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"?

Solution 1:

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.