From pycyn@aol.com Fri Sep 27 10:28:54 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_1_1_4); 27 Sep 2002 17:28:54 -0000 Received: (qmail 41163 invoked from network); 27 Sep 2002 17:28:54 -0000 Received: from unknown (66.218.66.217) by m1.grp.scd.yahoo.com with QMQP; 27 Sep 2002 17:28:54 -0000 Received: from unknown (HELO imo-m02.mx.aol.com) (64.12.136.5) by mta2.grp.scd.yahoo.com with SMTP; 27 Sep 2002 17:28:54 -0000 Received: from Pycyn@aol.com by imo-m02.mx.aol.com (mail_out_v34.13.) id r.5a.124d96ed (4529) for ; Fri, 27 Sep 2002 13:28:51 -0400 (EDT) Message-ID: <5a.124d96ed.2ac5ef52@aol.com> Date: Fri, 27 Sep 2002 13:28:50 EDT Subject: On what there isn't To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_5a.124d96ed.2ac5ef52_boundary" X-Mailer: AOL 7.0 for Windows US sub 10509 From: pycyn@aol.com X-Yahoo-Group-Post: member; u=2455001 X-Yahoo-Profile: kaliputra --part1_5a.124d96ed.2ac5ef52_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit [Long intro, skip to * or **] So, I was in Hay-on-Wye, a town on the Welsh boder (I think on the Welsh side, but don't quote me). Virtually the entire business district of this town is used and remainder book stores -- maybe three or four blocks ( a concept that makes no sense in England) on each of three streets, with some connectors as well. My wife was tracing down Elizabeth Goudge and was looking for what struck my fancy (and, it turned out, dictionaries of British place names and of Chinese characters that give the order of strokes -- to improve the look of my blocks and get me to a vague understanding of script). But what struck me was a copy of Non-Existent Objects, by Terry Parsons, a book I had heard of but never seen before. And cheap (even if I wasn't already in the "this is just monopoly money" mode -- which cost me when I got the conversions on my bills). * What Parsons has done is devise a logical system -- which he shows consistent -- in which non-existent objects can play fairly normal roles (as they seem to do in English, say). Thus, Sherlock Holmes and the golden mountain and a round square can all turn up in ordinary sentences -- and be quantified over, without shifting worlds or whatever other trick we try in explanation. Especially without introducing descriptions that do strange things when a search through the universe fails to turn up anything matching that description. In the process, he provides mechanisms for dealing with dealing with a number of points that have troubled our discussions of late: generic sofas, the Jeanie I dream of (but can never find), and so on. Of course, this treatment may not always be what we want, nor are all the problems dealt with -- intensional contexts remain at best partially solved, for example. And, all of this comes at a price -- a more complicated predicate system, with some rather surprising rules. Here is a brief overview to see whether it is worth working into Lojban. ** {roda zasti} is a Lojban tautology -- and is unexpressible in normal formal logic, where it is incorporated into the symbolism. This arises out of a confluence of two notions: "To be is to be the value of a variable" (Quine) and that being and existing are the same thing (not Quine, though he clearly agrees, with most logicians, at least since Russell). What happens if we allow quantified variables to range over things that do not exist? With a little care, not much, but the little bit is often helpful. We begin by distinguishing between nuclear and extra-nuclear properties and relations. While the line is often fuzzy, we can point to some cases of clearly extranuclear predicates, mostly old problematic ones: ontological ones like "exists" or "is fictional," modal like "is possible," intensional like "is thought about by Parsons," and siome new new that arise within the system itself like "is complete." Most other properties are neclear (at least until proven otherwise) and, further, every extranuclear property has a "watered down" version which is nuclear. Interestingly, relations in this theory are composed of properties, what we would call the various ways of plugging the relation, filling all the places but one with particulars. That aRb holds is then the conjunction of the claims that a has the property of being R to b and that b has the property of being Rd by a. The joker here is that, while for existing things these two claims always go together, for non-existing thing, they need not. Relations which have only nuclear properties in them ar nuclear (well, there may be some exceptions even here). Now what doesn't exist? The starting point is to allow that correponding to every set of nuclear properties (the empty set being iffy) there is an object. Some of these objects exist, most don't. Among the ones that don't are first of all the incomplete ones, the ones that do not have, for every nuclear property P, either P or its complement. In short, every object corresponding to a set that does not have a member of every complementary pair of properties. And, on the flip side, the overcomplete things, those whose set contains both members of some complementary pair. With those out of the way, most of what is left are possible things and so may exist or not, depending on the luck of the draw. They are just complete, but that doesn't guarantee their existence. If a thing does exist, then it has as noted all the components of any relation of which it has one and the full version of any watered down extranuclear property it has. This points to one philosophical nicety: a non-existent object can have the watered down version of existence -- so that we can talk about an existent gold mountain, for example -- but still not exist, have the extanuclear property of more or less the same name (to the dismay of at lest one verison of the ontological argument). Some useful non-existents. Sherlock Holmes, the object which correponds to the set of exactly those properties ascribed to him in The Canon. He is a native character in those books, but he may turn up as an immigrant character in others, where yet other properties are claimed for him. It is only at this point that we switch over to saying "in the book" about these further properties. In The Canon itself, London appears as an immigrant character, so has properties attributed to it "in the book" which it does not actually have. (There is also a London that is a native character in the book and so has exactly the properties attributed to it by the book. This is, of course, not really London but its surrogate, like it insofar as what properties it has goes -- but it, like Sherlock, is radically incomplete.) The generic sofa. This might well be the object corresponding to the set containing exactly the property "is a sofa." The interesting question then becomes how to ascribe proeperties to this non-existent object in ways that tell us something about existent ones -- and possible one, too. The theory does not deal with those questions, but provides a variety of frameworks for them. Other interfaces between existents and non-existents come with fairly clear rules. For example (a major one), existing objects never bear any nuclear relation to non-existents, though what we would normally take as the converse does not hold. Thus, though Holmes might have the proprety of being knighted by Queen Victoria, Queen Victoria does not have the property of having knighted Holmes (though her surrogate would). This means that what look to be relational statements need to be approached with care, since, when one term refers to a non-existent, either one of the component sentences is intended and so the sentence true or false depending on which one, or the whole is meant and the sentence false. (I assume, in fact, that the interpretation is normally the one that at least opens the possibility of truth: Holmes does not, in fact, have the property of being knighted by Queen Victoria, but it would usually be wrong to claim that "Queen Victoria knighted Holmes" was to be read in either the full relational sense or as about a property of Queen Victoria.) Some of Parsons' solution to problems are not built iinto the system or have feasible alternatives, so that, once non-existent object are allowed in the language, we can play with the details quite a bit. --part1_5a.124d96ed.2ac5ef52_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit [Long intro, skip to * or **]
So, I was in Hay-on-Wye, a town on the Welsh boder (I think on the Welsh side, but don't quote me).  Virtually the entire business district of this town is used and remainder book stores -- maybe three or four blocks ( a concept that makes no sense in England) on each of three streets, with some connectors as well.  My wife was tracing down Elizabeth Goudge and  was looking for what struck my fancy (and, it turned out, dictionaries of British place names and of Chinese characters that give the order of strokes -- to improve the look of my blocks and get me to a vague understanding of script).  But what struck me was a copy of Non-Existent Objects, by Terry Parsons, a book I had heard of but never seen  before.  And cheap (even if I wasn't already in the "this is just monopoly money" mode  -- which cost me when I got the conversions on my bills). 

* What Parsons has done is devise a logical system -- which he shows consistent -- in which non-existent objects can play fairly normal roles (as they seem to do in English, say).  Thus, Sherlock Holmes and the golden mountain and a round square can all turn up in ordinary sentences -- and be quantified over, without shifting worlds or whatever other trick we try in explanation.  Especially without introducing descriptions that do strange things when a search through the universe fails to turn up anything matching that description.  In the process, he provides mechanisms for dealing with dealing with a number of points that have troubled our discussions of late: generic sofas, the Jeanie I dream of (but can never find), and so on.  Of course, this treatment may not always be what we want, nor are all the problems dealt with -- intensional contexts remain at best partially solved, for example.  And, all of this comes at a price -- a more complicated predicate system, with some rather surprising rules.  Here is a brief overview to see whether it is worth working into Lojban.

**
{roda zasti} is a Lojban tautology -- and is unexpressible in normal formal logic, where it is incorporated into the symbolism.  This arises out of a confluence of two notions: "To be is to be the value of a variable" (Quine) and that being and existing are the same thing (not Quine, though he clearly agrees, with most logicians, at least since Russell).  What happens if we allow quantified variables to range over things that do not exist?  With a little care, not much, but the little bit is often helpful.

We begin by distinguishing between nuclear and extra-nuclear properties and relations.  While the line is often fuzzy, we can point to some cases of clearly extranuclear predicates, mostly old problematic ones: ontological ones like "exists" or "is fictional," modal like "is possible," intensional like "is thought about by Parsons," and siome new new that arise within the system itself like "is complete."  Most other properties are neclear (at least until proven otherwise) and, further, every extranuclear property has a "watered down" version which is nuclear.  Interestingly, relations in this theory are composed of properties, what we would call the various ways of plugging the relation, filling all the places but one with particulars. That aRb holds is then the conjunction of the claims that a has the property of being R to b and that b has the property of being Rd by a.  The joker here is that, while for existing things these two claims always go together, for non-existing thing, they need not.  Relations which have only nuclear properties in them ar nuclear (well, there may be some exceptions even here). 

Now what doesn't exist? The starting point is to allow that correponding to every set of nuclear properties (the empty set being iffy) there is an object.  Some of these objects exist, most don't.  Among the ones that don't are first of all the incomplete ones, the ones that do not have, for every nuclear property P, either P or its complement. In short, every object corresponding to a set that does not have a member of every complementary pair of properties.  And, on the flip side, the overcomplete things, those whose set contains both members of some complementary pair.  With those out of the way, most of what is left are possible things and so may exist or not, depending on the luck of the draw.  They are just complete, but that doesn't guarantee their existence.

If a thing does exist, then it has as noted all the components of any relation of which it has one and the full version of any watered down extranuclear property it has.  This points to one philosophical nicety: a non-existent object can have the watered down version of existence -- so that we can talk about an existent gold mountain, for example -- but still not exist, have the extanuclear property of more or less the same name (to the dismay of at lest one verison of the ontological argument). 

Some useful non-existents.
Sherlock Holmes, the object which correponds to the set of exactly those properties ascribed to him in The Canon. He is a native character in those books, but he may turn up as an immigrant character in others, where yet other properties are claimed for him.  It is only at this point that we switch over to saying "in the book" about these further properties.  In The Canon itself, London appears as an immigrant character, so has properties attributed to it "in the book" which it does not actually have.  (There is also a London that is a native character in the book and so has exactly the properties attributed to it by the book. This is, of course, not really London but its surrogate, like it insofar as what properties it has goes -- but it, like Sherlock, is radically incomplete.)
The generic sofa.  This might well be the object corresponding to the set containing exactly the property "is a sofa."  The interesting question then becomes how to ascribe proeperties to this non-existent object in ways that tell us something about existent ones -- and possible one, too.  The theory does not deal with those questions, but provides a variety of frameworks for them.

Other interfaces between existents and non-existents come with fairly clear rules. For example (a major one), existing objects never bear any nuclear relation to non-existents, though what we would normally take as the converse does not hold.  Thus, though Holmes might have the proprety of being knighted by Queen Victoria, Queen Victoria does not have the property of having knighted Holmes (though her surrogate would).  This means that what look to be relational statements need to be approached with care, since, when one term refers to a non-existent, either one of the component sentences is intended and so the sentence true or false depending on which one, or the whole is meant and the sentence false.  (I assume, in fact, that the interpretation is normally the one that at least opens the possibility of truth: Holmes does not, in fact, have the property of being knighted by Queen Victoria, but it would usually be wrong to claim that "Queen Victoria knighted Holmes" was to be read in either the full relational sense or as about a property of Queen Victoria.) 

Some of Parsons' solution to problems are not built iinto the system or have feasible alternatives, so that, once non-existent object are allowed in the language, we can play with the details quite a bit.
--part1_5a.124d96ed.2ac5ef52_boundary--