Return-Path: <@FINHUTC.HUT.FI:LOJBAN@CUVMB.BITNET> Received: from FINHUTC.hut.fi by xiron.pc.helsinki.fi with smtp (Linux Smail3.1.28.1 #1) id m0qmZ2N-00005LC; Mon, 19 Sep 94 06:05 EET DST Message-Id: Received: from FINHUTC.HUT.FI by FINHUTC.hut.fi (IBM VM SMTP V2R2) with BSMTP id 5224; Mon, 19 Sep 94 06:03:33 EET Received: from SEARN.SUNET.SE (NJE origin MAILER@SEARN) by FINHUTC.HUT.FI (LMail V1.1d/1.7f) with BSMTP id 5223; Mon, 19 Sep 1994 06:03:28 +0200 Received: from SEARN.SUNET.SE (NJE origin LISTSERV@SEARN) by SEARN.SUNET.SE (LMail V1.2a/1.8a) with BSMTP id 5606; Mon, 19 Sep 1994 05:02:14 +0200 Date: Mon, 19 Sep 1994 13:07:32 +1000 Reply-To: Desmond Fearnley-Sander Sender: Lojban list From: Desmond Fearnley-Sander Subject: Re: any X-To: lojban@cuvmb.cc.columbia.edu To: Veijo Vilva Content-Length: 3021 Lines: 64 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 ---------------------------------------------------------------------------- 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) ----------------------------------------------------------------------------