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Homonyms are two words that are spelled the same and sound the same but have different meanings. A definition is a statement of the exact meaning of a word, especially in a dictionary.

Cool as in cold must be a different word than cool as in calm. They're homonyms. If homonyms are two words that are spelled the same, spelling must be an arbitrary attribute of a word.

So, if I go find "cool" in the dictionary and see there are several different words with different meanings listed, what is "cool"? It doesn't refer to a specific word without context. Is it a phonic phenomena? What do I call "cool" in reference to the set of possible words it could be?

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    I disagree that the two meanings of cool are different words. They’re the same word with the same meaning, just applied in different manners. Bat in the senses of ‘small flying mammal’, ‘wooden thing you use to hit a ball’ and ‘flutter, blink’ is a better example of homonyms; those are three separate words. – Janus Bahs Jacquet Apr 12 '20 at 9:16
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    Cool in the emotional sense is a metaphor of the temperature sense. That's not the same as being a different word. – jlawler Apr 12 '20 at 14:42
  • The exact meaning of a word is an abstraction, which may or may not be achievable. For many words, it is a nonsense, because the scope of the word various between contexts and between speakers. – Colin Fine May 12 '20 at 15:06
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That distinction is often called a "sense" of a word, thus "mean" in the sense "average" / "cruel" / "intend" etc. People also call that a "reading".

  • Unlike the two senses of cool given in the question, I would definitely call the three senses of mean you cite different homonymic words, both because they’re not derived from a common base sense and because they’re etymologically unrelated. – Janus Bahs Jacquet Apr 12 '20 at 9:20
  • @JanusBahsJacquet but doesn't that test make your first and third sense of bat the same word? I think OP wants a term for a lexical item considered in isolation from its meaning i.e. thinks that if you call "cool" a word you are attributing some specific meaning to it, and wants a term that refers to it as a container without specifying any particular content. The Q assumes that "word" can only have one meaning, otherwise the argument doesn't go through. Even so, what about lexeme? – rchivers Apr 12 '20 at 12:18
  • @rchivers Ah, that may be. It’s not the clearest question I’ve seen; I may have misunderstood the intention. I don’t see why bat the mammal and batting your eyelids would be the same word? They’re neither semantically nor etymologically related (except to the extent that bats do bat their wings, but so do all flying creatures). – Janus Bahs Jacquet Apr 12 '20 at 12:25

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