Subject: On what there isn't

From: [email-masked]
Date: Fri, 27 Sep 2002 13:28:50 EDT

[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.