Re: sumti summary

[jorge@phyast.pitt.edu]

Some comments on pc's summary.

> Logical individuals are both unique and atomic, so that no kind 
> of quantifier applies to them: there is only one of each and it 
> has no parts.  The apparent fractional quantifiers for the 
> descriptors of these individuals are to be understood metaphorically
> , then.  pisu'o lo'i broda is not  part of the set of broda but 
> rather another (usually) set, a non-empty subset of lo'i broda. 

I agree with that.

> Similarly, pisu'o loi broda is not a part of loi broda or even 
> the massification of a part of lo'i broda, but the massification 
> of a subset (or , better for now, some collection of possibly less 
> than all brodas. 

I also agree.

> I think it follows from this that the implicit quantifier (if we 
> insist there is one) on lo'/le'i/loi/lei/ lo'e/le'e is _piro_;  

Here is where I disagree. I don't think that follows at all. 
I think {pisu'o loi broda} (as defined above) is an argument
that appears much more often than {piro loi broda} (as defined).

We are much more likely to talk about "some apples" as a mass than about
"all apples" as a mass. The reason why {pisu'o loi plise} is more useful
than {piro loi plise} is the same reason why {su'o lo plise} is more
useful than {ro lo plise}: we very rarely want to talk about all the
apples there are in the universe.

I would also say that {pisu'o lo'i plise} "a set of apples" would be 
more useful than {piro lo'i plise} "the set of all apples", if I thought
that talking about sets of apples was useful at all. Since I don't think
so, outside a discussion of logic or set theory, then I don't care much
which is the default there.  

For the case of {lei}, I agree that {piro} is the best, for the same 
reason that {ro} is best for {le}. In this case, we are talking about 
all of the ones we have in mind, and for definiteness it is much better
that we talk about the whole thing.

> The properties of masses appear best in the whole; whether 
> they carry over to submasses (i.e., massifications of subsets 
> of the set originally massified -- it really is hard not to 
> talk this way, but nothing hangs on it, I think, at this 
> point) is variable with properties and sorts of things 
> involved. 

What properties of masses appear best in the whole? If I say that I 
carry, buy, take, give, ask for, eat some apples, it is clear that 
I'm not talking about the mass of all apples in the universe. 
 
> I take the quantifiers on le/lo (and la?) seriously (logicians gotta) 
> and literally.  That is, I understand any sentence containing such 
> expressions as being general claims about things of the designated 
> kind, not mentioning or referring to any particular ones.  The 
> particular cases are covered only insofar as they fall under the 
> general claim.  Since we can presumably (certainly with le) get the 
> kind designated down to encompassing just the particular cases 
> intended, we lose no assertive power by the fact that we cannot refer 
> directly to individuals.  But the language does get more complicated, 
> because of the necessity of dealing everywhere with quantifier scope, 
> rather than less restrictive direct referential expressions.

Could you give an example where using {le re gerku} as a direct 
referential expression relieves us of the necessity of dealing with 
scope? I can't imagine how that could be possible, unless you mean 
to say that we would interpret it as {lei re gerku}.
 
> [...] Thus, it does seem that the move from embedded 
> expressions of this sort to logical representations, which must pass 
> through the prenex stage, does not pass through that stage simply by 
> pulling the expressions out to prenex position and replacing them by 
> anaphoric argument forms. 

It will be interesting to know what is the mechanism to interpret
the "embedded" expressions. I can't think of anything simpler than
the direct fronting to the prenex.

> For I take it (after months of discussion)
> that the embedded form and the prenex form above do not mean the same
> thing nor even related things on the same path to explicitness (the 
> consensus is that the embedded form covers three men and from three to
> nine dogs, three for each man; the prenex form, by logic, covers three
> men and three dogs, the same for each man).  

I suppose that "by logic" means "by the usual convention used in logic",
since there seems to be nothing illogical with the other possible 
convention. 
 
> On the subject of quantifiers, I take it the standard logic rules 
> apply: the universe of discourse -- the range of unrestricted 
> quantified variables -- is nonempty, as is any explicitly restricting > set, the broda of da poi broda.  Thus, ro implies su'o in all 
> contexts. 

I think that's unfortunate. For the cases when the speaker knows that 
there are no broda, it doesn't really matter much, because no one would 
want to use {ro broda} in that case unless with intent to mislead.

But the problem appears when the speaker doesn't know. For example,
I couldn't say "I promise to pay an extra dollar to everyone who 
finishes their work before noon", unless I am also promising that
at least someone will finish before noon, which is not normally
what I would want to do. 

> _le [n] lo broda_ covers conjunctively (unless specified with _su'o_) 
> [...]  I am not sure whether the [n] has to be explicit: 
> is _le lo broda_ legal?

No, it isn't legal, the [n] has to be explicit.

> I now gather that for xorxes
> lu'a attached to an expression that denotes a mass would be "at least
> one component of that mass".  Thus (I will not keep repeating my 
> caveat "if I understand aright") lua lo'i broda would be, in effect, 
> lo broda.

That's how I understand it, yes.
 
> But also, if _le girzu_ refers to some mass (as it seems to do most 
> often), then lu'a le girzu would cover "at least one component of  
> whatever mass _le girzu_ covers."   If this is right, then this would
> be non-problematic if there is only one group covered, but less 
> comfortable if there are several (at least one component of all = of 
> the massification of the intersection of the underlying sets?) though
> still intelligible and useful (barring the worry about whether any one
> thing is a component of all those masses). 

If there is no such thing, then the speaker is talking nonsense, just
like talking about "the fifth leg of that cat".

> So, if le girzu covered back to le ci gerku, lu'a le girzu would 
> amount to just su'o le ci gerku.  But it is not clear what would 
> happen if le girzu covered le ci nanmu and le ci gerku.

Same thing. At least one of the six individuals.

> Nor is it clear what to do with lu'a le/lo broda generally, i.e., 
> when le/lo broda does not obviously cover masses or sets (xorxes 
> has the set cases working like the mass, with "member" in for 
> "component").  

The problem is analogous to the meaning of fractionators attached 
to these things. I would not use it unless there are indentifiable
components.

> Xorxes' lu'o may seem to agree pretty much with what I took to be the > official line above: lu'o <individuals>  is "at least one mass whose 
> components are <individuals>."  But, for a given bunch of individuals,
> there is only one such mass, of course, 

Unless the individuals are not being referred to, but simply quantified
over. {lu'o ci gerku} is a mass of three dogs, but there are more than
one possible mass of three dogs.

> so the wording leads to the 
> question whether this means that  lu'o lo broda (for example) is loi
> broda or rather takes the implicit su'o into account and so covers 
> mases that have only some of the brodas in, what is elsewhere 
> described as pisu'o loi broda 

That's my intent, yes. With the added benefit of being able to
quantify over them, which is not possible for {[pisu'o] loi broda}.

Jorge