Is there a basis set of words for a language? [duplicate]

We define a word in a language using a set of other, agreed-upon words. In linear algebra, the set of basis vectors for a space are the minimum number of vectors needed to describe any other vector in the space. Consider each word in a language a "vector", which can be described using some "combination" of other words/"vectors". Is there a minimum set of words in a language that can be used to define all the words in a language?

• What do you mean by "define"? I don't think you can define the word "dog", but you can say things about dogs that might clarify what you are referring to. Likewise "enset" (a plant species). Feb 10, 2021 at 0:22
• Unfortunately, the analogy to vector spaces breaks down rather quickly. For example, you can multiply any vector in a vector space with a real number (or, more generally, a field), or you can add any vectors, and get another vector. But what is 3.5 times "unique" plus "dog" minus "artichoke"?
– jick
Feb 10, 2021 at 1:19
• The usual mathematical analogy is with prime numbers, leading to the theory of semantic primes. Feb 10, 2021 at 14:07
• @jick I don't think that normal mathematical operations would carry over for this analogy, but "adding" words together could be granting attributes (i.e. "unique" plus "dog" minus "artichoke" could correspond to a new "vector" (a new word in this case) that means "a rare dog not holding an artichoke". I'm straining the analogy at best, but I don't think the analogy necessarily breaks. Since every word in the English language has a definition made from other words, the language technically does have a basis, which in this case is the entire language. It may not be the smallest basis though. Feb 10, 2021 at 16:21
• @curiousdannii actually, that does answer my question pretty well! I suppose those 1000 primitives would be a good starting point to approximate a basis. I'll flag to mark my question as a duplicate since I think that other question covers it pretty well. Thanks for the discussion folks Feb 10, 2021 at 16:23