Message-Id: <m0qmmxv-00005XC@xiron.pc.helsinki.fi>
Date:         Mon, 19 Sep 1994 13:57:27 EDT
Reply-To:     jorge@PHYAST.PITT.EDU
Sender:       Lojban list <LOJBAN%CUVMB.bitnet@FINHUTC.hut.fi>
From:         Jorge Llambias <jorge@PHYAST.PITT.EDU>
Subject:      Re: any
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 4477
Lines: 116

lojbab:
> A quick skim of your article suggests that your new category of 'objects' may
> match our intended usage for "lo", but I will have to look at it further, and
> maybe ask more questions.

I think it doesn't. It certainly doesn't match the _actual_ usage.

Desmond:
> A feature of dr is the fundamental role in it of what I call
> *indeterminates*.  For example, if a and b are indeterminates of the sort
> number, then the *unquantified* sentence
>         a^2 - b^2 = (a-b)(a+b)
> is true.  a and b are *potential entities* of the sort number.  This may be
> the only information we have about them, or we may have total information
> about them (such as that a=5 and b=3) or we may have partial information
> about them (such as that a is positive).  In each case our sentence remains
> true: it is true by virtue solely of the fact that a and b are numbers.

This is not the case for Lojban {lo}.

For example:

        lo remna cu mamta mi
        A human being is mother to me

is true. Not by virtue of the fact that {lo remna} is a human being, but because
of the fact that there is one human being that is in relationship {mamta}
with {mi}.

> On
> the other hand, in the absence of specific information about a and b, the
> sentence
>         a^2 - b^2 = (a-b)^2
> (though a perfectly acceptable sentence) is neither true nor false.

Sentences with {lo} in Lojban are usually true or false.

For example:

        lo remna cu kalte lo remna
        A human hunts a human

is true only if there really is at least one human that hunts at least one
human. It's not a matter of giving values to each {lo remna}.

If "a" and "b" were replaced by {lo namcu} = "a number" in your sentence,
it would be a true sentence in Lojban, because there indeed exists at least
one "a" and at least one "b" that make it true.

> It
> becomes true in the presence of the information that b=0, and it becomes
> false in the presence of the information that a=5 and b=3.

That sounds like it might be more or less equivalent (at least for some
purposes) to Lojban {le}

        le remna cu mamta mi
        The human is mother to me.

is true if by {le remna} I mean the human who is my mother. In that sense,
you can say that it's neither true nor false in the absence of information
of what {le remna} is referring to, but that information is at least in
principle always obtainable (by asking the speaker who they meant by it).
>From what I understand, your "a" need not have a value obtainable even in
principle.

> I believe that indeterminates in this sense play a fundamental role in
> everyday reasoning as well as in mathematical reasoning.  Ordinary language
> accomodates indeterminates nicely.  The use of 'a box' in the sentence "I
> need a box." is an example.  It is a way of referring to something whose
> type is known, but about which we have no other information.

I think something like that is what I meant by my proposal of {xe'e},
although I don't have it that clear in my mind.


> Additional
> information that may be given serves to pin down what is meant:
>
> "I need a box."
> "You mean a cardboard box?"
> "Yes."
> "Here's one from the attic."
> "Great."
> "What are you going to do with the box?"
> >
> The dialogue starts with a total indeterminate (a potential entity of the
> sort box) and concludes with an entity that instantiates it.

The first two mentions of "box" are indeterminate (one of the sort "box",
the other of the sort "cardboard box"). The last one is an actual box.

In my opinion, as things stand now, we can only refer to the first type
in Lojban within abstractions.

> I do not think that classical logic accomodates or is even compatible with
> this notion --- I am going out on a limb here, and might be persuaded
> otherwise.  Indeterminates are not constants, and they are not variables,
> they require a *typed* language and they do away with the need for
> universal quantification.

I wouldn't know if they do away with it, but it would be nice to have them.

> It would be disappointing to me if lojban did not admit indeterminates in a
> simple way, but that's what the debate seems to suggest.  Am I wrong about
> this?

I think you're right. But maybe it's just me  :)

> I did not catch the beginning of the 'any' debate, so bear with me please
> if I'm covering old ground.

I don't think it is, but even if it were, we need to cover the same ground
many times before we, if ever, become familiar with it.

Jorge