I don’t think the two closed answers of “Have you stopped beating your wife ?” have such a well-defined meaning.
Since this is natural language, and I understand a no as meaning “I’m still beating her.” and I expect most people to interpret a no the same way as I, then it’s not from obvious why this interpretation is incorrect (if we ignore that the sentence is typically used as an example that has no good answer. Use “Will you stop smoking soon ?” which is less standard for the sake of the argument.)
If you interpret it strictly, an answer of “yes” puts you in the space of “I used to beat my wife, but I have stopped.” An answer of “no” puts you in the ambiguous space of “Either I used to beat her, and I still do, or I never have and therefore can’t have stopped.”
The question is which of those two possibilities people will assume. Which will depend on the context and what they already think of both you and the person asking.
I don’t think the two closed answers of “Have you stopped beating your wife ?” have such a well-defined meaning. Since this is natural language, and I understand a no as meaning “I’m still beating her.” and I expect most people to interpret a no the same way as I, then it’s not from obvious why this interpretation is incorrect (if we ignore that the sentence is typically used as an example that has no good answer. Use “Will you stop smoking soon ?” which is less standard for the sake of the argument.)
If you interpret it strictly, an answer of “yes” puts you in the space of “I used to beat my wife, but I have stopped.” An answer of “no” puts you in the ambiguous space of “Either I used to beat her, and I still do, or I never have and therefore can’t have stopped.”
The question is which of those two possibilities people will assume. Which will depend on the context and what they already think of both you and the person asking.