Message-Id: <199310131537.AA05729@eli.CS.YALE.EDU>
Date:         Wed, 13 Oct 1993 10:50:00 EDT
Reply-To: protin@USL.COM
Sender: Lojban list <LOJBAN%CUVMB.bitnet@YaleVM.YCC.YALE.EDU>
From: Art Protin <protin@USL.COM>
Subject:      Re: Lean Lujvo and fat gismu
To: Erik Rauch <rauch>
Status: RO

I wonder if John is trying to confuse me.  He quotes me and
comments:

>> The cleanup of the definition of small is more difficult,
>> but again a precise proof with imprecise terms should always
>> be suspect.  Any kind of nonsense can be shown with those.
>
> Exactly.  The point is that a great many natural-language
> predicates are inherently vague, not subject to formal
> definition.

but before that he quotes and comments:

>> I am afraid I don't see this.  Either of the two forms seem to
>> make sense:
>>
>>         X [is] not bigger-than [something-unspecified]
>>
>> and
>>
>>         X [is] reverse-relation bigger-than [something-unspecified].
>>
>> (or reordered for English speakers "[something-unspecified] [is]
>> bigger-than X").
>
> Doesn't work.  To deny that something is big is not the same as to
> deny that there exists something else which it is bigger than.
> I deny that a mouse is big, but I affirm that a mouse is bigger
> than something (e.g. a fly).

> Similarly with the colors.  Loglan "blanu" meant "x1 is bluer
> than x2", but Lojban blanu is just "x1 is blue", because "X is
> not blue" does not mean "There does not exist a Y such that X
> is bluer than Y", nor does it mean "For all Y, X is not bluer
> than Y".  The latter (universal) reading would construe "The
> sky is not blue" as true, because it is not as blue as a
> color-chip displaying focal blue.  The former (existential)
> reading would construe "Leaves are not blue" as false, because
> the color of leaves is closer to focal-blue than, say, the color
> of McIntosh apples.

First he presents something seemingly formal and then says
somethings are vague and not subject to formality.

First, the holes in the formality.  Why do you imagine that
the negation of the relation affects the existance of an
unspecified reference.  I use "not" in "X [is] not bigger-than
[something-unspecified]" to affect only the relationship
"bigger-than".  I am specifying that there exists a Y
such that X is not bigger than Y.  In computerese, "not"
placed immediately before the relationship binds to the
relationship, in this case, "bigger-than".

Now the bigger issue :-).

Big is an informal, fuzzy, relative type of concept.  Loglan
denied metaphysical absolutes and dealt with appearences.
What you said and the order in which you mentioned things
conveyed the focus and relative importance of your claims.
"X [is] bigger-than [something-unspecified]" can be true of
any X, but so can "X is big".  This has nothing to do with
the "[something-unspecified]", but is due to the relative
nature of the concept "big".  Thus, "X [is] not bigger-than
[something-unspecified]" is true of all X, since there can
always be found something bigger than X to be the unspecified.
Thus the claims "X [is] not bigger-than [something-unspecified"
and "X is not big" are more than sufficiently the same: "by
some scale of my choosing, X is not big enough for me call
X big".  The "[something-unspecified]" is something I can
choose, even after the fact, that represents a point close
to the threshold that I used to claim "X is not big".
The something-unspecified is any something that can make the
statement correct.  I said the thing.  I meant the thing.
I don't lie.  And I can select explicitly or implicitly
the thing that makes the statement correct.  And the
something-unspecified does not have to exist in reality,
it can exist in my imagination.  And I am not interested
in any language that requires excessive precision where
I don't want to be precise.

    An aspect of logical-ness of Loglan was that it was
supposed to express only the precision desired and to make
that degree of precision obvious.  Thus, informality was
obviously informal, and formal proofs obviously had all
the precision needed.  I liked that.  It was supposed to
make things like the "heap paradox" so obviously imprecise
as to be immediately discounted as proofs.

    thank you all,
    Art Protin


Arthur Protin <protin@usl.com>
STANDARD DISCLAIMER: The views expressed are strictly those of the author and
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