THOUGHTS ABOUT "OTHER"/"ANOTHER"

In English, "other" and the related "another" have different logical meanings.  Sometimes "another" can mean "another of the same kind," as in "I'll have another cookie," meaning, "I'll have an additional cookie."  But the same words in a different context could have a different meaning.  "I can't eat cookies with nuts, could I have another cookie?", meaning, "Could I have a cookie of a different kind?" The Collins dictionary spells this out here.

https://www.collinsdictionary.com/us/dictionary/english/another

Hebrew and Aramaic have the same logical ambiguity in their words for "other, another." Lexicographically, should these different logical meanings form part of a dictionary entry?  We saw above that the Collins dictionary does do this for English.  But Hebrew and Aramaic dictionaries do not divide the senses up in this way.  Since I have written a couple of dictionaries, and am working on another (!), I'm wondering about it.  If a particular sense  is completely context-dependent and not signalled by some grammatical difference, is it part of the "meaning"? If not, does it belong in the entry?

Of course, this is part of the age-old lexicographers' polysemy dilemma. When do different contextual modulations of a word's meaning become identifiable as different senses? And is there a principled way in which to spell out how these different meanings are related? E.g., is one more basic, and the others (!) have emerged from it in some identifiable way (metonymy, metaphor, or the like)?

Or in the case of "other," if there is no clear way in which one sense diachronically presupposes another (!), and no difference in phonological form or morphosyntactic frame, do these senses inhere in the word at all?  Perhaps not.  Perhaps here instead of polysemy we have vagueness (in the technical sense of a word that is just non-specific about certain features).

 In that case, how do we deal with these issues in the dictionary? It might be possible to incorporate the necessary vagueness into the definition itself.  In the case of "another/other" (Heb. אחר, Aramaic אוחרן), we have to start with the fact that the word is anaphoric, that is, it always refers to something already mentioned in the discourse, the antecedent.  What "another/other," etc. means as an adjective is "not the antecedent, but similar to it." In any particular context, either the "not the antecedent" (different) or the "similar to it" (second, additional) part may be highlighted.  The logical freight of "another/other" depends on the meaning of the antecedent, not on any inherent semanteme in the adjective itself.

In Gen 26:22 for instance, we have "And he removed from thence, and digged another well," in context, an additional well; a second token of the same type (well).  In Gen 29:19, we have "And Laban said, It is better that I give her to thee, than that I should give her to another man." Here the antecedent (the man Jacob) is a type with a single token (the man who is Jacob); hence another man does not mean "a second man, in addition to Jacob" but "a different man, who is not Jacob."

Therefore an entry based on a clear semantic understanding should express the word's vagueness, which is modulated by the context.  Semitic dictionaries have done this mainly by simply using European glosses that are themselves vague.  I'm not sure this is the best approach, but I'm still thinking about the best way to approach this.