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--- In jboske@yahoogroups.com, "Jorge Llambías" <jjllambias@...> wrote:
>
> On 9/15/06, John E Clifford <clifford-j@...> 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 general
> > problem of moving from extensional to intensional objects. The rest
> > of this paragraph 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}?
Yes, which is/are the property/ies of being a broda, that is, (a)
certain intensional object(s), properties.
> > 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}.
Yes, though the intensions of these particular predicates are
inherently less interesting, since the diversity tends to decrease
rapidly as one goes up the up hierarchy.
> 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?
>
We are generally not saying that in the sense that that way of saying
it comes from a different conceptual system. It is generally thought,
however, that in fact the two items are the same. They can be
represented separately, however, if there is some reason to do so (not
too easily in Lojban, which is surprisingly poorly set up for this).
It has to be admitted right now that the way that CLL, for example,
talks about {lo ka (ce'u) broda} also gets a couple of notions
somewhat confused: sometimes identifying it (apparently) with \xBx and
sometimes (though it rarely says explicitly) with ^\xBx, i.e., with B
and ^B. As to the "has" idiom, it is so vague that it is not clear
just how it is to work except that "x has the property of being blue"
means "x is blue" and {ckaji} is no clearer.
> > 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 extensional expression in one sense; it is intensional only in the
> > sense that what it refers to is an intensional object. "intensional
> > 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.
Well, that depends upon what you take the relation of wanting to be
between. One end is clearly a person, a wanter. The other end
appears to be an object or an event. But when we apply this answer in
its most literal way, it turns out paradoxical: we can only say we
want specific things, as it were, not just anything that happens along
of the right sort, and we can't say we want things of sorts that don't
exist at all, and if we say we want one thing, we also have to admit
we want everything identical with that thing (even though the identity
is unknown to us) and so on. None of these seem true of wanting as we
experience it. So, wanting, however we may express it, is a different
relation -- presumably one from a wanter to a different thing or else
a much more complex relation between a wanter and a thing. The
general solution has been to take the first course, because the second
requires introducing a whole new class of relations which, when
finally sorted out, can best be explicated using the first procedure.
Because the sorts of problems that arise if we take the second place
of the relation to be a thing are just the sort of problems that arise
when an intensional object is treated as an extensional one, the
obvious change of object is from an extensional object to its closest
intensional one, the sense of the expression used to describe it, as
it were. As is apparent, the relation between what is going on and
what we say about it is rather close and so it is not perhaps
surprising that properties turn out to be (or are usually taken to be)
also the senses of predicates. The most obvious alternative is to
take it to be a propositional function, but that turns out to be
extensional which ever way it is defined (to a truth value or to a
set). There may be other alternatives, but they do not seem to have
been explored in the relevant contexts (i.e., for logics) and what is
said about them ? Platonic Ideas, for example ? seem reflected pretty
well in the property = sense approach. (I have to admit that things
are getting a little crowded on the first abstract level here ? never
mind intensional ? in that we have ? not necessarily distinct ?
senses, properties, propositions, events, propositional functions,
sets and probably a few more. And I am not sure how to sort them out
? and not sure anyone has.)
> 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.
Well, the point is simply convenience. If we often want to say "the
intension of ?" (and terms are at least as common ? maybe more so ? as
predicates) a simple device would be nice. And it does appear that we
do often want at least to be able to say "the intension of?." For
example, although we may fudge it, we want to be able to say {mi djica
[the intension of] lo gerku}, where that intension is presumably the
individual concept that is the sense of {lo gerku} and probably turns
out, when all is said and done to be lo ka gerku (or at least some
member of that bunch).
> > 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.
None of these things are relationships, so I assume you mean the
relationship between the first of them and the second in each case.
They seem to be cases of reference to a specific member of the
extension of some predicate and a reference to a more extended
referent class ? what one depending upon what you want to say about
these items (and sometimes a very amorphous set altogether, if what
you want to say is sufficiently vague. But there don't appear to be
two different sorts of things here, just the extension of a predicate
under various circumstances.
> 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?
I see that they all have something in common, but I don't see it as
being some special as to deserve a label and a lot of metaphysical
talk about it. Working out what are the circumstances under which the
expression we use (suppose we use something like {lo broad} for all of
them) works in one way rather than another is an interesting question;
whether to call it a token or a type is not (unless that is a
shorthand ? or muddled ? way of asking the circumstances question).
>
> > 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.
Here it seems we differ. I think that what you seem to be covering
with tokens and types is often very important in the object language:
it makes a difference whether I am taling about a few elephants in
that enclosure over there or (perhaps in a very different way, though
with the same words) about elephants past, present and yet to come,
here, there, and everywhere else that elephants are (or were or will
be) ? or someplace in between. And I want to be able to be explicit
about what I am doing, without actually going into all the details ?
which I often could not really do even if so inclined).
> > 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.
Yes, that follows. We can use{lo ka ?} similarly, but that does not
produce anything much new ? except for a changing extension,
properties have a rather uneventful life.