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--- In jboske@yahoogroups.com, "Jorge Llambías" <jjllambias@...> wrote:
>
> On 9/16/06, pycyn <clifford-j@...> wrote:
> >
> > 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.
>
> "\xBx" is a term, so I can understand what you mean when you say
> that CLL sometimes identifies lo ka ce'u broda with \xBx.
Well, "term" is a relative term: I take you to mean "the thing that
goes in the argument place of a predicate" or "what refers to an
entity" in contrast to "predicate" as "what refers to a truth function
on entities" (or something like that, depending on just how your
metalanguage is set up. The problem is (partly) that Lojban (and
English) is type-flat, expressions of all different types are treated
as the same -- they can all substitute for thing-variables (though
only predicates can substitute for predicate-variables, a Lojban
feature). Thus, "\xBx" is a first-order predicate (refers to a truth
function from individuals -- stricly speaking -- to truth values), but
it can also be an argument to a second order predicate. thus, whether
it is a term or not depends on how it is used. As a predicate, it has
the same referent to "B" (the rule of lambda conversion: \xBx(a) = Ba,
for all a). That "^\xBx" refers to the same thing as "^B" is by
convention (since the fact that two expressions are coreferential does
not normally guarantee that they have the same sense, e.g. "centaur"
and "unicorn" in the real world). In Lojban, {lo ka broda} serves the
term use of "B" or "\xBx" (the latter is better, since it looks more
like a term somehow). At least sometimes. At other times it seems to
perform the term function of "^\xBx," that is, of "^B," referring to
the sense of the predicate (in Montagovian language, a function from
possible worlds to truth functions). The predicate functions
performed, of course, by "B" itself. This makes it somewhat difficult
to read some of the things said about because (Englsih being as flat
as Lojban) it is not clear which of "B" and "^B" is meant -- the same
words having different import in the two cases. I have regularly
taking {lo ka broda} as {^broda}, but I am now wondering whether this
is the best approach (leaving the ambiguity without resolution is
clearly the worst, but we are going to need something for "up,^" in
any case and not yet obviously something for "down, v"). The demotion
of {lo nu...} suggests that B would be a better choice. But some
contexts appear to require intensions (though we know what to do in
those cases) and the analogy with {du'u}, which clearly has to be
intensional, points in the other way.
> If "^X" means " the intension of 'X' " then I can understand what you
> mean by saying that CLL may identify lo ka ce'u broda with ^\xBx
> or with ^B.
>
> But I don't understand what you mean when you say that CLL
> sometimes may identify lo ka ce'u broda with B, because "B" in all of
> this seems to be a predicate, not a term.
See above.
>
> > > 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, in Montague talk again, an intensional object is a function from
possible worlds to whatever it the extensions of whatever kind of
thing involved: a truth function or an individual or a sentence or...
I don't insist on Montague talk; I only use it because I am used to it
and it seems to be pretty standard (even the people with all sort of
perfectly good objections to it at least know how to use it). The old
chestnut about "it can't be an exprssion referring to that type of
thing because we don't want that type of thing" is going to apply in
the same way against your sort of types as well: we don't want the
property or the type, we want a token of that type an embodiment of
that property. OK so here is where down does come in: part of the
working out of the meaning of "want" has to include a down applied to
whatever intensional thing is put there. In English, this step is
hidden because we get only the down version, "a dog," showing. In
Lojban, as a logical language, it makes for greater consistency (and
not having to remember the list) to leave the intension showing.
> > 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.
>
> Yes.
>
> > 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,
>
> That's only problematic if you don't allow the specific thing to be
a type
> (or whatever you want to call it, see below).
But -- as noted above -- I don't mwant a type; I want an ultimate
token. I am not even sure what can be meant by "has a dog type:" how
do it play with it? what do I feed it? And so on through the things I
want to do with a dog. So this theory has a down piece built in, too.
the only virtue of the intension system over the type system is that
the rules of the intesnion system (and how to apply them in the
analysis of natural languages) are at least partly worked out, while
the type theory -- applied outside linguistic objects -- seems at best
only beginning. (I will pass over the issue of whether a type can
actually be a specific thing.)
> > and we can't say we want things of sorts that don't
> > exist at all,
>
> Why not? We can say all sort of things about things that don't exist
> at all. "X wants Y" does not entail "Y exists". That's not paradoxical.
Oh, as you know, exactly the same problem arises with "there is" as
with "there are" -- you can't wish something into the universe of
discourse any more than you can wish it into reality. You can expand
tre universe of discourse, of course, but wanting something doesn't do
it. (Not that the back reference to something you want is not "it
is..." but "it would be...;" the expansion is in a subordiate,
hypothetical world, not in the actual universe of discourse where the
want is expressed. Notice, in the universe where what you is sure to
be, you don't wantit(because you have it), while in the universe where
you want it, it may not be. (Incidentally, the fact that some move
fails in the real world -- where variable range over only the
extension of {zasti} -- means that it fails, since the real world is a
universe of discourse, too.)
> > 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.
>
> We have to admit it as soon as we become aware of the identity, not
> before.
All right, change tht sentence from what you have taken literally to
what was intended, namely that one thing entails the other (whethr we
know it or not).
> If we know that we want X, and we know that X=Y, then we know
> that we want Y. The "problem" here is taking relative identity for
absolute
There is only one kind of identity: "a = b" is true just in case "a"
refers to exactly what "b" refers to. I am not at all sure what is
meant by "relative" and "absolute" then. I see two possibilities --
which come to the same thing and are better expressed by saying what
is going on rather than apparently inventing a new (or even two new)
kinds of identity. 1: a is relatively identical to b if the identity
holds in a particular situation but not all situations (possible
worlds, say) Today John Dillinger is the most wanted man in the
nation, but tomorrow the most wanted man in the nation may be Al
Capone. Absolute identity is when the identity holds in every
(possible?) situation. The largest asteroid is the largest planetoid
(well, it used to be, but now that they are tinkering with
terminology, who knows. 2. Relative identity holds when the expression
are taken as referring to their extensions: a = b, I hit a /I hit b.
Absolute identity holds when the expressions refer to their senses
(it's harder to give examples here because there are so few cases of
identity of sense, the following is tentative depending on what the
Astronomical Union is up to today) the largest asteroid = the largest
planetoid, I am looking for the largest asteroid/I am looking for the
largest planetoid. These come to the same thing, because the sense of
an expression is (Montaguely again) a function that picks out the
referent of that expression in every world. If two sense are the same,
then, they pick out the same thing in each world, and any two
functions that do that are the same. Thre problem arises, then,
because one and the same expression can be used both ways, with no
sure way to tell them apart (before trying some the logical moves, at
least). If we pick the wrong one, we apply an inappropriate further
premise (the identity of the wrong things) and so get the wrong
results. So, the suggestion is, in a logical language, where not
reasoning invalidly is valued as a design goal, we should distinguish
the two possible referents of a single expression into two separate
expressions and avoid the problem.
> identity. The reasoning:
>
> (1) X = Y
> (2) Z wants X
> --------------------
> (3) Z wants Y
>
> is perfectly sound.
Well, it's valid -- it can't bre sound unless both premises are also
true, which is hard with variables.
> When (2) is true and (3) is false, then (1) must be
> false, and if we are tempted to say it is true then we must be using "X"
> and "Y" to refer to something different in (1) than in (2) and (3).
Exactly -- as I have been saying all along. the only issue is
whether, to p[revent this, we refer to the two different things by
different expressions, thereby eliminating the problem.
> > > 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.
Well, I started looking for the relationships among the various pairs,
rather than that between the first and second member of each. but I
caught on after another sentence or two.
> I thought that's what I said: "For me, the relationships between: <list>
> are all the same relationship."
>
> > 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.
>
> Right. So if I say "this is a picture of the ant first noticed in
California
> in 1908" there shouldn't be any intensional context problem with it
as long
> as we are able to figure out the pertinent extension of the
predicate under
> the circumstances.
This seems to suggest that the type-token distinction is some how
related to the extension-intension distinction. I don't see any
reason to think that, but I may have missed something. I do gather
that you want to use the type-token distinction to solve some problems
for which I would use intension-extension. Since, to solve the
problems, types will turn out to be intensional entities, this seems
to me only to be either redundant or superfluous, not wrong.
> > I see that they all have something in common, but I don't see it as
> > being so 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 broda} 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).
>
> I agree, of course. The label in itself is inconsecuential, but it
seems to
> be pretty standard, so why not use it?
It is standard for dealing with linguistic items, what (if anything)
carries over to other realms is not clear. Nor is it clear that it is
needed even for linguistic items -- given that we already have
properties and generality modes.
> To summarize:
> Intensional contexts can be characterized by three "anomalies"
> (according to
<http://plato.stanford.edu/entries/intensional-trans-verbs/>):
> (1) failure of interchange of identicals
> (2) ambiguity between "specific" and "unspecific" reading of the object
> (3) failure of existential commitment
Well, I tend to equate 2 and 3 since they are both easily seen as
consequences of scope differences -- is the quantifier inside or
outside the context.
> (1) is resolved by not confusing relative identity with absolute
identity.
That is by noting that the expression refers to its referent or to its
sense.
> Two things can be the same F while remaining two separate logical
objects.
> (<http://plato.stanford.edu/entries/identity-relative/>)
What does this mean? Are there ordinary objects and logical objects?
What sort of thing is the latter? I suppose this means that two
different senses may bring us to the same thing. So, once we see that
the issue is about the senses, not the thing, the problem disappears
(this latter is more clear than talk of logical objects, which is at
least misleading where it is not simply muddled).
> (2) is resolved by allowing that the referent of an expression can vary
> with context in the type-token axis. The "specific" reading
corresponding
> to the "token" reading, and the "unspecific" reading to the "type"
reading.
> (<http://plato.stanford.edu/entries/types-tokens/>)
The specific-general axis does not seem to have any relevance here,
though I assume you are going to show how it does. This seems just to
be a consequence of an external reference (specific) versus an
internal one. the latter is general only in the sense that it cannot
be taken as pointing to anything in the domain (since the objects
referred to are feom a different domain).
> (3) is resolved by not confusing membership in the universe of discourse
> with existence. Members of the universe of discourse are not required
> to satisfy the predicate {zasti}. Mentioning something does not commit
> one to its existence.
Sorry, the existence trick doesn't really work. If the move fails
when the quantifiers mean "exist," since that restricted domain is
also a domain. But, in fact, the move fails for the broader domain as
well, since the things you want don't enter the domain where you are
wanting. That is, wishing won't create what you want (sorry 'bout that).