1.8. The problem of “any”
Consider the sentences
(Combining definite and indefinite numbers into a single number is discussed in Section 1.1.) There is a subtle difference between
Example 1.47
and
Example 1.48.
Example 1.48
tells us that, in fact, there are people who go to the store, and that they walk across the field. A sumti of the type
su'o da poi klama or ro su'o da poi klama
requires that there are things which
klama.
Example 1.47
, on the other hand, does not require that there are any people who go to the store: it simply states, conditionally, that if there is anyone who goes to the store, he or she walks across the field as well. Lojban universal claims alone don't imply the corresponding existential claims. This conditional form mirrors another Lojban translation of
Example 1.47
:
Although
Example 1.49
is an existential claim as well, its existentiality only implies that there are objects of some sort or another in the universe of discourse. Because the claim is conditional, nothing is implied about the existence of goers-to-the-store or of walkers-on-the-field, merely that any entity which is one is also the other.
There is another use of
“any”
in English that is not universal but existential. Consider
Example 1.50.
I need any box that is bigger than this one.
Example 1.50
does not at all mean that I need every box bigger than this one, for indeed I do not; I require only one box. But the naive translation
does not work either, because it asserts that there really is such a box, as the prenex paraphrase demonstrates:
What to do? Well, the x2 place of
nitcu
can be filled with an event as well as an object, and in fact
Example 1.51
can also be paraphrased as:
Rewritten using variables,
Example 1.53
becomes
So we see that a prenex can be attached to a bridi that is within a sentence. By default, a variable always behaves as if it is bound in the prenex which (notionally) is attached to the smallest enclosing bridi, and its scope does not extend beyond that bridi. However, the variable may be placed in an outer prenex explicitly:
But what are the implications of
Example 1.53
and
Example 1.55
? The main difference is that in
Example 1.55
, the
da
is said to exist in the real world of the outer bridi; but in
Example 1.53
, the existence is only within the inner bridi, which is a mere event that need not necessarily come to pass. So
Example 1.55
means
Example 1.56.
There's a box, bigger than this one, that I need
which is what
Example 1.52
says, whereas
Example 1.53
turns out to be an effective translation of our original
Example 1.47. So uses of
“any”
that aren't universal end up being reflected by variables bound in the prenex of a subordinate bridi.