Re: any

[Desmond Fearnley-Sander <dfs@HILBERT.MATHS.UTAS.EDU.AU>]

Hello.  I am new to lojban and this list.  I had intended to be a passive
observer, but feel constrained to contribute to the 'any' debate.  My
interest in lojban springs from the fact that at the level of grammar its
aspirations are very much in sympathy with those of a programming language
we are implementing.  The language is called dr.

A feature of dr is the fundamental role in it of what I call
*indeterminates*.  For example, if a and b are indeterminates of the sort
number, then the *unquantified* sentence
        a^2 - b^2 = (a-b)(a+b)
is true.  a and b are *potential entities* of the sort number.  This may be
the only information we have about them, or we may have total information
about them (such as that a=5 and b=3) or we may have partial information
about them (such as that a is positive).  In each case our sentence remains
true: it is true by virtue solely of the fact that a and b are numbers.  On
the other hand, in the absence of specific information about a and b, the
sentence
        a^2 - b^2 = (a-b)^2
(though a perfectly acceptable sentence) is neither true nor false.  It
becomes true in the presence of the information that b=0, and it becomes
false in the presence of the information that a=5 and b=3.

I believe that indeterminates in this sense play a fundamental role in
everyday reasoning as well as in mathematical reasoning.  Ordinary language
accomodates indeterminates nicely.  The use of 'a box' in the sentence "I
need a box." is an example.  It is a way of referring to something whose
type is known, but about which we have no other information.  Additional
information that may be given serves to pin down what is meant:

"I need a box."
"You mean a cardboard box?"
"Yes."
"Here's one from the attic."
"Great."
"What are you going to do with the box?"
>
The dialogue starts with a total indeterminate (a potential entity of the
sort box) and concludes with an entity that instantiates it.

I do not think that classical logic accomodates or is even compatible with
this notion --- I am going out on a limb here, and might be persuaded
otherwise.  Indeterminates are not constants, and they are not variables,
they require a *typed* language and they do away with the need for
universal quantification.

It would be disappointing to me if lojban did not admit indeterminates in a
simple way, but that's what the debate seems to suggest.  Am I wrong about
this?

I did not catch the beginning of the 'any' debate, so bear with me please
if I'm covering old ground.

Desmond FS

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Desmond Fearnley-Sander
Department of Mathematics, University of Tasmania
GPO Box 252C, Hobart, Tasmania 7001, AUSTRALIA
EMAIL: dfs@hilbert.maths.utas.edu.au
PHONE: (002) 202445 (from in Australia)
                +61 02 202445 (from outside Australia)
FAX: (002) 202867 (from in Australia)
          +61 02 202867 (from outside Australia)
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