Re: opacity and ol' uncle tom cobleigh

[Jorge Llambias <jorge@PHYAST.PITT.EDU>]

Great essay on opacity!

There are two main points I disagree with: Firstly, I don't think it is a
good idea to mix fictional universes with opaque contexts, they seem to
me to be two clearly distinct issues. Secondly, I think we should speak of
opaque references rather than opaque contexts, otherwise we fail to
identify the root of the problem.

>         Unmarked opacity seems to be at the heart of much of the recent
> discussion.

Unmarked in English. In Lojban there is no unmarked opacity ever (at least
in theory), with or without the existece of xe'e.

> Because the globally opaque context, fiction, goes unmarked
> in Lojban (as in most languages), we came to think that _lo_broda_
> referred even when there were no brodas and even though we noted that
> "_lo_<nonexistent> seems to take us to a context where <nonexistent> do
> exist."

Why is fiction globally opaque? Fiction only changes the default universe.
lo <nonexistent> takes us to a context where <nonexistent> exists only if
we accept that the claim is true. It is a chicken-or-egg situation. Do we
have a universe, in which we analyse the truth value of statements, or do
we have true statements, which describe and define the universe?

It doesn't matter what approach we take, the meaning of the sentence is
independent of that. The sentence has a meaning, given a universe we can
decide whether or not the sentence is true, or, given that it is true we
know some fact about the universe.

In practice, since we don't know all there is to know about the universe,
and we don't believe that everything said is automatically true, we make
assumptions. But again, the meaning of a sentence is what we want to be
clear on. Then we can worry about how it fits with the universe, and with
what universe.

But opacity is orthogonal to fiction. In a fictional universe, we can have
transparent and opaque contexts. In the default universe, we can have
transparent or opaque contexts. Tranparency/opacity relate to meaning.
Fiction/reality relate to truth values or universe of discourse.

>         Opaque contexts seem to need three things to fit in with a logical
> language.  First, they have to be marked so that we do not violate logic
> by inappropriate inferences involving them.

Totally agreed. This, I think has been accepted by everybody, because nobody
proposed to let the unmarked form have the opaque meaning.

I don't understand the part about the fiction marker, but I don't see
how it relates to opacity. Opaque references are not the same as references
to fictional objects.

>         The second thing opaque contexts need is a way to get back in
> touch with the real world from within.

My problem with this is that I don't agree that opaque contexts lose
touch with the real world. If I need a box to put my books in, "I"
is a real world reference, "to put my books in" is a real world
reference (for the x3 of nitcu) and "a box" is an opaque reference,
but has not lost touch with the real world, it just isn't an ordinary
reference to at least one box, nothing at all to do with fiction.

> This is part of a general problem
> of afterthought quantifiers and the like, one of the uses of "any" and "a
> certain"  -- and other context leapers --in English. I was sorry to see
> that Cowan withdrew his proposal for _lo_, since it was at least moving in
> the direction of making it -- and its quantifiers, default or expressed --
> into such a leaper, and thus useful again rather than redundant.

Could you explain this? The way I understood it was that the su'o quantifier
of {lo} would come in before all negation or universal quantifiers of the
rest of the sentence, rather than in the order of appearance, i.e. it would
always have maximum scope. This is merely interpreting the quantifiers in
a different order, I don't see how it would help with the opacity question.

> But I
> think that a better plan would be a local mark to indicate jump out of the
> context to the highest level available (and maybe others for steps in
> between?).

But this can be done already by using the prenex. I agree that it is
cumbersome, but it is also not very much needed.

> I realize that I reversed the significance of Xorxes' _xe'e_
> in suggesting it for that purpose, but it catches the general idea  (and
> can we please try it quickly and then give it a real word rather than the
> VERY hard to say experimental _xe'e_?)

It's not so hard :) I was thinking of {ne'e} as its final realization,
but I think I don't like the reversed significance you want to give it.
We don't really need a mark like that, at least I don't see when it would
be useful.

> I am not sure whether such a mark
> can unambiguously be used both to get out of intensional contexts and out
> of truth-functional ones like the antecedents of conditionals and
> negates, the classic home of leapers, but we should try with just one mark
> first.

That's too hard for me to understand without examples.

> Or, perhaps, we can some conventions about at least some
> of these contexts: no one seems to have problems with the opacity of "me"
> in the imperative "Give me a hammer",

Why would "me" be opaque there? I don't think specific references can be
opaque, even if they are inside abstractions. "Give me that hammer" is
likewise not opaque, because both "me" and "that hammer" are specific
references.

That's why I prefer to talk about opaque references, rather than opaque
contexts. It is not the fact that there is an imperative that makes
the sentence opaque. It is the fact that there is a nonspecific reference
inside an imperative, i.e. it is existentially quantified inside,
not outside the abstraction. Universal quantification doesn't seem to be
affected by this.

> but the "hammer" is a problem, since
> I can equally we demand a nonexistent, like Santa asking for a unicorn.

Yes, but the opacity is independent of whether it exists or not. It would
be equally opaque in a fictional universe where unicorns and Santa do
exist. And in "give a unicorn to Santa", the opaque reference is "a
unicorn", while the reference to the equally nonexistent "Santa" is
transparent. In "give that unicorn to Santa", there is no opacity,
although it can only be satisfied in a fictional world.

Jorge