In computer science, there is a theorem that says any machine able to perform six basic primitives can compute any computable problem. Is there a similar theorem in linguistics that specifies certain qualities a language requires to be able to express any conceivable idea?

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    It's not a theorem, it's an axiom: any language can express any idea some other language can. It means that if we take any language, e.g. Sanskrit, and it can express the idea X, it means all the rest of the languages can express the idea X, too. In other words, a text in a language can be translated to all the other languages. That's true for all the natural languages. – Yellow Sky Sep 21 '19 at 13:39
  • The answer is "no", since we can't tell you what the essential properties are. You can get some opinions, though – lists of possile properties. – user6726 Sep 21 '19 at 14:36
  • Six or even one. Natural languages usually have more or less well defined structure (syntax) but always poorly defined interpretation (semantics), so a property analogous to Turing completeness cannot be proved rigorously. This vagueness is inevitable as human perceptions and ideas are subjective and blurry, much harder to pin down than idealized mathematical operations on bit patterns. – ngn Sep 21 '19 at 15:17
  • What's called a "language" in computer science has very little resemblance to human language. For instance, no human language is composed only of imperatives. As for theorems, forget it; linguistics deals with data, and science can't prove anything. Proof is only possible in tautological systems like mathematics. – jlawler Sep 22 '19 at 2:27