Subject: Re: [lojban] Tidying notes on {goi}

From: [email-masked]
Date: Sun, 29 Jul 2001 14:56:26 EDT

In a message dated 7/28/2001 10:02:29 PM Central Daylight Time, 
[email-masked] writes:

> But {da'o} clears the references of all pro-sumti, xy included.
> My objection was to {da'o}, not to {da goi xy}.
> 

I misunderstood your point, I think, and got off on a craziness of my own in 
addition. I could, I suppose, defend myself on a loophole (pc resorting to 
cauistry! How shocking!) by noting that {da'o} is only listed as clearing 
KOhA and GOhA and {xy} is BY. But we will want to clear the other as well, 
short of {ni'o} and this seems the right way to do it. So, how else can I 
get what I want here. The answer seem to lie in the matter of scope of 
quantifiers. xorxes has made one suggestion, which goes against 16:14 (pp 
410-1). On the other hand, it fits in nicely with 7:13 (p. 162): "bound 
variable prosumti generally last until rebound," which then points to 16 for 
details. (That same section has a discussion of {da'o} supporting its more 
general cancelling role.) But 16:14 actually says that generally the scope 
of a bound variable carries over ijeks but not over {.i} alone -- although no 
one holds that that too strictly in informal style (talking here aways about 
bridi level -- i.e., officially prenex -- placement, not buried in abstracts 
or relatives [! is this right? another part of the problem to look at] ). 
Further, the shifty ones that started this whole problem have absolutely 
shortest scope for their shifted meaning (whence the {ge...gi...} in my 
example). Thus in {ci da darxi reda leda canpa}, the shovel(s) pertain(s) to 
the three, not the two, for the scope of the reda is just its occurrence, not 
anything around it:
{ci da re de zo'u da darxi de leda canpa} (except that the reda probably 
can't be fronted as things are now set up). 
I screwed up on {da'o} even if I were right about what it cleared, since I in 
fact just wanted to clear the variables used in the general claims being 
brought into the proof from outside (we need to consider the effects of 
{da'i} on quantifier scope -- it clearly does not go from in to out and only 
sometimes from out to in) so that they would not affect the internal 
vartiables. But the {.i} rule would do that and generally if we want to go 
beyond that scope with variable, we are actually working with some kind of 
instance, wherther introduced by {goi} or not, so that we can do with those 
short scope rules.

<xy works everywhere you would use the bare
da within the scope of the original quantifier. Sticking a second
quantifier on xy would be incorrect from my point of view. Sticking
a second quantifier on da would recycle that variable as a new one,
but as a bonus you keep the poi-restriction of the original so you
don't have to repeat it.>

This isn't by the Book, of course, and parts of it are shakey altogether. 
{xy} is an autonomous term, however it came into the discourse, so it ought 
to be quantifiable in any way -- why would it be the only kind of term not? 
The recycled {da} with the same restriction would be handy sometimes, but 
almost as suspect as the subquantifier version (which may, come to think of 
it, having been aiming at something like this after all). And we have a 
variety of other -- an better -- ways to do the subquantifier trick and 
probably the "same restriction" cases as well (sweeping the mess into the 
obscurity of just what {le} and {lo} mean -- for which obscurity we are at 
least occasionally very thankful). 

The problem of really good ways to deal with pluralities, especially those 
where the members appear first in different structural places, remains and 
is, as I said, much more important that the quibbles in a corner about 
quantifiers. xorxes has a start; can it be genralized to a fulness (not -- 
ever in Lojban -- a completeness)?