Re: quantifiers

[jorge@phyast.pitt.edu]

(This goes to pc with cc to Lojbab and John Cowan, not to the list.)

I read the summary you sent to Lojbab, but we didn't have occasion of
discussing it much during Logfest. I had some comments about it, mainly
about what is the most useful default quantifier for {loi}, and about
{lu'a <individuals>}, but I didn't bring my copy of your post with me.
Could you send me one if you still have it?

It was suggested during Logfest that these discussions were too arcane
for the list, and might be too intimidating for some people. I think
John Cowan is going to set up a special list for these arcanities, 
meanwhile here is my answer. (It is not very clear that anybody else
is reading this anyway.) 

> 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....  

Supposing that {la djan} refers directly to one individual, that would 
be something like {la djan e la bab e la haris}. But aren't the logical
manipulations on that term exactly the same as the ones that apply to the
quantified form {ro le ci nanmu} ? 

My question is: supposing that {le ci nanmu} is not universally
quantified, but is rather a "multiple referring expression", i.e. just
like a singular term but with more than a single referent, then how is
any expression containing {le ci nanmu} with this referring 
interpretation any different from the same expression as a universally 
quantified term? 

I don't see any possible difference. {la djan e la bab e la haris 
cu batci lo gerku} is just like {ro le ci nanmu cu batci lo gerku}. 
I don't see what is the difference that referring is supposed to 
make. The same thing with {la djan a la bab a la haris cu batci 
lo gerku} and {su'o le ci nanmu cu batci lo gerku}.

> 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). 

Could you give an example where using {le ci nanmu} with the referring
interpretation would save us from worrying about scopes?

> 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. 

I think that with {le} you do get to them. The only way that the 
listener knows what the speaker means by {le re nanmu} is if they 
agree on what the two referents are. The description by itself is 
not much more than a clue, since both speaker and listener know that 
there are many more men than the two in question. When using {le}, 
the quantifiers range over particular referents. If you call the 
form "John and Bob and Harry" direct reference to individuals, then
so should be "each of the three men in question".  

> 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. 

That's the case for {lo}, because indeed the description should be
in that case our only guide as to what objects we are talking about.
But for {le} that cannot be the case, since the objects are not
identified by the description alone. The description is merely a
way to refer to them. The only reason that we can't say that 
{le broda} is a singular term is that it may refer distributively 
to more than one object, which is precisely what singular terms 
don't do. But I don't see the problem in seeing {le <n> broda} as
a string of <n> singular terms connected with {e}.   

> In the
> reconstruction, we are not in the scope of a quantifier, then, but
> simply stringing along the same referring expression as needed. 

How can that be possible? {la djan e la meris cu ponse lo mlatu} 
expands to {la djan cu ponse lo mlatu ije la meris cu ponse lo mlatu},
so {lo mlatu} is under the scope of {la djan e la meris}. The only
way that we can ignore the scope is if the sentence is not expandible,
which is the case for masses: {la djan joi la meris cu ponse lo mlatu},
in which case the first term is indeed a singular term. That would 
correspond to {lei re prenu cu ponse lo mlatu}, which can't be expanded.
But I don't see what you mean by "stringing along the same referring 
expression" when it is not a singular term. Scope will always be 
relevant when the referrents are more than one and taken distributively.

> 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. 

But when using {le} we don't need to specify our objects with any 
precision. The listener is taking more into account than the mere
description in order to know what we mean. (Indeed, the description 
need not even apply, although in general to be useful it has to apply.)

> 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. 

Again, I ask for an example where taking {le re broda} as a referring
expression simplifies anything. I don't see how it could.

> Ah yes, the other advantage:
> no prenexes needed, since referring expressions can occur in matrices.

But in Lojban no prenexes are needed for the quantifier case either.

Jorge