Re: [lojban] non-ka properties

[John E Clifford <kali9putra@yahoo.com>]

Part of the problem seems to be with the notion of non-ka properties.  A case 
could be made, I think, that all and only properties are referred to by 
ka-expressions.  There are, to be sure, a large number of other abstract 
objects, often related to properties somehow, which are referred to by 
expressions using other members of KA (and maybe other form classes).  So, the 
first question is, is this a question of whether these other things are also 
properties or whether these -- and ka-properties as well -- ought to be referred 
to using expressions like ce'u and kau, which officially belong elsewhere (or 
here but in more restricted situations: ce'u in functions, kau in indirect 
reference).  


Let's start with things, recognizing that things in Lojban can be of any degree 
of abstractness (and may be of different degrees depending on how you are 
looking at them).  They are referred to by noun phrases: names, descriptions and 
an array of pronoun forms.  In fact, reference to something in this way is what 
guarantees that, for present purposes, it is a thing.

Things have qualities (and maybe quantities as well).  These are referred to by 
predicates (relations are included here),  Strictly speaking, predicates refer 
to Cantorian classes of things, the extension of the property.  To say that a 
thing, referred to by a certain noun phrase (ko'a, say) has a certain quality, 
referred to be a certain predicate (broda), is to say that that thing is in the 
class of things (in the present universe of discourse) referred to by that 
predicate expression.  That is, "ko'a broda" is true just in case ko'a is a 
member of the class referred to by "broda," {x:x broda} (to an acceptable degree 
for fuzzy cases).  Along side this there is also the membership function of 
broda, le ce'u broda (?), which returns a value (in [0-1]) for each object, 
representing the amount that that object is in that class (~ has that property) 
and the characteristic function, le ni ce'u broda (?),  which returns a value in 
[T - F] to indicate, for each argument, how true is the claim that that thing 
has that property.  Neither of these latter things is a property, but rather a 
function from things to numbers (or something like them).  


A property is not only abstract, it is intensional; that is, it takes us out of 
the real world into the Cloudcuckooland of possible worlds (or something else to 
the same effect and less easy to understand).  So, the actual property, 
brodaness, le ka broda, is (say -- we can place this a number of ways) a 
function from possible worlds to classes in those worlds, such that, in each 
world, the class is the extension of "broda" in that world.  So, a property, 
while a function, is neither the membership function nor the characteristic 
function and neither of these is the extension/referent of a predicate 
expression.

There are a mess (literally?) of other intensional objects floating around in 
Lojban: proposition, events and the like.  The two noted are the only ones that 
are likely to be confused with properties, since there are parallels among 
them.  Thus, if ko'a is a member of {x:x broda}, then "ko'a broda" is true, the 
event le nu ko'a broda  obtains and the proposition le du'o ko'a broda is true. 
But notice that the things involved are very different: a physical object (a 
sentence) and two intensional objects, a class of possible worlds and a function 
on functions in possible worlds..

I will assume that I have performed adequately my usual feat of confusing the 
issues completely, but hopefully the answer to these questions is in their 
somewhere (that or the pony).

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