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pc:
> a.rosta@hidden.email writes:
> <<
> Ergo, since I mean "proposition" strictly (I think), the interrogativoid,
> qkau, variety of du'u abstraction -- call it du'u1 -- should be
> expressible on the basis of the variety of du'u -- du'u2 -- that
> expresses properties/relations/incomplete propositions.
>
> 1 {du'u2 ce'u broda} = x1 is the property of being broda
> 2 {du'u2 ce'u broda ce'u} = x1 is the broda relation
>
> 3 {du'u1 ce'u broda} = {du'u ma kau broda}
> = x1 is a (true) completion to {du'u2 ce'u broda}
> >>
> I suppose you meant "should NOT be expressed," though I don't see
> why.
No, I meant "should be able to be expressed" -- there should be a
way to do du'u+Qkau on the basis of du'u+ce'u.
> {du'u makau broda} is the predicate that applies to all
> propositions that fit the form of {makau broda} (NOT just the true
> ones),
I've been writing "(true) completion" because sometimes we need
the 'true' to be there and sometimes we need it not to be there.
So that's a further issue to be addressed later on down the line.
(When we need the 'true' to be there we can say "ge jetnu gi du'u",
but that might prove a bit too cumbersome.)
> so {le du'u la djan broda cu du'u makau broda} is
> transparently true -- assuming {la djan} has a referent -- event if
> {la djan broda} is false. It is thus different from {du'u ce'u
> broda} which is the characteristic function of {broda} or the proerty
> of all true propositions that amount to propositions of the form
> given (I never have worked out which is tidier).
Right, but within these two different types of expression, the
function of makau and ce'u is the same -- it's just a blank, an
unbound variable, an empty slot. The difference between them is
that they signal which type of du'u is involved -- the du'u that
simply inherits the meaning of the bridi within it, or the du'u
that is a set of completions to the bridi within it.
> <<
> I conclude that {du'u1} and {du'u2} should be expressible by different
> cmavo. {du'u1} is the one that deviates from current Lojban, so
> would call for an experimental cmavo ({du'au}, say), if only in order
> to allow for a lexicosyntactic form that is closer to logical form.
> >>
> It seems to me that {du'u ce'u} is the most deviant, though in a
> systematic way(i.e., the other abstractors work in the same way).
You'll need to explain more, since I don't understand this.
> <<
> So how about when ce'u and qkau combine? E.g.
>
> 4 mi se cfila loi du'u ce'u prami ma kau
> "Who I love is a flaw in me"
>
> 5 {mi se cfila loi du'au ce'u goi ko'a zo'u jetnu
> fa lo'e du'u ce'u prami ko'a}
>
> {du'au} has to be in NU because it must have its own prenex; a lujvo
> wouldn't suffice.
> >>
> Why {loi}? If it is a function, then the notion of a cooperation is
> out of place; if a predicate, then just {lo} is enought -- again, no
> cooperation is needed, just the cases that apply (with {mi} in for
> {ce'u} or amounting to that). And, of course, {le} is best of all,
> since you can make truth the deciding factor.
I won't bother explaining my reasons for choosing loi, because I am
not confident in them.
> As for 5, equations in two unknowns are not easy to solve either. I
> suppose that you can define these things this time so that 5 is
> correct, but doubt that that definition will cohere with the next one
> or the last one befoe now.
>
> <<
> I know I'm the only one who cares whether we can say (5), but
> setting that aside, would you agree that (5) serves to express
> explicitly the logical form that (4) is shorthand for?
> >>
> Well, I have serious doubts about defining {makau} in terms of {ce'u}
> (and conversely) because I think that ultimately they have both
> different scope and different quantity ({ce'u} is universal and
> transcendental, {makau} is particular and, if not immannent, then at
> least less transcendent.
I see both ce'u and makau as (as I said above) equivalent to an
unbound variable.
--And.