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Motivation: words in a dictionary are defined in terms of other words, but at some point it becomes circular: words defined by other words that have also been defined using some of the same words. Thus every dictionary must have a minimum set of words that are not defined but can be used to define the rest of words in the dictionary.

The study should not be that difficult to do, just enumerate all the subsets of words from the smallest to the largest, and see which is the smallest set that suffices to define the rest of the words in the dictionary.

My intuition is that this can perhaps tell us what are the core set of basics concepts that a mind (or a robot) needs to "understand", and the rest can be generated by definitions.

Question: I wonder if somebody can point me to any such study, assuming some exists. Thanks

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The study should not be that difficult to do, just enumerate all the subsets of words from the smallest to the largest, and see which is the smallest set that suffices to define the rest of the words in the dictionary.

I think you should consider a different definition of circularity. You have a minimum set of words in the defining vocabulary whose definitions are assumed to be known. Then for the rest of the words in the dictionary we need to order them such that their definitions use only the words from the minimum set OR words that have have been defined previously.

This is known as the minimum feedback arc set problem and it is actually quite difficult to solve or even to get a good approximation. Basically, starting from an existing dictionary and reordering it to get rid of circular definitions is not possible.

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"every dictionary must have a minimum set of words that are not defined."

I'm not sure about that. If the dictionary is truly unabridged (and uses only non-antiquated terms in the definitions themselves), every definition would end up being circular in some way. Lexicography is not geometry.

I think some of the primitive concepts may be undefined in the manner you're thinking of (and as described in the cited Wikipedia article). But undefined concepts ("semantic primitives") are different from undefined words.

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  • What is an undefined concept? I.e. can you give an example of a defined concept, versus an undefined concept?
    – user6726
    Sep 30 '15 at 0:32
  • Undefined concept was a bad choice of words on my part. Perhaps "atomic concept" might have been a better term to describe a concept which itself cannot be decomposed into more fundamental concepts. In any event, I was thinking that Euclic deliberately started with undefined terms, then moved to axioms, and went on to derive logical conclusions. He did that for the sake of logical rigor (avoiding circular arguments). I don't think dictionaries strive for logical rigor. Semantic accuracy, yes. Logical rigor, not so much. Sep 30 '15 at 12:45
  • I suggest that the problem lies in the desire for self-containedness, i.e. defining words in terms of other words, and disregarding experience. Circularity is avoided via ostensive definitions. In that way, all definitions reduce to perceptual experiences.
    – user6726
    Sep 30 '15 at 16:12

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