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The other day, I was chatting with one of my linguist friends when I realised that one of the technical terms he was using, although it seemed familiar to me from my mathematical background, actually has a completely different meaning in linguistics. The term is lemma and a quick bit of additional research showed me that there are several other distinct uses of the word in different fields...
To start with the mathematical one, as that's closest to being my native language, a lemma is a proposition that is principally intended as a stepping stone towards another result rather than as an end in itself. This definition can tend to downplay the importance of lemmas (or lemmata, to give the more classically formed plural), as they can often be quite deep and interesting results in their own right and many of them end up being very useful in proving a number of (often quite disparate) theorems.
Apparently I once caused quite an interesting coffee-time discussion amongst the mathematicians of Nottingham University. When I was an undergraduate there (about 12 years ago), I asked my tutor about the difference between a proposition, a theorem and a lemma; he wasn't sure, so he raised the question with his colleagues. Their consensus, which I've later discovered seems to be shared by most mathematicians, is that there is no formal distinction. Instead, it's a mixture of personal preference, convention and tradition. A proposition is the general term for a mathematical statement that is proved (whether or not the proof is given); a theorem is a proposition that is considered to be especially important or difficult and a lemma is one that is mostly of interest as a means of proving another proposition (or perhaps several). By contrast, a conjecture is a statement that is believed (at least for the sake of argument), but not yet proved, to be true.
Anyway, enough of the mathematical digression and on with the parade of lemmas...
According to Wikipedia, there are two distinct uses of the term lemma in linguistics. The most common one, which I believe is how my friend was using the term, denotes the canonical form of a word. Many words can appear in different forms. For instance mouse/mice is an English noun in singular and plural forms, while a verb can appear in several different forms (e.g. sing, sings, sang, sung). The canonical form is the one which appears as the headword in a dictionary, i.e. it's the form of the word that you would look up. Some dictionaries also contain entries for other word forms, especially irregular ones, but generally refer you to the canonical form to find the actual definition.
The word lemma is used differently in psycholinguistics, where it means the abstract conceptual form of a word that is first mentally selected, before your brain figures out details of morphology and pronunciation. Not altogether different from the general linguistic usage, but a slightly different shade of meaning.
In logic, a lemma is a statement that is simultaneously the conclusion of one argument and the premise of the next one. To me, that sounds pretty much the same as the mathematical use of the term.
In all these uses, the etymology of lemma is apparently from the Greek word λαμβανω (lambano), which means to take (actually, it means "I take" because the canonical form of Greek verbs is the 1st person singular, while for English ones it's the infinitive), via the Greek word λεμμα (lemma), meaning a premise or something received.
Another, completely different, use of lemma is in botany, where it refers to a type of leaf found in grasses. This word, although it has the same form as the other English lemmas, comes from a different Greek word λεμμα (lemma), meaning a husk or shell. This one ultimately derives from the word λεπειν (lepein), meaning to peel (NB this is an infinitive in Greek - I'm not sure of the canonical form of this verb).
Apart from being an interesting little study of etymology and a glimpse into several different academic worlds, this example highlights one of the dangers of jargon - words don't always mean what you think they mean!
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