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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.
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.
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.
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"? 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.
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. If we make them opaque, we have problems with exterior
restrictions on quantification: how, if at all, are they imported?
Winter: MIT, John Cowan
Keio, INRIA, firstname.lastname@example.org
Issue lots of Drafts. http://www.ccil.org/~cowan
So much more to understand! http://www.reutershealth.com
Might simplicity return? (A "tanka", or extended haiku)