Re: The Distribution Problem

[CJ FINE <C.J.Fine@BRADFORD.AC.UK>]

On Tue, 1 Dec 1992 protin@com.usl wrote:

>
> The distributive property does not derive from the meanings of the
> words being grouped but from the meaning(s) of the connectors.

No, it doesn't.  It derives from the meaning of tanru-modification.

Consider the meaning of predication and tanru modification from the point
of view of formal (Montagu) semantics.


In this formulation, a selbri is a mapping from a tuple of possible sumti
to {FALSE, TRUE} - in other words, a characteristic function on tuples of
sumti (-referents).
            n
        b: S  -> {T,F}

[There are two different ways in which this function can be regarded
as a set. Either, in the universal interpretation of mappings, it can be
treated as a subset of the cross-product of the set of tuples and {T,F};
or more usefully it can be identified with that subset of the set of
tuples which it maps to T. All these ways of describing it are equivalent].

Then giheks are the ordinary set operations on these functions, thus
"gi'e" is the intersection of the functions (or their corresponding
subsets). Since the functions are characteristic functions, the range of
the resulting function is the intersection of the ranges of the selkanxe.

A jek in the seltanru of a tanru, or a selbri which is not a tanru, works
in the same way.

But when we get to the tertanru, we have an entirely different semantic
operation involved.

Tanru modification is a restriction of the function (or its equivalent
set). The nature of the restriction is (explicitly) not defined in the
language - all that is defined is that the range of a tanru is a (not
necessarily proper) subset of the range of its seltanru.

This means that there is NO GENERAL SPECIFIABLE RELATION whatever between
the range (characteristic set) of the tertanru, and that of the tanru.
Given that there is no general relation, it is clearly unreasonable to
expect the relation that happens to exist in particular cases to
distribute over jek-connection. It may happen to do so - but that will
depend on the meaning, not only of the particular terms used, but also of
the tanru modification in the case.

So where does this leave us?

I believe that it is not in general valid to distribute a jek in the
tertanru (it works in the seltanru). You are free to use
        cmalu je nixli ckule
in a distributive sense, when the nature of the modification you intend
lends itself to this; but I, as hearer, have as much freedom as in any
tanru to interpret it differently.

Note one implication of this: if you assume that jeks can be distributed,
it appears to make sense to allow them to modify the seltanru in different
ways.  My argument shows that this in invalid.
Thus
        cmalu ckule gi'e nixli ckule
may certainly mean 'small school for girls', but I suggest that it is
perverse to allow
        cmalu je nixli ckule
to mean the same thing, because it is very hard to find a meaning to
attach to the constituent "cmalu je nixli" that allow this. I suspect that
this is a bigger problem for our use than the original point Iain made.

        Colin

I haven't yet managed to work out, in this theory, why jeks do not work
properly in selgadri.  I will give it some more thought.