1.6. Variables with generalized quantifiers

So far, we have seen variables with either nothing in front, or with the cmavo ro in front. Now ro is a Lojban number, and means “all” ; thus ro prenu means “all persons” , just as re prenu means “two persons”. In fact, unadorned da is also taken to have an implicit number in front of it, namely su'o , which means “at least one”. Why is this? Consider Example 1.9 again, this time with an explicit su'o :

Example 1.33.

su'o	da	zo'u	da	viska	mi
For-at-least-one	X	:	X	sees	me.

Something sees me.

From this version of Example 1.9 , we understand the speaker's claim to be that of all the things that there are, at least one of them sees him or her. The corresponding universal claim, Example 1.16 , says that of all the things that exist, every one of them can see the speaker.

Any other number can be used instead of ro or su'o to precede a variable. Then we get claims like:

Example 1.34.

re	da	zo'u	da	viska	mi
For-two	Xes	:	X	sees	me.

Two things see me.

This means that exactly two things, no more or less, saw the speaker on the relevant occasion. In English, we might take “Two things see me” to mean that at least two things see the speaker, but there might be more; in Lojban, though, that claim would have to be made as:

Example 1.35.

su'ore	da	zo'u	da	viska	mi
For-at-least-two	Xes	:	X	sees	me.

which would be false if nothing, or only one thing, saw the speaker, but not otherwise. We note the su'o here meaning “at least” ; su'o by itself is short for su'opa where pa means “one” , as is explained in Section 1.1.

The prenex may be removed from Example 1.34 and Example 1.35 as from the others, leading to:

Example 1.36.

re	da	viska	mi
Two	Xes	see	me.

and

Example 1.37.

su'ore	da	viska	mi
At-least-two	Xes	see	me.

respectively, subject to the rules prescribed in Section 1.1.

Now we can explain the constructions ro prenu for “all persons” and re prenu for “two persons” which were casually mentioned at the beginning of this Section. In fact, ro prenu , a so-called “indefinite description” , is shorthand for ro DA poi prenu , where “DA” represents a fictitious variable that hasn't been used yet and will not be used in future. (Even if all three of da , de , and di have been used up, it does not matter, for there are ways of getting more variables, discussed in Section 1.1.) So in fact

Example 1.38.

re	prenu	cu	viska	mi
Two	persons		see	me.

is short for

Example 1.39.

re	da	poi	prenu	cu	viska	mi
Two	Xes	which	are-persons		see	me.

which in turn is short for:

Example 1.40.

re	da	poi	prenu	zo'u	da	viska	mi
For-two	Xes	which	are-persons	:	X	sees	me.

Note that when we move more than one variable to the prenex (along with its attached relative clause), we must make sure that the variables are in the same order in the prenex as in the bridi proper.