Re: quantifiers

[jorge@PHYAST.PITT.EDU]

> pc
> The rule of thumb about masses is that a mass has the sum of the
> properties of its components, where "sum" is taken in a rather broad sense,
> which includes "logical sum"., i.e., disjunction.  So, by that rule, if I buy
> an apple, the mass of all apples (and a large number of its submasses) is
> also bought by me (and so, presumably, I buy it too).

I don't see it. If you sum the property that I buy it, for every component
of the mass of all apples, then the contribution to the sum of my buying
just one of them is insignificant. I don't see any reasonable way of
summing the property of my buying it, for all the apples, and getting as
a result that I buy them all. Almost all of them don't have that property,
so the sum must surely be very close to not having it.

>         Take the present case: "I buy the apples for three dollars."  This is
> pretty clearly about a mass, the three dollars is the sum of the prices of the
> individual apples, which prices are either uniform or weight-dependent (if
> the latter, the individual prices are not calculated but rather we get the
> sum of the weights and price the mass accordingly). But what mass is it?
> Not the mass of all apples, clearly, but just the mass of these apples, the
> ones I bought (offered to purchase, originally).  Buying has a specifying
> effect on what is bought, moving it, in effect, from _lo_ to _le_ (or at least
> _lovi_).

It could just as well be non-specific: "I buy some apples for three dollars."

> But then, it IS the whole of the mass that one buys for $3. So, the
> first maxim of this investigation is to get the right mass to talk about to
> begin with.  Now, loivi plise  is a submass of loi plise and we know that
> the property "bought by me for $3" does not go from submass to mass.

So, by that rule, {mi te vecnu loi plise fo lei ci rupnu} would be false?

I still think that is a reasonable thing to say, and that {pisu'o loi plise}
is the most useful default for {loi plise}. (It is the one that has been
used so far, too. A lot of the use that has been made of {loi broda} would
become wrong if it was taken to be the whole mass of all broda.)


pc:
>         I agree that no one who knows there are no unicorns -- or, as I
> would say, is in a universe of discourse that does not include unicorns --
> would say any sentence with _ro pavyseljirna_ in it.

Ok.

> It follows that
> someone who does say such a thing is in a universe which does include
> unicorns, so the subject is non-empty.

I don't see how that follows. It may be that the one who says such a thing
does not know whether the class is empty or not. This will most often occur
with classes defined in terms of future events that by their very nature
are unknown. Precisely in those cases, we don't want to say that the
universal is false when the class turns out to be empty. If the speaker
knows that the class is empty, then the question does not arise, because
the speaker has no reason to use the universal.

If I say "Everyone who answers all the questions correctly will get an A",
then am I predicting that someone _will_ answer all the questions
correctly? If nobody does, was I lying?

pc:
> For the general point (order determines...) I
> keep having to come back to the point that this is a logical language and a
> certain point, when we get down to the logic, what logic says goes. So,
> scope maybe, but that need not always cover subordination at least in the
> functional sense, and so on.  At least I hope not, or Lojban is going to be
> very hard to be accurate in, much worse than English.

You insist that there is something horribly illogical about the
possible subordination of numerical quantifiers, but you haven't explained
how to accomplish that in the prenex. I really don't see why it would be
harder to be accurate with a subordination convention.

i,n:
> Are you saying that if {le ci nanmu} is a singular term, then
> {le ci nanmu cu batci lo gerku} (or even {li'o... da poi gerku})
> there is only one dog, because there is no universal quantification?
pc:
> My turn not to understand.  _le ci nanmu_ can hardly be a singular term,
> since it says on its face it is about three men, taken distributively (and
> conjunctively).

I think he meant to say "multiple referring term". You have said that
there is such a thing that is different from the universally quantified
one.

> Further, there is universal quantification (presumptively,
> since we haven't bracketted that rule yet in this discussion, that I can
> remember),

But you haven't yet explained (or just give an example) what changes with
or without that rule.

i,n:
> It just so happens
> that in certain circumstances (consecutive particulars, consecutive
> universals, but I don't see it at the moment for consecutive numerics)
> you can prove that the meaning is unchanged by reversing two quantifiers
> - there's a commutative law in effect - and thus the subordination
> is irrelevant.
pc:
> As far as the prenex is concerned, we agree, however much our
> terminology may differ.  In the matrix, however, the common wisdom --
> which I am going along with (willingly in this case) -- holds that the order
> changes things and that even with consecutive quantifiers of the same
> type, nesting makes the later a function of the earlier, i.e., they are not
> commutative.  The consecutive numerics are just a special case of
> consecutive particulars.

Consecutive particulars are commutative in the matrix. {lo nanmu cu
pencu lo gerku} is identical to {lo gerku cu se pencu lo nanmu}.
It is only with numerical quantifiers that there is a possible difference.

Jorge