookie and no one else can? (1)
Or is this proposition actually saying that "if anyone can eat this cookie, it is necessarily Jenny" but not asserting that Jenny can indeed eat this cookie? (2)
If (1) is true, then that would mean that "one and only one" is the same as "only one".

BillJ · Answer

[Only Jenny] can eat this cookie.

Your example can be broken down into two propositions:
[1] "Jennie can eat this cookie".
[2] "Nobody other than Jennie can eat this cookie".
Proposition [1] is a presupposition: it is [2] that constitutes the foregrounded part of the information, the main assertion. The "other than" component of the main proposition is based on the focus, i.e. Kim.

Only one vs. One and only one

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