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On 9/15/06, John E Clifford <clifford-j@hidden.email> wrote:
Well, I do see that the case for {nu} pointing to an intenssional
object is rather circumstantial. So drop that, relieving the need to
find something for occurrences and leaving only the genral
problem of moving from extensional to intensional objects. The rest
of this paragraaph puzzles me: properties and propositions are paradigm
intensional objects, not extensions at all but rather what determines
the extension of the expression in question -- predicates or sentences
as the case might be.
What is "the expression in question" in {lo ka broda}? Is it {broda} or
{ka broda}?
I can see that {lo ka broda} uses in some sense the intension of
{broda}, but surely it refers to the (members of the) extension
of {ka broda}?
It is precisely the whole predicate, {ka broda} or {du'u ti broda}, that
refers to such objects (or rather {lo ...} refers to such objects and the
full predicates are true only of such objects). The objects are the senses
of the inner predicates (as opposed to some set (or bunch) of brodas
which is that predicate's extension).
In other words:
The predicate {broda} has an extension and an intension (let's say it's
a one place predicate for simplicity). {lo broda} refers to the (members
of the) extension of {broda}.
The predicate {ka ce'u broda} also has an extension and an intension
(like all predicates). {lo ka ce'u broda} refers to the (members of the)
extension of {ka ce'u broda}.
If I understand correctly, what you are saying is that {lo ka ce'u broda}
refers to the intension of the predicate {broda}, which happens to be the
extension of the predicate {ka ce'u broda}. But I'm not very clear that
the intension (meaning) of a predicate is the same thing as the property
that an object satisfying that predicate has. When we say that an object
has the property of being blue, we are not saying that the object has the
meaning, or the intension, of the predicate "is blue", are we?
Even if you don't buy into model theory of this sort, the property of being a broda is clearly a different thing from just being a broda, which is what the extension would appear to be.
I know the kind of things that can be said in Lojban about the property
of being a broda, for example that it is had by some object:
{lo ka ce'u blanu cu se ckaji ti}. What kind of thing can be predicated
in Lojban about being a broda, and how do we refer to being a broda?
It seems to me it would be {nu}:
lo nu jbopre cu pluka mi
Being a lojbanist pleases me.
la djan pu troci je snada lo nu mikce
John tried and succeeded at being a doctor.
These predicates don't behave -- in one sense -- any different from
others: the extension of {ka broda is just the property (or properties)
of being a broda and {lo} picks these (this) out. So, {lo ka broda} is
an extesnional expression in one sense; it is intensional only in the
sensse that what it refers to is an intensional object. "intesional
expression" is shorthand for "expression that refers to an intensional
object." How were you using it (or since you didn't use it, how were
you taking me to be using it)?
I'm still not quite sure what an intensional object is. I can understand
what the intension of an expression is (the property of the expression
that one uses in order to figure out what its extension is, the sense or
meaning of the expression), but that can't be what you have in mind here,
because when we want something we don't want a property of an
expression, we don't want a sense or a meaning.
It seems to me that (except when talking about language) we would never
really want to refer to intensions. We would not want a grammatical
converter to create a selbri meaning "x1 is the intension of <predicate>".
A common selbri ({smuni} perhaps?) is all that would be required.
I don't see the connection between intensions and types at all (except, of course, that if types are going to help with the opaque problems, they will be intensional). Indeed, outside of linguistic items I don't see the use of types at all (and I think the linguistic cases can be dealt with without types as well).
For me, the relationships between: the "a" I just wrote - the "a" that is the first letter of the alphabet the flag on the mast with a hole in it - the flag of this country the liquid in this glass - the liquid that freezes at 0 C and boils at 100 C the V3i that my friend bought - the V3i manufactured by Motorola the ant I found crawling on the table - the ant first noticed in California in 1908 John's running, which I'm seeing now - John's running, which occurs every Tuesday are all the same relationship. It makes little difference whether we choose the metalinguistic labels "token"/"type" to talk about this relationship, but I see no reason to treat them differently. Is there some other term that you prefer to cover all those relationships, or is your position that those relationships have nothing in common and thus don't deserve a common label?
Notice, that, if we really need the token type distinction, we can -- as you say -- no single marker will help (even though I think there are absolute tokens, if you start to talk that way) and we can always spell out what we mean as much as need be.
That is my position. I do not propose the type/token distinction to be grammar coded in any way. It is merely a metalinguistic distinction useful in figuring out or describing, in the metalanguage, what things are in a given universe of discourse for a given interpretation. The distinction would hardly ever need to be made in the object language except when used to talk about language.
In particular, if {lo nu...} refers to occurrences, we can use it in various
modalities, whether we bother to mention that or not -- or, indeed, given
Lojban's weakness in this area, even can mention it. I don't see that
token/type can do much more and introduces a messy metaphysics (or
a redundant one).
All I would add here is that we can use {lo broda} too in all the modalities
that we can use {lo nu ...}. There is no need to single the {nu ...} predicate
out from all other predicates.
mu'o mi'e xorxes