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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".

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    It's not saying it, exactly. You have to distinguish what's being asserted from what's being presupposed. Propositions that are asserted can be negated; propositions that are presupposed can't. If you say it's false that Only Jenny can eat this, then you're negating the assertion that someone else can eat it, but not the presupposition that Jenny can. That can't be negated by negating the sentence's assertion. For details, see Larry Horn's classic paper on the topic. Commented Jul 10, 2020 at 23:48
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    The question seems to have nothing to do with logic (or the use of one), but purely to do with which sense of can is being used: ability or permission. Which means that, without clarification, the meaning is completely ambiguous. (1) Only Jenny has the ability to eat this cookie. (2) Only Jenny has permission to eat this cookie. Commented Jul 11, 2020 at 1:51
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    "One and only one" is not the same as either "only one" or "only Jenny" "Only Jenny can eat this cookie" is indeed saying that Jenny can eat this cookie but no one else can. Please note that is a rare correct usage of "only." In most cases, "only" is placed wrongly, spoiling the real meaning. Could that be confusing you? The idea of "if anyone can eat this cookie, it is necessarily Jenny" not asserting that Jenny can indeed eat this cookie appears more bewildering than anything else. Could you re-phrase it, for clarity? Commented Jul 12, 2020 at 19:10
  • Only context will give the correct answer to the question. There is no context.
    – Greybeard
    Commented Mar 28, 2023 at 14:27

2 Answers 2

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[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.

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It means "if anyone can eat this cookie, it is necessarily Jenny." But it strongly implies that Jenny can eat the cookie. This is because it will be assumed that there was some reason you didn't make the stronger claim "nobody can eat this cookie"; you would most likely only avoid the stronger claim if it were false, in this case because Jenny can eat the cookie.

It's similar to how "some of the students can eat these cookies" does not entail that there are any students who can't eat the cookies, but it does strongly imply it, since it is assumed that there was a reason why you didn't just say "all of the students can eat these cookies."

To illustrate this point:

  1. Only Jenny can eat this cookie; in fact, even Jenny can't eat them.
  2. Only Jenny can eat this cookie; in fact, Jimmy can eat it also.

Note that (1) is awkward, but only (2) is self-contradictory.

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