Posted July 21 1996
Newsgroups: sci.physics,sci.math,sci.chaos,sci.skeptic,sci.bio,sci.cognitve,alt.consciousness,comp.ai.philosophy
References: <31EE6908.1B18@well.com> <837726994snz@longley.demon.co.uk> <4sokg5$hb7@sjx-ixn2.ix.netcom.com> <4sr39h$8cc@sun4.bham.ac.uk> <837897287snz@longley.demon.co.uk>
Subject: types of opacity (Was [Fwd: Re: Naturalism] )

In case there are young and impressionable lurkers perhaps I should
explain why the type of opacity Longley refers to (or rather Quine
referred to and Longley quotes him as referring to) and the type of
opacity Minsky was referring to are totally different.

1. Frege/Quine Referential Opacity (intensionality):

Suppose I go to France for my holiday, and I spend some time in Paris,
including visiting the Eiffel Tower, and the following is true

    S1. The Eiffel Tower = the tallest building Aaron saw on holiday

Notice that this entails
    S1a. The height of the Eiffel Tower = the height of the tallest
         building Aaron saw on holiday

The following week I am back at work discussing with a salesperson the
information in a database package he is flogging. He says

    S2. The database can tell you the height of the Eiffel Tower

He is (let's suppose) making a true statement because the database has
the information and you can easily get at it using a standard form of
query.

A lurking logician then says: from S1 (or S1a) and S2 I can infer S3,
So:

    S3. The database can tell you the height of the tallest
            building Aaron saw on holiday

The salesperson objects that S3 is false, as the database knows nothing
about Aaron. I.e. you can't assume substitutability of coreferential
expressions will always preserve truth (or falsity) in statements about
what information is in the database.

Frege, as far as I know, was the first to study the fact that in
sentences of these forms

        I1: X can tell you Y
        I2: X knows that Y
        I3: X believes that Y
        I4: X intends that Y

and many others, Y is a referentially opaque context (also known as an
intensional context) because substitution of a referring expression for
another with the same referent does not always preserve truth value.
I.e. Leibniz' law of indiscernibility of identicals does not hold.
(Frege talked about a notion of "sense" (or "Sinn" in German) of a
referring expression, which he claimed was the true referent in such
context, but not everyone likes his answer.)

Contexts where Leibniz' law does hold are called referentially
transparent (or extensional).

Attempts to use quantifiers (All, Some, Most, etc.) in connection with
referentially opaque contexts can lead to logical puzzles and
paradoxes. This is often summarised in the slogan: You cannot quantify
into a referentially opaque (intensional) context.

Sentences that include referentially opaque (intensional) contexts
cannot be expressed in predicate calculus, although attempts have been
made to extend predicate calculus with intensional operators to allow
such things. (E.g. See the book on the development of logic by William
and Martha Kneale).

The situation is more complex than some philosophers realise

(a) because there are contexts where sentences of the above forms I1,
I2, etc. are interpreted as extensional, and

(b) because many people assume wrongly that such intensional contexts
depend on some sort of psychological state of a person being involved. I
deliberately chose the database example to show that the phenomenon has
nothing to do with whether a person is involved but can arise wherever
there is a system that contains information, and you try to talk about
the information in the system.

2: Minsky Opacity
Now suppose the database stores information about the people who
interrogate it and tries to form generalisations about different users.
It then uses those generalisations to guide the way that it answers
questions (e.g. how it orders candidate responses to questions that are
ambiguous). Suppose also that there is no way of asking the system what
information it has stored about your pattern of interests, nor which
algorithm it is using to answer your questions.

I.e. there's something about the system that is opaque to you in that
you can't see into it or find out about it.

This is the kind of opacity that Minsky was talking about. He rightly
notes that a complex information processing system may be composed of
many concurrent, interacting, subsystems, which do not have access to
all the internal states and processes of other sub-systems, though they
may have partial access in some cases. (This is commonplace in software
engineering.)

SUMMARY: TWO KINDS OF OPACITY
Thus we have referential opacity as the case where you can refer into a
system and talk about the information it contains, but not beyond it
despite the linguistic appearance of referring beyond it to the Eiffel
Tower.

    User ---->-----Database-->|    Eiffel Tower

And Minsky opacity, where you can't even refer into the system because
either it will not answer your questions or it cannot.

    User       |<--Database
                   Algorithms

(I've reversed the arrow because the first case involves the user
referring to something in the database and the second case involves
information not being able to flow from the database to the User.)

Each type of opacity can occur without the other. One is an
implementation detail concerning accessibility from outside a system,
the other is a feature of the logic of reference to the contents of an
information structure.

Note:
I had previously written:

> > I am beginning to think Longley is not a person but the world's best
                                             ^^^^^^
> > Eliza-like computer program, incorporating a very sophisticated
> > neural net for pattern recognition, a very powerful content
> > addressable memory which works at the level of syntactic (e.g.
> > verbal) similarity, and a store of (right adjusted) canned texts
> > plus a collection of soft rules for triggering their selection and
> > output.
> >
> > It's really very impressive.

To which David Longley <David@longley.demon.co.uk> responded:

> Our concept of "person" is folk psychological as I have tried  to
                 ^^^^^^^^
> make   clear   by  the  material  from  Personality   Theory   in
> "Fragments". People just are not consistent across contexts,  and
> what  they "understand" tends to be context and content  specific
> ....... etc. ....

This version of Eliza can make self-referential jokes.

Excellent!

I look forward to meeting its author one day.

Aaron