Re: quantifiers

[Gerald Koenig <jlk@NETCOM.COM>]

>
xorxes pa cusku le di'u

>
>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.

The construction:
1. ro lo ci nanmu ku goi da ci lo gerku ku goi de zo'u tu'e da pencu de

>> 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}.

I have no objection if you want to substitute ko'a for da in the
sentence, with the meaning of they1, and ko'e for de with the meaning
of they2. My point of view is that the parser output is the only
well defined grammar standard at the current moment, and both versions
parse the same. So I don't see the problem with da, but out of respect
for yours and pc's grammatical sensibilities I am using koHa with goi.

The construction means to me (apparently I am talking only to myself):

For each of all three men I call X, for each of the only three dogs
that there are, which I call Y, X touches Y.

I meant for the X and the Y to correspond to the z1 and w1 in pc's
example, but it appears this meaning is not coming across.  In his
example w1 ranged over, represented, w,v, and u which were dogs.

Now that pc has clearly stated that ci broda means all three broda and
that the underlying number explication is the Russell/Whitehead
expression, I would like to go on to a set rendition of his sentences:

pc sentences:
1. for every relevant man z1 and every relevant dog w1, zi touched w1
2. for some relevant man z1 and every relevant dog w1, zi touched w1
etc.
-----end pc sentences
where z1 ranges over x,y, and z; and w1 ranges over w,v, and u. z1 are men,
w1 are dogs.

To convert the Russelian number to a set of three, I say
lo'i ci nanmu                       The set of three men
To extract the members (individuals) of the set I say
lu'a lo'i ci nanmu                  The members of the 3 set;
           also corresponds to the range of pc's z1 variable,
           also called " relevant man"
To assign the above to a pronoun-like expression I say
goi da/ko'a lu'a lo'i ci nanmu      x or it1 standing for one man.

pc 1) would then be

ro lu'a goi ko'a lo'i ci nanmu ku ro lu'a goi ko'e
lo'i ci gerku ku zo'u tu'e ko'a pencu ko'e

Fo each of the individuals, ( aliased as it1) of the set of three men; for
each of the individuals, (aliased as it2) of the set of three dogs, it1
touches it2.

pc has remarked that "each" has has a one by one trait of going over
the range of the variable until all objects are accounted for; it is in
this sense that I interpret this sentence. It really has the flavor of
a prolog predicate to me, where there is recursion. That is it means to
me that each individual ko'a is taken in turn until all are used up;
The same for the ko'e.

The rest of his sentences are similar, just substituting the other
quantifiers for ro. If there is a question about this use of lu'a, the
sentences can still be expressed using cmima, in fact that's the way I
first wrote them. These sentences are not put forth as models in
conciseness. The usual relation between precision and prolixity is in
force.


xorxes> quotes djer>>:
>> I think "re nanmu cu pencu re gerku" is more than two ways ambiguous.
>
>
>> 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.)

I don't mean to quantify "the dogs" with all, getting eight dogs
petted. English doesn't put a default quantifier there. Neither do I
wish to say that each owner pets only his dogs. I just mean each man
could pet his own dogs or there could be a swap, or it could be one
owned and one of the friends petted, or any two dogs could get
neglected and both owners pet the same two dogs. Exactly whose they are
and who does the petting, as well as the number, is indeterminate from
the English sentence. Talk about opaque!

ro lu'a lo'i re nanmu ku goi ko'a  re lu'a lo'i vo gerku ku
goi ko'e  zo'u tu'e ko'a pencu ko'e

({<[(ro BOI) (lu'a {<lo'i [(re BOI) nanmu] ku> <goi ko'a GE'U>} LU'U)] [(
re BOI) (lu'a {<lo'i [(vo BOI) gerku] ku> <goi ko'e GE'U>} LU'U)]> zo'u}
tu'e {ko'a <pencu [ko'e VAU]>} TU'U)

I take this to mean:

For each of two individuals from the set of two men, (hereafter called
they1) for each of two individuals from the set of 4 dogs,(hereafter
called they2); they1 touches they2.

or:
Each individual man from the 2-set of men touches 2 individual dogs
from the 4-set of dogs.
or: Each of the 2 men touches 2 of the 4 dogs.
or: ro lo re nanmu cu pencu re lo vo gerku
(or {<[ro BOI] [lo ({re BOI} nanmu) KU]> cu <pencu [({re BOI} {lo <[vo BOI
] gerku> KU}) VAU]>})

This last has shifted out of set talk.  I had more to say on this but as
I finished saying it my system went down delaying this posting and
losing my comments. I will be off line for a week, hope all have a good
time at lojfest.


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

xorxes:
> >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.  >

djer:
With this classification of the meaning of the sentences I was
trying to get at the number of dogs touched; whether just 2, or 4, and
also the number of dogs that are selected from. pc just told me in no
uncertain terms that there was a big difference between lo ci gerku and
ci lo gerku, namely the size of the universe of dogs, and with my
animal shelter example I am trying to show that. I didn't mean in III
to imply that all the dogs were touched. The difference between II and
III is the number of dogs on the scene who are potential touchees. That
may not matter in this example, but it would if some of the dogs were
rabid.


ro lu'a lo'i re nanmu ku goi ko'a  re lu'a lo'i ro gerku ku goi ko'e
zo'u tu'e ko'a pencu ko'e

({<[(ro BOI) (lu'a {<lo'i [(re BOI) nanmu] ku> <goi ko'a GE'U>} LU'U)] [(
re BOI) (lu'a {<lo'i [(ro BOI) gerku] ku> <goi ko'e GE'U>} LU'U)]> zo'u}
tu'e {ko'a <pencu [ko'e VAU]>} TU'U)


For each individual of the two set of men, tagged ko'a,  for two
individuals of the all-set of dogs, tagged ko'e, ko'a touches ko'e.
V
Each of two men touch two dogs selected from all the dogs there are in
the universe of discourse.
V
ro lo re nanmu cu pencu re lu'a lo'i ro gerku
({<ro BOI> <lo [(re BOI) nanmu] KU>} cu {pencu <[(re BOI) (lu'a {lo'i <[ro
 BOI] gerku> KU} LU'U)] VAU>})
V

Each of the two men touch two ofthe members of the set of all dogs

>
>
>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.

It is not my goal to get all the meaningful lojban expressions into
predicate calculus.  Actually I'm hoping lojban will ultimately be more
expressive than any living natural language. What I would like to see,
however, is that any predicate calculus expression whatsoever be easily
expressible in lojban. It is pretty clear to me we can't put lojban
into first order pc because we are already dealing with sets and second
order predications. I think it would be a big constraint on the
language to try to back translate everything into pc. You may remember
from the language shifter cmavo I proposed last fall though that I think
it would be a good idea to have the capability to confine a word, a
sentence or a discourse to first order language when wanted. It would
prevent getting lost at times in a world of abstractions. I still think
it's a good idea, but probably the least understood and liked of
anything I've proposed on this list.


>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.

You may remember from the "ago" discussion that I agree that
grammaticly enforced long circumlocutions are not my cup of tea.
Actually right now I could use a cup of tea; after composing this long
post I think I finally understand massification; it's the state of my
mind right now. I hope these ideas are more discrete to you.


djer