Message-Id: <199310121914.AA23449@eli.CS.YALE.EDU>
Date:         Tue, 12 Oct 1993 15:12:46 -0400
Reply-To: Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Sender: Lojban list <LOJBAN%CUVMB.bitnet@YaleVM.YCC.YALE.EDU>
From: Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Subject:      Re: Lean Lujvo and fat gismu
To: Erik Rauch <rauch>
In-Reply-To:  <199310121800.AA24499@access.digex.net> from "Art Protin" at Oct               12, 93 01:57:00 pm
Status: RO

mi'e .djan. .i mi pu cusku di'e

> > It is this sort of fuzziness which caused the Lojban engineers
> > to remove the comparative places from many gismu.  As Art Protin
> > recently posted, Loglan "groda" historically meant "x1 is bigger
> > than x2 by standard x3" and "x1 is big" was interpreted as "x1
> > is bigger than something-unspecified".  (Institute Loglan has
> > never had an equivalent of "zo'e").
>
> > This gimmick breaks down in many cases, though: "x1 is not big"
> > obviously cannot be so rewritten.

la .art. cusku di'e

> 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.

> Also, the "heap paradox" seems very lame.  A heap is not precisely
> defined and then a formal proof fails because of this imprecision
> does not strike me as a really interesting paradox.  The
> proof/paradox falls apart if I define a heap as
>
>         a gravitationally stable aggregate of items such that
>         there is no 2 available dimensional view that permits
>         precise counting of the constituent items.

(I presume this means "available 2-dimensional view".)

> Then the heap ceases to be a heap when the constituent items
> can be counted either because enough have been removed or
> those items have been rearranged to distinguish each item.

Sorry, this definition is no more precise than the intuitive meaning.
Consider the notion of being able to count N objects precisely just by
looking at them.  For values of N up to six, this is easy for anyone.
If the objects are properly arrayed, N can be much larger; it is easy
to count the 48 stars on the pre-1958 American flag because they are
arranged in a 6 x 8 array.  Zacharias Dase, the calculating prodigy,
could accomplish the feat for N=43 (sheep in a field).  Nonetheless,
for N=10000, no one can count the objects.

But nevertheless, there is no value k which represents the exact boundary
between what is and what is not countable, such that a "pseudo-heap" of k
objects is countable, whereas a "true heap" of k+1 objects is not.
Therefore, the paradox returns.   There simply is no lower limit on the
size of a heap.

(Reply to Dave: I was, of course, dealing with the intuitive notion of a
heap, not any computer-science sense of the term.  The CS heap has all
sorts of properties which do not apply to the physical heap -- the terms
represent at most polysemy, and probably full homonymy, like the algebraic
vs. the physical uses of "ring".)

> 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.

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