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In programming languages, there is a concept of turing completeness - whenever a system reaches "turing completeness", it is capable of emulating any programming language and, thus, as expressive as them. It is not hard to be turing-complete: very simple systems such as the turing-machine, the λ-calculus and cellular automata are turing-complete, meaning they're as expressive as any modern, fully featured programming language.

I wonder if human languages have a similar phenomenon. Is there a small set of words which is enough to express everything else?

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    Related: Finite set of meaning blocks language – lemontree Jan 29 '17 at 20:46
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    first, you got it wrong. turing completeness does not mean "emulating any progrrammimg language". virtually every programming language in use goes far beyond turinng for a simple reason: turing don't do I/O. – mobileink Jan 30 '17 at 0:03
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This is of course highly debated, but some linguists would answer yes, there is a small set of words/concepts common to all natural human languages. The major theory currently representing this view is the Natural Semantic Metalanguage, which posits that there are around 66 core 'semantic primes' which are both irreducible and universal. These primes are usually words, but some will in some languages be expressed by affixes or set phrases.

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I think it is an interesting question, but immensely difficult to answer.

First of all, expressions are dependent on both meaning and structure in natural language. In other words: do you want to know a minimal number of structural operations? Or do you want to know a minimum number of lexical items? There is a clear trade-off between the two. If you increase the number of structural items or combinations, you need less lexical items and it works the same way around. The trick for natural language would be in finding a perfect equilibrium, but I admit that I have no way to straightforwardly approximate that.

You asked for words, so I will assume lexical items (but keep in mind this is not all there is to it). Lexical items can always be recombined to fit new phenomena, but this in principle is a social activity. Look at Mandarin, for example. Combining several semantically distinct characters can give a meaning for a completely unrelated concept. In principle, this means you can have a large amount of concepts covered with relatively little words. Again, this comes down to combining in a smart way. Let's assume the word A, B and C. That gives you at least 27 possibilities (3*3*3) of meanings (including the options A A A, B B B and C C C). This is just one way of doing it and probably very unnatural at some point (imagine saying "cheese cheese cheese cheese" and it means "I went swimming yesterday"). But it is possible. In Dutch, my first language, we also have the option of verbalizing nouns. We do it with everything and it works pretty well. So "vis", meaning "fish", becomes "vis-(s)en", meaning "to fish".

To end, I think we need to establish something else before asking your question. How many concepts are the minimal number of concepts needed? I think making the tool is less difficult than setting a goal, in this case. Perhaps someone else has a good suggestion to that.

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