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Many words have multiple meanings. Sometimes they are related (like "theory" as opposed to "practice", versus "theory" as in "scientific theory"), but sometimes they’re completely different (like "dye" as in "colourize" versus "die" as in "stop living", or even the singular of "dice").

Dictionaries usually list several meanings for each lemma. I’m wondering if anybody knows what the average is for an English word? (For that matter, is it known for other languages?)

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A gazillion.... –  Noah Feb 14 '13 at 12:48
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Well, there's two separate things here.

The example die is in fact three separate words. What were dien and dee in Middle English, became different words spelled die in Modern English. What was spelled deie still has a separate spelling dye. They're homophones, and in the case of the two words spelled die, homonyms; two separate words with the same spelling and pronunciation.

When we come to senses, the difficulty is in how we define the boundary between senses.

(The capacity for words [and symbols, signs, gestures and other units of communication] to have multiple meanings, is called polysemy. Ironically polysemy appears to be monosemic.)

Many senses are very close to each other, and the lexicographer must decide whether they are truly separate enough to count as senses. Figurative uses becomes "full" senses if used heavily, but at what point does this happen? Does an inventive figurative use invent a new sense immediately?

If I've an idiosyncratic use for a word, should you count that as a sense? If a sense listed in the dictionary is marked as archaic should you still count it? What about dialect or colloquial?

Do we count the available productions? Just about any noun can be used in an adjective way, is that another sense? If not, is it another sense if it's a particularly common use of that word?

Also, which words do we count, and do we weigh the results in some way? It would be very easy to produce an answer of "just over 1", by taking every technical word with a limited use such as alpha-dimethyl-cyclohexylethylamine, alphamethyl-phenethylamine and so on, which tend to be monosemic. (And to have several other names, most of which are also monosemic).

Conversely, taking the most common 121 nouns and 70 verbs and counting senses according to the Wordnet dataset in this study came up with an answer of 7.8 senses per noun, and 12.0 per verb.

So that's one answer, though the above should make it clear that we could come up with answers that were very different to those.

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Thank you for the very elaborate answer! I know that there were many different possible answers; I was really looking for a source that had made some study of this (and defined criteria) — I should probably have included that info in my question. Also, I didn’t know polysemy. :-D –  Martijn Feb 14 '13 at 12:46
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The study I link to is one such, though you will find others with it as a starting point. Lots of others! Especially now you know polysemy for your searches. –  Jon Hanna Feb 14 '13 at 12:58
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I was going to say '2' and be done with it. –  Mitch Feb 14 '13 at 13:19
    
Jon gives a fine analysis of the 'what constitute separate words?' and 'what constitute distinct senses of a single word?' problems. He also highlights the lexicographer's dilemmas. There is a deeper problem, in that words are used to express and communicate perceptions (whether about hypotheses or mountains), and 'no two people's 'blue' is the same'. The sense we attach to a word is coloured (sorry) by the experiences we have had. Someone summed this up: 'All words are infinitely polysemous' (even alpha-dimethyl-cyclohexylethylamine) (but possibly excluding mirbane). –  Edwin Ashworth Feb 14 '13 at 17:36
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Yes, that really affects the senses. –  Edwin Ashworth Feb 15 '13 at 16:12
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