Message-Id: <m0sdjdZ-0000ZHC@xiron.pc.helsinki.fi>
Date:         Wed, 2 Aug 1995 15:36:59 EDT
Reply-To:     jorge@PHYAST.PITT.EDU
Sender:       Lojban list <LOJBAN@CUVMB.BITNET>
From:         jorge@PHYAST.PITT.EDU
Subject:      Re: quantifiers
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 5096
Lines: 115

> djer:
>         Well, it becomes another story with the introduction of the "cu
> broda".  In my sentence it is just "[ro] lo ci nanmu ku goi da..." The
> predication with pencu is with that second order "da" which is equated
> to "[ro] lo ci nanmu ku".  The parser output demonstrates that the "goi
> da" makes this assignment.

The construction is grammatical, it just doesn't make that much sense.
{da} is a bindable variable (like usually "x" in logic), while {goi} is
used to assign values to fixed variables (like usually "a" in logic).
You are mixing the two things and I'm not sure what you mean by it.

> There is no x or da that stands for one
> individual object in my sentence.

Then using {goi} doesn't make sense. It is used to assign individuals
to fixed variables like {ko'a}.

> >(3a)  EuEv ( u=/=v & prenu(u) & prenu(v) &
> >             & ExEy ( gerku(x) & pencu(u,x) & gerku(y) & pencu(u,y)
> >               & x=/=y & Az ( (gerku(z) & pencu(u,z)) -> (z=x V z=y) )
> >             & ExEy ( gerku(x) & pencu(v,x) & gerku(y) & pencu(v,y)
> >               & x=/=y & Az ( (gerku(z) & pencu(v,z)) -> (z=x V z=y) )
> >           & Aw ( ( prenu(w)
> >             & ExEy ( gerku(x) & pencu(do,x) & gerku(y) & pencu(w,y)
> >               & x=/=y & Az ( (gerku(z) & pencu(w,z)) -> (z=x V z=y) )
> >               -> (w=u V w=v) ) ) )
> >
> >(Probably there are some brackets missing.)
>
> Sorry, my brain cannot parse (3a) past line 5.

The part after line 5 makes sure that no more than two persons touch
two dogs. If you leave that out, it only says that at least two persons
touch two dogs. (The "do" in line 7 should be a "w".) Every w for which
there are exactly two dogs such that w touches them, must either be u or v.

> I think "re nanmu cu pencu re gerku" is more than two ways ambiguous.

I agree, but all the other ambiguities for the literal English involve
masses, so they are not really relevant here. (One third possibility
is that it mean that two different persons for each dog touch each of
the same two dogs, but that would not be acceptable for the unmarked
Lojban expression, because it nests the quantifiers in reverse order.

> I
> am thinking of three scenarios; probably there are more:
>
> I. One man with two dogs takes them for a walk. He meets a friend; they
> pet the dogs.

That's the second interpretation, if the owner pets each dog, and the
friend also pets each dog. The English "they pet the dogs" is looser
than that. It doesn't really require each of the four relationships
to hold.

> II. Two men each walking two dogs meet; they pet the dogs.

Each man pets four dogs? I don't see how you can get this meaning
out of {re prenu cu pencu re gerku}. If each man pets his two dogs only,
then that's the meaning that seems we are finally agreeing on.)

> III. Two men visit the local animal shelter where all the dogs in town
> are quarantined; they pet the dogs.

What dogs? Each man pets all of them? Then again I don't see how you get
that interpretation for {re prenu cu pencu re gerku}. If each man pets
two dogs, then that's the same as II.

> Case three is best handled in second order as sets, in my opinion. If
> you want to see something really ugly (by your standards), I'll try to
> find it and parse it again.

I don't really want to see basic expansions. It is easier if you explain
what you mean. {re prenu cu pencu re gerku} is true if two people each
touch two dogs, whether it is in the animal shelter or in the park where
they meet. The consensus seems to be that the two dogs don't have to be
the same for each person, (but may be the same, of course).

> >(Djer, I wrote down those ugly expansions for your benefit, I hope you
> >like them! :)
> For sure I like them, because my main concern for our new language is
> that it is detached from the parts of predicate calculus that are known
> to work, and that are relatively free of controversy.

It isn't really detached from them. But it is not the case that you can
simply substitute each simbol of predicate calculus with a Lojban word
and get all the meaningful Lojban expressions there are. Lojban is much
richer than that.

> I believe that
> lojban should always mirror the best in logic, and accept whatever
> changes that implies.

I agree.

> That is the strongest foundation for all the
> other marvelous simplifications that lojban affords.  There is a big
> difference between a set of logical rules, and a set of culturally
> defined arbitrary rules; the former is universal and durable, the latter
> is parochial and ephermeral. "Russell's Abomination", the expression of
> number without numbers, has withstood all assaults for almost 100 years
> now and looks as indestructible as the machine of Turing or the theorem
> of Pythagoras. To me, that's beautiful.

To me too. But don't confuse the idea with the symbols you write down.
The idea of how you can represent "the dog bites 44 men" using only
the basic quantifiers is beautiful, the actual formula that you would
have to write down is ugly if anything is.

> Warm regards,
> djer

Igualmente,
Jorge