# Does "one of us is a child of yours" mean "exactly one of us is a child of yours" or "at least one of us is a child of yours"?

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.”)

• Welcome to EL&U PiMan. Your question sounds pretty much like a puzzle. Commented Aug 11, 2021 at 0:30
• XD I know! It kind of is, but the issue I'm having with this "puzzle" has to do with the meaning of a certain phrase, so that's why I'm posting my question here. Commented Aug 11, 2021 at 0:36
• The statement is ambiguous, in my view. Some expressions in English are that way! ☺️ Commented Aug 11, 2021 at 0:53
• Perhaps I should edit the description. I mean, there are elements of logic in the description, but that's not what I'm focusing on. The focus is on the meaning of the phrase "one of us is a child of yours." Commented Aug 11, 2021 at 1:27
• This, as tchrist strongly hints, depends on the preferred analysis. In logic, the answer is no. But standard English, unlike logic, is subject to the imprecise laws of implicature. In the given example, Alice is being deliberately obfuscatory (there is admittedly a remote possibility that the family often speak in precisionist language). She is breaking the fourth ... Commented Aug 11, 2021 at 12:08

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.

• I think that you are perfectly correct, Lawence. After all if someone came up to me as I was about to get in my car and said "Excuse me but one of your tyres is flat" I would expect to be able to put the spare wheel on and drive away. I wouldn't expect more than one to be deflated. Similarly if someone strummed a chord on a guitar, pulled a face at the discord and said "One of the strings is out of tune" I wouldn't expect him to have to retune all the strings, just the one that was out. Commented Aug 11, 2021 at 23:46
• That is a good point. What's more, Alice and Bob need not suppose that their parents need telling who are their children. There is practically no context in which anyone would need to utter the statement being discussed. So we can't glean contextual clues, because we don't know of any context any clues might be gleaned from. Commented Aug 12, 2021 at 7:29
• In other words, as a matter of semantics, the sentence is true, but as a matter of pragmatics, it would be an odd, misleading, confusing, infelicitous thing for Alice to say, because 'one of us' implicates (even though it does not logically entail) 'exactly one of us'. Examples like this usually appear in logic exercises that are designed to distinguish what words, strictly speaking, mean and how they are usually, typically used in real-life communication (taking into account the conventions and expectations that surround their use, but are not a part of their meaning). Commented Aug 13, 2021 at 15:34