scope

[ucleaar <ucleaar@UCL.AC.UK>]

> xorxes:
> Given two quantifiers Q1 and Q2, there are three possibilities of
> subordination:
> (i)     Q1(Q2)  i.e. Q2 subordinate to Q1
> (ii)    Q2(Q1)  i.e. Q1 subordinate to Q2
> (iii)   Q1-Q2   i.e. Q1 and Q2 are coordinate.
> In the case of the men and dogs, (iii) is the round robin,
> and (i) and (ii) are three independent dogs for each man and
> three independent men for each dog, respectively.
> But when the quantifier is {ro} or {su'o}, these three cases
> are degenerate.
[a] > If Q1 is {ro}, then (ii) and (iii) are the same.
[b] > If Q2 is {ro}, then (i) and (iii) are the same.
[c] > And so if both
    > Q1 and Q2 are {ro}, then all (i), (ii) and (iii) are the same,
    > which is right, since multiple {ro}s commute.
[d] > If Q1 is {su'o}, then (i) and (iii) are the same.
[e] > If Q2 is {su'o}, then (ii) and (iii) are the same.
[f] > And so if
    > both Q1 and Q2 are {su'o}, then all (i), (ii) and (iii) are
    > the same.

Just so. As far as I can see, we simply need to decide which is
to be the default (we favour (i)) and how (ii-iii) can be achieved,
in forethought and afterthought. You came up with a neat suggestion
for doing (iii) in afterthought, which somehow relied on (iii)
rather than (i) being the default for innermost or outermost quantifiers
or something or other - obviously I forget the details, but whatever
it was it was nice. As for getting (iii) in forethought, there's
{e} in prenex. For (ii) in forethought you just use the right word
order. For (ii) in afterthought, my proposals of a few weeks ago
form a basis for a solution (which is non urgent, so I'm not at present
too concerned that people found them both confused and confusing).

> pc:
> What is the other quantifier in each case? the other of _ro_ - _su'o_?

Yes, according to me (who speaks without either logji or lojbo authority).

> Or might it be a numeric?

No (again, according to me). The lexical expression {re prenu cu klama}
has the logical form
without the goatleg rule:
  "Ex set(x) & cardinality(2,x) & Ay [member(y,x) -> prenu(y) & klama(y)]"
or with goatleg:
  "Ex set(x) & cardinality(2,x) & Ay [member(y,x) -> prenu(y)]
   & [member(y,x) <-> klama(y)]"
(NB I assume those predicates actually have a number of other places,
which I've not bothered to indicate.)

I keep on saying this because it strikes me as the maximally (and
therefore optimally) simple analysis. Our inventory of logical objects
consists of just two quantifiers, plus predicates, plus variables,
plus constants.

> I take it that "subordinate" here means that the choice of the
> instantiations of the subordinate is a function of/depends
> on the choice for the superordinate.

Yes, at least in as much as it affects the truth of the proposition.

> I guess my problem is what does "the same" mean?

Truth-conditionally.

> While AxAyFxy is equivalent to AyAxFxy (case iii with _ro_?)

Case (i), but Jorge's [c] holds, so it is equivalent to (iii).

> AxEyFxy does not entail (and so is not equivalent to) EyAxFxy, so
> the two do not seem to be coordinate.

Correct. [Please assume the requisite hedges & denials of authority
on my part; I can't be bothered to keep adding them.]

> Similarly, ExAyFxy is not entailed by AyExFxy and so they are not
> equivalent nor coordinate. Or do you have some other sense of
> coordinate in mind?  I do not understand this passage at all.

Here goes. Interpret "Q1" and "Q2" in Jorge's exposition to denote
***LEXICAL*** "quantifiers", i.e. not only {ro} and {suo}, but
also other members of selmao PA.

{ro} gives "A" (universal) in logical form. {suo} gives "E" (existential).
All the other lexical-quantifiers give "E... A..." in logical form, as I
said above.

Now, suppose in syntax you have two lexical-quantifiers, Q1 & Q2
in that order. Here are the logical forms for subordinate and
coordinate scope.

  Q1 superordinate to Q2:
  "Ev ... Aw [member(w,v) -> broda(w)], Ex ... Ay [member(y,x) ->
    brode(y)"
  Q1 subordinate to Q2:
  "Ex ... Ay [member(y,x) -> brode(y), Ev ... Aw [member(w,v) ->
    broda(w)]"
  Q1 coordinate with Q2:
  "Ex, Ev ... Ay, Aw"

This is written in haste. If it needs further clarification, I'll give
it.

And