Message-Id: <m0tI7i2-0000ZUC@xiron.pc.helsinki.fi>
Date:         Tue, 21 Nov 1995 23:16:56 -0600
Reply-To:     Steve Hazel <hazel@TURING.CS.STEDWARDS.EDU>
Sender:       Lojban list <LOJBAN@CUVMB.BITNET>
From:         Steve Hazel <hazel@TURING.CS.STEDWARDS.EDU>
Subject:      more on logical issues
To:         lojban@cuvmb.columbia.edu
Content-Length: 2118
Lines: 39

well, i am quite new to lojban, but i can answer a question asked by
jorge llambias in a recent post --

>  All even prime numbers greater than three are multiples of 27.
>  Yes, indeed there are no even prime numbers greater than three.
>
>Is that really bad English?

While the English syntax is not flawed, the logic may be.  The basic question
here, I think, is whether or not it is logical to say that a nonexistant thing
or nonexistant things ("even prime numbers greater than three") can be given
properties ("are multiples of 27").  By the rules of both math and English,
the second statement ("Yes, indeed...") is illogical.  In math, a multiple
of an integer is any number that can be calculated by the multiplication of
that integer by another integer.  Since a nonexistant number cannot be
calculated, there is a logical error in the first statement ("All even
 numbers...") and therefore there is also a logcal error in the second, agreeing
 statement.  In the English statement there is also a logical error.  To say
"indeed there are no even prime numbers greater than three" is to say that
such numbers simply _are not_.  This creates a paradox when paired with the
"yes", which agrees that these numbers "are greater than three" -- English
would indicate that this is false, since such numbers, as stated abo _are not_
at all!
A simple logical reduction of the situation:
 All things in group A are in group B.
 True - Also, things in group A do not exist.
As you can see, it's not very simple at all - the question is:
 "Can group B contain nonexistant things?"
The nuances of the English language make this difficult to express without
creating a paradox in meaning, since the English indicates that things
in group A have to EXIST in group B.  A better wording might be:
 Group B contains all things group A contains.
But I question whether this conveys the origional intent of the statement.
In this case, the answerer is permitted to say, logically, that although
group A is an empty set, group B contains all that group A contains.

Hope this has been at least somewhat helpful.

=Steven Hazel=