Numbers and articles

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So far, we've looked at three articles: la, for cmene, le, for sumti, and li for numbers. So li bi is 'the number eight.' Actually, outside mathematics, li is not used very much. What we usually want to say is things like 'three people,' or 'the two women.'

Note for mathematicians: Lojban has a number of words to deal with basic mathematics, and also an incredible number of words to deal with just about any mathematical expression you can think of, in a separate subset of the language (The Complete Lojban Language, Chapter 18.) But you can't expect everything in a beginners' course.

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We can use numbers either before or after le. For example,

ci le gerku

means 'three of the dogs', while

le ci gerku

means 'the three dogs.'
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What do we do, though, if we just want to say "three dogs"? For this we need another article, lo. The logic of lo is pretty complicated, but it basically means 'something which really is,' which nine times out of ten is the same as English a or some. (Translating Lojban grammar into English like this is a mortal sin — damned under the name of malglico; but even so, this is the best thing to do with lo at this stage!)

Note for logicians: lo prenu cu klama expresses the proposition "There exists at least one person, such that that person goes."

By contrast, the cannot mean the same thing as lo. In English, the dog doesn't mean just 'something which really is a dog', but more like 'something which really is a dog, and which I already have in mind.' (That's how "A dog came in. A dog was black" and "A dog came in. The dog was black" are different.) Lojban sidesteps this problem by using le gerku 'something which I'm going to call a dog'. It's up to the audience to put together what the speaker had in mind when they called it le gerku, just as it is the audience's job in English to work out what dog the speaker had in mind.

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So ci lo gerku means 'three of those which really are dogs', or in plain words, 'three dogs'. lo ci gerku, however, means that we are talking about [one or more of] the only three dogs in the world, which is not something you'd really want to say. (Mathematicians and logicians can look up the relevant parts of The Complete Lojban Language if they want clarification on this issue — or for that matter on the differences between lo and le.)

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Now consider the English sentence Three men carried a piano. This sentence has two potential meanings, as does any sentence involving a plural in English. You could be saying that the sentence holds true for each individual of the group. If the men involved are Andy, Barry, and Chris, you might be saying that Andy carried the piano, and Barry carried the piano, and Chris carried the piano. Alternatively, you could be saying that the sentence holds for the group as a unit: no one carried the piano individually, but all three men carried it together.

Natural languages typically leave it up to context and plausibility to determine which of the two interpretations holds. But Lojban is a logical language, and so does not tolerate this confusion! le and lo force the individual interpretation. That is, if I say

ci lo nanmu cu bevri le pipno

I mean that each of the three men (nanmu) carried (bevri) the piano (pipno). And if I say

ci lo gerku cu batci mi

I just mean that three dogs bite me. Maybe one dog bit me in the morning, one in the afternoon, and one at night, or maybe I mean that I have been bitten by a dog three times in my life. There is nothing to say that the three dogs have anything to do with each other.
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But if you want those dogs, or those men, to be considered as a unit, you'd say

lu'o ci lo nanmu cu bevri le pipno
lu'o ci lo gerku cu batci mi

lu'o means 'the mass composed of', and in effect converts a bunch of individuals into a coherent unit. In the case of the dogs, for example, it makes them a pack. If you're a fan of computer strategy games, think of lu'o as like the 'group' command for units (there's also an 'ungroup' command, lu'a). Moreover, since the dogs act as a pack, it is not necessarily true that each of them individually bit you: it is actually enough that one of them bit you, for the pack to have bitten you.
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With le things are simpler. While le pano ninmu means 'the ten women', lu'o le pano ninmu means 'the ten women treated as a group or mass'. Let's imagine that ten women I have in mind kiss me on ten separate occasions. (Hey, I do get to write these lessons for my own amusement, after all...) I could then say

le pano ninmu cu cinba mi

in which case I'd consider myself quite fortunate. However, if I say lu'o le pano ninmu cu cinba mi, I mean that the ten women kiss me en masse, in which case I would consider myself either blessed or harrassed (maybe I'm a rock star or something.) It does not necessarily mean that each and every woman kisses me; simply that I was mobbed by a group of ten women and kissed by one or (probably) more in the process.
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lu'o le and lu'o lo are very useful concepts, even without explicit numbers, and there are shorter ways of saying each when no number comes between them: lei and loi respectively. So the three men carrying the piano could be expressed as loi nanmu cu bevri le pipno, and the throng of women kissing me (!) as lei pano ninmu cu cinba mi.

For advanced students only: Once you have been involved with Lojban for a while, you will notice that you will see loi a lot, and lu'o lo hardly ever. In fact, by default the expression loi nanmu cu bevri le pipno, without a number, implies that all of mankind was somehow involved in carrying the piano. Strictly speaking, that's true (if three men carried the piano, then Man carried the piano.) But it's not really the most specific way of expressing what's going on.

So how do you get the number 'three' back into an expression like loi nanmu cu bevri le pipno? You cannot say loi ci nanmu cu bevri le pipno, because that means that there are only three men that exist in the universe. You cannot say ci loi nanmu cu bevri le pipno, because the three men act as one mass, and not as three masses. As it turns out (by extension of a little-known mechanism documented in The Complete Lojban Language, pp. 132–133), the way to do it is loi ci lo nanmu cu bevri le pipno: "The mass of three out of [all] men carries the piano."

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Exercise 2

In the following English sentences, are the emphasised nouns individuals (prefixed in Lojban with le or lo) or masses (prefixed in Lojban with lei or loi)?

  1. The students listened to the radio.

  2. The students built a radio.

  3. I bought sugar.

  4. I bought radios.

  5. Elephants live to an old age.

  6. Elephants have flat ears.

  7. The students liked talking about elephants.