From LOJBAN%CUVMB.BITNET@UBVM.CC.BUFFALO.EDU Fri Dec 22 04:32:35 1995
Reply-To: Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Date: Fri Dec 22 04:32:35 1995
Sender: Lojban list <LOJBAN@CUVMB.BITNET>
From: Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Subject:      du'u continued
To:         lojban@cuvmb.cc.columbia.edu
Status: OR
Message-ID: <_rmqWu7qXcH.A.RtF.nu0kLB@chain.digitalkingdom.org>

And, Cowan, and whomever wrote:
>> > > So duu is really a one place predicate, denoting a class of sentences.
>> > > Or rather, duu is used in a range of one-place predicates, each of
>> > > which denotes a class of sentences.
>> > Or rather still, "du'u" is used in a range of two-place predicates, each
>> > of which relates a class of propositions (not sentences) to the sentences
>> > which express the proposition.  (Again, "proposition" = "0-adic
>> > intension".)
>>
>> This is what I was denying, I think. Here goes again: {duu} is used in
>> a range of 2-place predicates, each of which relates a proposition to
>> the sentences that express the proposition. This is tantamount to
>> a 1-place predicate, just as "cousin of John" is effectively a 1-place
>> predicate - the x2 of "cousin of John" is of course John, so it seems
>> a bit pointless to have "le se cousin-of-John" to refer to John.
>
>Having read what we said very carefully, I think that you are right and
>I am wrong, but I am by no means certain.

If du'u is a one-place predicate then "da du'u broda" has some
properties - is it a relation, a sentence or what?  I'm not sure what a
"class of sentences" is, alas, but I am sure that "da" is NOT a class,
though all possible values of da might be members of a class.

There are an infinite number of Lojban sentences that express any
particular relation.  (Take any sentence and insert "sese" before the
selbri, and you have another sentence for the same relation.)  So with
have a relationship between an infinite set sumti and a single sumti.

Now perhaps the argument is that we have no non-self-referential way to
fill in the x1 of "du'u bridi" i.e. we are forced to say "le du'u bridi
cu du'u bridi", and hence the sumti place is meaningless.  Actually
rather, we are converting a grammar structure that is a bridi into a
particular kind of a sumti, which is what all the "LE+NU" constructs do.
But of course the fact that we are dealing with different grammatical
categories alone makes the "conversion" worthwhile AND gives us another
way to fill in the place.  We CAN say "ko'a du'u bridi", and thereafter
ko'a is a sumti that has the properties of representing both a bridi
relationship, and indirectly the infinite set of sentences that stand
for that bridi.

lojbab