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I vaguely remember having heard that one can formally prove that no amount of (successful) communication between two people ensures that the assigned meaning of their words converges. I think it had something to do with Wittgenstein's thoughts on colors.

It would be great to get a reference and/or name for that statement.

Thanks in advance for any help on the matter. Cheers, Lukas

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You might refer to Wittgenstein's problem of rule following (Regelfolgenproblem): No matter on how many uses of a word two people agree, they cannot be sure they will agree on any further uses.

The reason is that there are no rules that would govern the use of a word in a natural language. Hence, they cannot be following the same rule.

The lack of rules entails that the meaning of a word cannot consist in such a rule. It must consist in the use itself (according to Wittgenstein).

Now, as there is no rule and as there are infinitly many possible uses of a word, the agreement on some uses of a word does not allow to draw any conclusions about the portion of common uses altoghether and thus of shared meaning.

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On the formal side of things, Tarski's undefinability theorem makes similar arguments.

The theorem applies more generally to any sufficiently strong formal system, showing that truth in the standard model of the system cannot be defined within the system.

Of course, Tarski's actual proof is in a far more exacting mathematical form regarding the truth value of statements. Amusingly it is still subject to itself!

We also have a computational equivalent, if that is preferred. Rice's theorem states that all non-trivial semantic properties of programs in a Turing Complete language are undecidable.

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  • And I am morally obliged to link Guy Steele's Growing a Language speech (and its transcript) when people ask about communicating the meaning of words. While he clearly sidesteps the particular requirement you seek (converged meaning without a common language to build from), his particular sidestep is still fascinating to me. – Cort Ammon Jun 30 '20 at 15:55

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