So here's something I was pondering about. Let's say there are 2 people A and B. A says a sentence with a double entendre and B asks for a clarification. For example:

A: Miners Refuse to Work After Death

B: Do you mean the ghost of a miners refused to work after death or do you mean the miner refused to work after someone else's death?

A: Obviously, the latter!

Notice B was able to clarify A what A meant with one question.

Now, here's my question can one construct a finite sentence/stanza/book which can be only clarified only via an infinite number of questions?

I'm more interested in the axioms used in arriving at the answer than a simple yes/no

  • My guess would be to make up a statement where the clarification questions loop back on themselves. Statement involves "A", "A" means "B,C,D", "C" means "A, X, Y".
    – Dave
    Sep 30 at 16:25
  • @Dave I should have thought of that. Interestingly, I think this also shows language is never circular. For example a dictionary would be useless if I look up the definition of courageous it will say brave but then for brave is says courageous. Sep 30 at 16:31
  • I am.not sure exactly what you are getting at here. If the first person gives more specific details then there are less questions one can ask. The issue is person A is not specific enough where there has to be additional questions. Be specific & detailed in the first place & you avoid the issue altogether! As far as some dictionaries they are circular. For instance look up human being & often the dictionary will define that as a person. Look up person & that will often define that as a human being. That goes to show we really may not KNOW what a human being is! Can you show otherwise?
    – Logikal
    Sep 30 at 19:13
  • 1
    There are certainly mathematical examples. It takes infinitely many yes/no questions (or binary digits) to fully specify any noncomputable real number. Of course this is not a real-world situation so I'm not sure if you'd find it of interest.
    – user4894
    Sep 30 at 19:35
  • "Clarification" is inherently vague, and depends on presumed cognitive habits and shared background as much as on the meanings themselves, if not more. You'd be surprised how simple a thing can be that cannot be clarified with any number of questions. See Carroll's What the Tortoise Said to Achilles for an infinite sequence of questions that still fails to "clarify" a modus ponens.
    – Conifold
    Sep 30 at 20:43

Person A's mind emitted the claim, and person A's mind is not infinitely complex. If person B understood person A's mind perfectly - or at least, sufficiently - then person A's motivations for emitting the claim would be clear, and person B would have no further need for clarification. Because person A's mind is not infinitely complex, a finite number of questions would be sufficient, in theory, to reveal the inner structure of person A's mind at the necessary level of detail.

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