Message-Id: <MAILQUEUE2-102.931013191607.480@hylkn1.Helsinki.FI>
Date:         Wed, 13 Oct 1993 13:41:59 -0400
Reply-To: Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Sender: vilva
From: Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Subject:      Re: Lean Lujvo and fat gismu
To:         lojban@cuvmb.cc.columbia.edu
In-Reply-To:  <199310131538.AA17016@access.digex.net> from "Art Protin" at Oct
              13, 93 10:50:00 am
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mi'e .djan. .i la .art. cusku di'e

> I wonder if John is trying to confuse me.

Never.

>  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.

"a great many" is not synonymous with "all".  I was referring specifically
to your definition of "heap", which I find unsatisfactory.

> 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".

Ah.  I should have specified that I (since it was I who introduced
negation into the discussion) was referring to logical (i.e. contradictory)
negation.  "X is not blue" means "It is false that X is blue" here and
throughout, as distinct from "X is non-blue", (i.e. scalar negation).
Loglan has never made this distinction properly, but Lojban does: "na"
is logical negation only, so "ko'a na blanu" means "It is false that X is blue".

> 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".

All this can be done with the current place structure of "barda", which is
"x1 is big in dimension x2 by standard x3".  The x3 place serves the purpose
of your "some scale of my choosing", but explicitly rather than implicitly.
By using a reference scale rather than a reference object, we avoid
negation paradoxes, because a scale can still exist even when a reference
object does not:  "Andromeda is big on-scale galaxies".

The color gismu don't have an explicit place for the standard, but one
can be added using a BAI tag such as "ci'u" (on scale ...) or "le'a"
(in category ...) or "ci'e" (in system ...).

>     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.

No such luck, I'm afraid.  There is no way to tell by inspection alone
whether the key predicates of an argument are vaguely or precisely defined.
Formally, "dilcu" (x1 is the quotient of x2 and x3 with remainder x4) is
indistinguishable from "derxi" (x1 is a heap of material x2 at location x3),
although one can be precisely defined and the other not.

--
John Cowan              sharing account <lojbab@access.digex.net> for now
                e'osai ko sarji la lojban.