quantifiers

["John E. Clifford" <pcliffje@CRL.COM>]

xorxes:
(3)     Ex Ey ( Ez broda(x,z) & Ez broda(y,z) & x=/=y &
                Aw ( Ez broda(w,z) -> (w=x V w=y) ) )
I must admit that I am not familiar with standard logic notation
other than the basic stuff so I accept that. But then is there no
standard shorthand for (3)?  The shorthand expressed by (1) must
necessarily be for (2)?
pc
re da zo'u da broda de
is probably right for (3): each da might have a different de, which seems
to be the crucial point.

xorxes:
What would this be:
(4)     reda zo'u su'ode zo'u da broda de
I suspect this should be more like (3). Maybe using two prenexes like
that is the answer? My initial reaction to that is a heartfelt "ptui",
but maybe that's how it is.
pc:
I am unsure what a double prenex might mean (aside from being a literal
contradiction).  I suppose it says something about the relative scopes,
which may be the issue.  I'll agree to the ptui for sure.

sos:
[> P]utting Lojban
> quantified sumti (which is damned near all of them) in Lojban prenex
> position rather than embedded is a clarifying notational device. That
> does not mean, however, that the clarifying device has to consist
> simply in taking the sumti out of the matrix and putting it in prenex
> position and putting an appropriate anaphora sumti in its old place.
Nor does it necessarily mean that it has to be something more complicated
than that!
pc:
True, but given that there are more embedded structures than
simple prenex structures, it seems likely that most embedded structures
will have more complicated prenex structures than simple fronting.  But,
if there is only one quantified expression embedded or if all of them are
universally quantified, they do simple front (I think -- but I'll bet
someone knows a case where...)

xorxes:
Somewhat as an aside, one has to be careful with the "general rule"
about how to expand {e}. For example:
        lo prenu cu prami la djan e la meris
does not expand to:
        lo prenu cu prami la djan
        ije lo prenu cu prami la meris
but rather to:
        lo prenu cu prami la djan
        ije py prami la meris
pc:
Right, since repeating the lo prenu literally would change the meaning of
the embedded part (to a possibly different selection from the prenus).  I
am not sure that that difference applies to the earlier case, however,
since there it is precisely the form establishing the identity of the
referents that is to be separated out.  I suspect that what I said was the
result -- ci lo nanmu e ci lo gerku zo'u ny pencu gy goes to ci lo nanmu
zo'u ny pencu gy ije ci lo gerku zo'u ny pencu gy -- is not quite right,
 but I do not see a clear way to do this without losing the intended
independence of  ci lo gerku.  ci lo nanmu zo'u ny pencu ci lo gerku
ije... fails in just that way (ci lo gerku is subordinated to ci lo
nanmu again) though at least there is no free anaphoric term floating
around without an antecedent.

xorxes:
You say that standard logical notation favours
the coordinating case in this instance, but the subordinating case is
real as well, and since it is arguably the most common, perhaps it should
get the more convenient notation.
pc:
But we agree that the subordinating case, the nine-dog pat, has the easier
Lojban form: ci lo nanmu cu pencu ci lo gerku.  We were looking for a
relatively easy form for the other, three-dog pat.  The LOGIC of the nine
dog pat is harder, but the Lojban is not.

sos:
> I cannot, at this point -- and
> can't imagine that there was a time when I could -- explain to someone
> who does not seem the difference between referring directly to an
> individual and making a general claim about all or some individuals of a
> certain kind what that difference is,
Ah, but you are changing the question! Referring directly to an individual
is not the same as referring directly to several individuals. Lojban's
claim that it doesn't distinguish between plural and singular falls apart
if you limit descriptions to singular reference.
What you never explained is how something like {le re gerku} can be
different if taken as a universal quantification or as a direct reference
to two individuals.
You said that the two interpretations of {le pa gerku}, universal
quantification and singular reference, were at least equipollent
(if I got the word right). Why not the same for {le re gerku}?
pc:

Referring directly to several individuals is just like referring directly
to one individual only you do it several times in quick succession: John
and Bob and Harry and....  Hey, I said I can't seem to do this for even
one individual, so why complain that I can't do it for several.  I can
say a bit about what the effects of the difference is and the first of
these would be that I could stop worrying about those damned scopes, for
reference is a fixed item once and for all (as far as the context goes,
anyhow).  We have these two guys in all their particularity (even if
they are not identified) and we can talk about them.  With the
quantified version all we can say is that there are two guys that
satisfy and increasingly more complex set of conditions; we never get to
talk about the guys because we never get to them.  We keep describing
more and more what such objects must be like but never get to the
objects themselves, whereas the referential usage starts with the
objects as given and then tells us more and more about them.  In the
reconstruction, we are not in the scope of a quantifier, then, but
simply stringing along the same referring expression as needed.  Now, if
the tale we tell about the things we are referring to is true, then the
corresponding existential claim (binding up all those referring
expressions with particular quantifiers  - or universal if we pick the
right class to restrict to) is true also.  And, if the quantified form
is true then there are somewhere some guys of the kind such that
 if we replaced the variables by expressions referring to them we would
again get a true tale. And, if our predicates are rich enough, we can
probably specify which critters to use for this telling almost
perfectly. So all the facts get covered either way (and all the fictions
too, of course) but they are covered in different ways and the work of
doing the quantifier way is markedly greater -- in most cases -- from
that of the referring way. The number of things to be quantified in or
referred to does not matter, except that the larger the value on the
quantifier the more complex the underlying logic becomes, progressing
geometrically (or nearly), while adding a new referent requires but a
single addition at the point of introduction, while new quantifier
s require changes all over the place: in the non-identities (often more
than one set of these), in the requantifyings, and so on as well as in
the prenex where the introduction is made.  Ah yes, the other advantage:
no prenexes needed, since referring expressions can occur in matrices.
pc>|83