Note before reading: Even though there are elements of logic found in this description, that does not mean that this question belongs in the Mathematics or Puzzling stack exchange. This is because my question focuses on the meaning of a phrase, not how I should determine the phrase’s truth value. Please carefully read what I’m asking for.
Suppose you have only two children, one named Alice and another named Bob. During one quiet evening, Alice and Bob walk up to you with no explanation, and Alice says, "One of us is a child of yours." Is Alice telling the truth?
I'm having a hard time answering this question because I'm not sure how I should interpret the statement "one of us is a child of yours." I've asked a few people this question, and about half of them say that Alice is not telling the truth because they interpret the statement "one of us is a child of yours" as "exactly one of us is a child of yours." The other half of people say that Alice is being truthful because they interpret "one of us is a child of yours" as "at least one of us is a child of yours." Which way should I interpret the statement "one of us is a child of yours”? Is more context needed? Is it too ambiguous?
When we come across statements like "Josh has five apples,” it is often implied that he has exactly five apples (i.e. the word “exactly” is implicit), so I was thinking that maybe "exactly one of us is a child of yours" is the way to go. Would that be right? (If it is, that would mean that Alice was wrong when she said “one of us is a child of yours.”)
Best Answer
English is a contextual language, as are all natural languages, I’d imagine.
There is a joke that asks how many months have 28 days. The expected answer is one - February, and only when it’s not a leap year. The joke’s answer is that all months have 28 days, and most have several more.
This highlights the role of presuppositions in communication. Without context to constrain an interpretation, common usage and perceived intent influence the way a statement is heard.
In your example, the unmarked statement would be for Alice to say, “We are your children”. Including the plural “us” and specifying the singular “one” sets up an expectation that some unique quality of the specified individual is being discussed. This induces the natural reading that Alice uses “one” to mean “exactly one” in your example.
Context can change the natural reading. For example, if the context was a set of puzzles or riddles including the above 28-day joke, Alice’s “one” might be broadened to “at least one”. In your example, though, the natural reading is so strong that even such a context would likely be considered to be contrived. The reason the 28-day joke works is that the “at least” interpretation is unnatural or at least unexpected in the given setting.