quantifiers

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

I see I have forgotten to "dot my tease and cross my eyes" >>6)3.  What I
meant was that, while A and I have existential import, E and O do not
(Dodo's system and a better solution to the conflicts within the
"tradition"  -- all with existential import -- than the "modern" version
-- only particulars have import).  Negation shoving (I did not really
think xorxes was concerned with duality, but that was what he said) is now
a snap: not A is O, and conversely, not I is E and conversely (they are
contradic tories as I said).  Obversion will not allow for complete
definitions, since the products have the wrong import: su'o broda naku cu
brode has existential import for brodas, while xu'o (I think that was what
I called it) broda cu brode does not (and conver sely for the opposite
obversions and correspondingly for E and A).  Contrapositives don't work
either, for the same reason -- but we rarely use them anyhow (nor
obverses, for that matter).  Of course, this does give another way for
getting importless form s and the new form is sometimes easier to deal
with than the conditional form, in spite of the fact that it uses double
negations of a sort: no broda cu naku brode versus ro da broda nagi'a
brode (clearly cases where there are advantages are not the simp le
forms).  That is, given TWO non-contradictory forms (contraries,
subcontraries or subalterns), we can define the other two and also all the
forms with the opposite existential import: the complete range of basic
quantifiers.

        This version of the existential import question (version six of
the systematic 16) is, like all of them, a little odd.  While lack of
import comes naturally to E (to say that no S are P clearly is as easily
satisfied by there being no S as by none that t here are being P), the
usual reading of O -- Some S is not P -- seems to force existential import
for S.  Of course, what we often say, "Not every S is P" is a little less
forceful. But xorxes proposed "all except at least one" seems to get
existential im port for S without getting the requisite negative force.
Indeed, it seems almost to force the "some are, some are not reading,"
although I expect that, in Lojban, da'a ro is legal -- and a very backward
way to say no.

xorxes on >pc
> Actually, I would not really take 1a and 1b to mean the same as 1d
> although they turn out to be true on the same occasions (assuming,
> to avoid much more muddling matters, that all the brodas are in the domain
> of discourse or that restriction is to a subdomain).
That's what I meant by "meaning the same". I am not claiming that they
would not have different connotations. What I meant was that in a logical
argument I could jump from any one to the other.
pc:
OK.  But then, since ci da poi nanmu ku ci de poi gerku zo'u da pencu de
"means the same as" ci de poi gerku ku ci da poi nanmu zo'u da pencu de
(and do not even have different connotations that I can think of), and
since, in the latter the dog reference is clearly not in the scope of the
man reference, it must not be so confined in the former either.  That is,
this is just the thing for the three-dog, three-men assertion.  The
reason that this works is because both quantifiers have been overtly
separated from the matrix which joins them, pencu, which, thus, plays no
part in the specification of the ranges of the quantifiers.  In the
simpler form, ci da poi nanmu cu pencu ci de poi gerku, the fact that
the quantifiers are embedded in the matrix forces us to take the matrix
even into account in defining the range of at least the dogs.  Xorxes
claims that this is just one way of specifying how to do it but has
neither proposed an alternate way of achieving the differentiation he
wants (his will not work, as noted) nor shown in what way this proposal
-- which is completely general and motivated by Lojban syntax as well as
logical syntax -- is inadequate nor has he proposed an alternative. The
And proposal involves sets essentially -- and xorxes disapproves of them
-- and -- insofar as it has been spelled out -- does not seem to differ
significantly from my proposal in any other way.  (I hope you, And, will
jump in at this point and show that that last appearance is wrong and
give details).

xorxes on >pc:
> In this case certainly the change is not a superficial one (as it is in
> the parenthetically mentioned case) but a profound one that alters the
> whole underlying structure of the sentence, syntactically and logically.
If you define it like that. My point is that there is no need to.
> Syntactically (one story anyhow, others are parallel) the sentence shifts
> from one with a predicate (pencu) head to one with a quantification head.
Yes, but that may just be two different notations for the same thing.
> Logically, the scopes of the quantifiers are changed (at least -- I think
> rather more is involved).
The simplest definition would be that they not be changed.
 pc: I am not clear just where definitions come into this, once the
grammar of Lojban has been set up, which was done in respense to a number
of factors which have nothing to do with the present problem.  The most
that seems left is to say that this radical change in structure has an
insignificant effect on the meaning of the sentence.  Again, the cases
involved here are but special instances of quite general alterations (or
relationships between two structures) and I think it can be demonstrated
that the general rules under which these fall have generally significant
effects on meaning.  So, what xorxes really needs at this point is a
reason why these few cases should be exceptions.  The simplest case is to
follow the general rule, not introduce an exception.

        All of this does make me long again for referential expressions,
which do spare us all the scoping problems of quantifiers.

sos:
> xorxes:
> I would read it as "there are exactly two men for which there are
> exactly two dogs such that...", i.e. for each of the men.
> pc:
> I do not see why you want to read the "for which" in there, since it is
> not in there.
To make the English clearer
pc:
Why not just use "and," which isn't there either but makes the English
clearer without introducing an extraneous element of subordination?

xorxes:
[I]t is a matter of definition which notation expresses which claim.
pc:
I am not sure that I agree, but if it is, then let us agree to take a
nice simple form -- only appropriately more complex than the simplest one
for the simplest case -- and use it for the other related case. Again I
offer the prenex form, which is about t he right size and is at least
free from obvious defects under existing and independently motivated rules.
pc>|83