Message-Id: <MAILQUEUE2-102.931012192100.288@hylkn1.Helsinki.FI>
Date:         Tue, 12 Oct 1993 13:20:02 -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: Veijo Vilva <VILVA@viikki21.helsinki.fi>
In-Reply-To:  <9310121706.AA19359@getafix.oasis.icl.co.uk> from
              "I.Alexander.bra0125@oasis.icl.co.uk" at Oct 12, 93 06:06:07 pm
Content-Length: 1544
Lines: 36

mi'e .djan. .i la .i,n. cusku di'e

> Pardon my ignorance, but what on earth is the "heap" paradox?

mi fraxu do la'edi'u

The "heap" paradox is as follows.  Consider a heap of sand grains.  It is
obvious that if we take away a single grain, we still have a heap.
So we have the materials for a mathematical induction:

        BASE: This particular pile of sand is a heap.
        RECURSION: If a pile of sand is a heap, the same pile of sand
                with one less grain is a heap.

We can repeat the recursion step until we have left only a single grain,
and we seem to be committed to saying that this single grain is still a heap!
Worse yet, we can remove the last grain as well, leaving a "heap" with
zero grains of sand.  This is an offense against common sense.

Another version of the same paradox works up from below rather than down from
above.  "1 is a small number, and if any number is small, so is its successor.
Therefore, all numbers are small."

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.

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