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).
    – user6726
    Feb 10, 2021 at 0:22
  • 2
    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.
    – curiousdannii
    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


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