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``Who Did You Pass On The Road? Nobody'': Lojban And Logic
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Consider the English sentence
8.1) Anyone who goes to the store, walks across the field.
Using the facilities already discussed, a plausible translation might be
8.2) ro da poi klama le zarci cu cadzu le foldi
All X such-that-it goes-to the store walks-on the field.
Everyone who goes to the store walks across the field.
But there is a subtle difference between Example 8.1 and Example
8.2. Example 8.2 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 ``ro da poi klama''
requires that there are things which ``klama'': Lojban
universal claims always imply the corresponding existential
claims as well. Example 8.1, 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. This conditional form mirrors the true Lojban translation
of Example 8.1:
8.3) ro da zo'u ganai da klama le zarci
gi cadzu le foldi
For-every X: if X is-a-goer-to the store
then X is-a-walker-on the field.
Although Example 8.3 is a universal claim
as well, its universality 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
8.4) I need any box that is bigger than this one.Example 8.4 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
8.5) mi nitcu da poi tanxe
gi'e bramau ti
I need some-X which is-a-box
and is-bigger-than this-one
does not work either, because it asserts that there really is
such a box, as the prenex paraphrase demonstrates:
8.6) da poi tanxe
gi'e bramau ti zo'u mi nitcu da
There-is-an-X which is-a-box
and is-bigger-than this : I need X.
What to do? Well, the x2 place of ``nitcu'' can be filled with an event as well as an object, and in fact Example 8.5 can also be paraphrased as:
8.7) mi nitcu lo nu mi ponse
lo tanxe poi bramau ti
I need an event-of I possess
some box(es) which-are bigger-than this-one.
Rewritten using variables, Example 8.7 becomes
8.8) mi nitcu lo nu da zo'u
da se ponse mi gi'e tanxe
gi'e bramau ti
I need an event-of there-being an-X such-that
X is-possessed-by me and is-a-box
and is-bigger-than this-thing.
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:
8.9) da poi tanxe
gi'e bramau ti zo'u
mi nitcu le nu mi ponse da
There-is-an-X which is-a-box
and is-bigger-than this-one such-that
I need the event-of my possessing X.
But what are the implications of Example
8.7 and Example 8.9? The main
difference is that in Example 8.9, the
``da'' is said to exist in the real world of the outer bridi;
but in Example 8.7, the existence is only
within the inner bridi, which is a mere event that need not
necessarily come to pass. So Example 8.9
means
8.10) There's a box, bigger than this one, that I needwhich is what Example 8.6 says, whereas Example 8.7 turns out to be an effective translation of our original Example 8.1. So uses of ``any'' that aren't universal end up being reflected by variables bound in the prenex of a subordinate bridi.
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Previous
Grouping of quantifiers |
``Who Did You Pass On The Road? Nobody'': Lojban And Logic
The Lojban Reference Grammar |
Next
Negation boundaries |