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This question was prompted by a friend who is a fluent speaker of English but not a native one.

Consider the following cases:

  • I either eat the apple or the orange. I eat: apple XOR orange.
  • I eat either the apple or the orange. I eat: apple XOR orange.

No difference.

Now consider:

  • The banana either costs more than the apple or the orange. banana > apple XOR banana > orange
    • That is: The banana costs more than the apple or the orange, but not both.
  • The banana costs more than either the apple or the orange. banana > apple AND banana > orange
    • That is: The banana costs more than both the apple and the orange.

My friend asked me, as a native speaker, to first confirm that this was the correct logical translation and then to explain just what the hell is going on here. What rule governs the distinction in the second pair of propositions?

Usually in these cases, I just explain it away as some form of idiomatic expression: "Sometimes either/or means exclusive-or and sometimes it means and. It's just the way it works."

However, I did notice one thing here. This distinction arises in the propositions involving a comparison between subject and objects: less than or more than.

Am I on to something? Anybody have a more coherent explanation?

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    The problem with "or" is that it is ambiguous between exclusive "or" and inclusive "or". On top of that, there are syntactic ambiguities in natural language, so it is not always clear what is "connected" to what. – GrimGrom Jul 23 '16 at 2:53
  • You're right that in comparisons (and elsewhere) "either" can mean "both." See this related question: english.stackexchange.com/questions/95559/… – GrimGrom Jul 23 '16 at 3:01
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Consider your sentence:

  1. The banana costs more than either the apple or the orange.

You have noticed that there is a reading of this sentence where it means:

  1. The banana costs more than both the apple and the orange.

This sentence, in turn, means:

  1. The banana both costs more than the apple and costs more than the orange.

It is recognized in Oxford Dictionary (as well as in this related question) that "either" is sometimes used to mean "both," as evinced by this definition:

[DETERMINER]

Each of two

'the road was straight, with fields on either side'

Now, this definition holds that "either" is a determiner. But in the kind of example you point to, it is clearly a conjunction ("either... or").

But your conjunction example can easily be transformed into a determiner-involving variant:

  1. The banana costs more than either of them.

This should convince you that the sense of "either" as a determiner meaning "both" might get extended to a conjunction.

So although Oxford doesn't mention it, we can form a corresponding definition for "either... or" as "both... and".

Here is another example of "either... or" being used to mean "both... and":

  1. Fido likes either ice cream or bacon before bed.

It seems to me that this kind of use is licensed only in contexts where there is a connotation of choice, but I can't formulate a more precise rule. Maybe someone else can.

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    ugh this is why I hate the word or. I wish society would just collectively decide to eliminate it in favor of 'xor'. 'And' and 'xor' is all you need folks. And don't ask me if I like cake or ice cream because I clearly like both. – user180089 Jul 23 '16 at 3:48
  • oh, I forgot about 'nor'. You need that too <_< – user180089 Jul 23 '16 at 3:50
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    @V0ight, I agree. What happened to turn-of-the-century logicians trying to invent the perfect language?! But interestingly, this question is more subtle than just involving a distinction between exclusive "or" and inclusive "or". – GrimGrom Jul 23 '16 at 3:52
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    what about Lojban? I don't know much about it as I'm not a linguist – user180089 Jul 23 '16 at 3:56

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