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RE: [jboske] Opacity and belief
> I figured out, after much reading of philosophy papers, what the trouble
> is with quantifying into belief contexts (i.e. using a variable declared
> in an outside prenex within the du'u bridi). It rests on whether du'u
> in Lojban is transparent or opaque
I thought it had been decided by uncontroversial consensus that it is
opaque, as a by-product of the well-motivated rule that quantifiers
export to the prenex of the localmost bridi in left-to-right order.
However, read on, because we possibly understand different things
> Cicero is Tully. That is, la kikeron. du la tulius. The predicates "me
> la kikeron." and "me la tulius." are true of the same (singular) object,
> namely Marcus Tullius Cicero, the greatest Roman orator. The sentence "la
> kikeron. du la tulius." is true because the contexts of "la kikeron." and
> "la tulius." are both *transparent*: equals can be replaced with equals
> *salva veritate* (preserving truth values)
> Now the *sentences* "Tully is bald" and "Cicero is bald", viz
> la kikeron. krecau" and "la tulius. krecau" are distinct. The sentence
> "lu la kikeron. krecau li'u du lu la tulius. krecau" is false, because
> the contexts of "la kikeron." and "la tulius." are both *opaque*: equals
> cannot be replaced with equals *salva veritate*
> What we haven't nailed down is the abstract bridi "du'u la
> kikeron. krecau" and "du'u la tulius. krecau"? Are these true of
> different (noematic) objects, or of the same object? The difference is
> important because Ralph, who does not know that Cicero is Tully, believes
> (i.e. is disposed to assent to the claim) that Cicero is bald but does
> not believe (i.e. withholds assent from the claim) that Tully is bald
Partly it depends on whether we say that Cicero and Tully are
intensionally equivalent, i.e. synonymous, or merely extensionally
equivalent. For Clark Kent and Superman, I think it is clear that
they are not synonymous. For Cicero and Tully, or Jorge/xorxes,
Nick/nitcion, Bob/Lojbab, it's harder to argue that they aren't
synonymous -- mere unconditioned allomorphs, in a certain sense
--, in which case we are talking not about which du'u Ralph believes
but rather which sedu'u Ralph would give the thumbs-up to.
> If Lojban beliefs de dicto work like this, as seems plain, then
> we must conclude that lo du'u la kikeron. krecau cu na du lo du'u
> la tulius. krecau, because the two du'u clauses refer to different
> propositions. What's different about them is not the referents of the
> singular terms "la kikeron." and "la tulius.", but the way in which
> those referents are referred to (the so-called "mode of presentation")
> If du'u-contexts are truly opaque, then we don't know what it means to
> insert variables in them that are quantified outside the du'u
We can't insert externally-bound variables into sedu'u, but I don't
see the problem when they are inserted into du'u.
> But then what is the status of "da poi du me la kikeron. zo'u la ralf
> krici lo du'u da krecau"? Is this true iff Ralph is disposed to assent to
> "Cicero is bald"?
No (whether or not the two names are synonymous).
> What if he is disposed to assent to "Tully is bald"?
> What if he is not disposed to assent to either, but is disposed to assent
> to "The greatest Roman orator is bald" (supposing that he has no name
> for this man). We don't know because the critical mode of presentation
> material is outside the du'u-bridi
In all these scenarios the sentence is true.
> We can't waffle on this stuff. We have to be able to establish the truth
> value of "lo du'u ... cu du lo du'u ..." where the ellipsized sentences
> are the same except for interchanging singular terms of identical
> referents. If we make them equal (transparency), then we can't move
> between beliefs and dispositions-to-assent, which seems counterintuitive
> and dire.
I think that is the right way to go, not dire, since disp-to-ass
needs to be distinguished from beliefs precisely when there is a
distinction between different linguistic expressions of the same
> If we make them opaque, we have problems with exterior
> restrictions on quantification: how, if at all, are they imported?
What would be an example of where we'd want to do that?