I say true because there is indeed one rock in front of your house (it is also reasonable to say that there are two rocks). However, my teacher is claiming that the statement is false and sees the statement as "There is only one rock in front of your house." Who is right? Is there a certain theorem or definition that settles this debate?

Sidenote: I notice this is similar to the question "How many months have 28 days", the answer being 12.

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    $\begingroup$ This isn't a math question as much as it is a question about word use. I think most people would interpret this use of "one rock" to mean "at least one rock" but of course it might also mean "exactly one rock". It's ambiguous so, if it matters, the writer should clarify which is intended. $\endgroup$ – lulu Nov 17 '20 at 16:19
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    $\begingroup$ Is (s)he a math teacher? From the logic point of view, it is definitely true that there is a rock in front of your house. The claim is not saying "there is exactly one rock in front of your house", which would be false $\endgroup$ – Manlio Nov 17 '20 at 16:19
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    $\begingroup$ This is really a question about good communication. If the other person understands what you mean, then the communication is successful. There are times when "one rock" means "only one rock", and there are times when it means "at least one rock". If the context is not clear, then use more words. $\endgroup$ – Théophile Nov 17 '20 at 16:20
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    $\begingroup$ It's an ambiguous statement and depends entirely on how the speaker is defining language and arguments for either interpretation can be valid. If "There are n rocks" means "the cardinality of the rocks is n" then your teacher is correct. If it means "there exist two distinct rocks" then your are. If I heard the statement by itself I'd interpret it as the teacher does, but if I heard this as part of the question as to whether "there is one rock" is true or false I'd interpret it as you did as I'd assume that is the point. ... Just nod and say "I see".... $\endgroup$ – fleablood Nov 17 '20 at 16:26
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    $\begingroup$ @J.W.Tanner Yes, it's a classic (and in my opinion, annoying) riddle; see the last line of the question above. Related: xkcd.com/169 $\endgroup$ – Théophile Nov 17 '20 at 16:33

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