% ITALLC96 Submission
%
% This is a LaTeX file and compiling it once will suffice to
% obtain a printable dvi file.
%
% Author:
%
% Varol Akman, Professor                  +90 312 266-4133 (secr)
% Department of Computer Eng.                        -4126  (fax)
%   and Information Science                          -4305 (home)
% Bilkent University                      akman@cs.bilkent.edu.tr
% Bilkent, Ankara 06533       http://www.cs.bilkent.edu.tr/~akman

\documentstyle[12pt]{article}

\setlength\textheight{8.75in}
\setlength\textwidth{5.75in} 
\pagestyle{plain} 
\sloppy
\begin{document}

\def\otwo#1#2{{\cal O}_{#1} (#2)} % Oracle macro with 2 args.
\def\oone#1{{\cal O} (#1)} % Oracle macro with 1 arg.
\def\undertext#1{$\underline{\smash{\hbox{#1}}}$} % Underline macro.

\title{\huge \bf ORACLES AND NOTIONS\thanks{Detailed abstract of a
contributed paper submitted to the {\em Second Conference on
Information-Theoretic Approaches to Logic, Language, and
Computation\/}, Regent's College, London, U.K. (21--24 July,
1996). This is original work and is not being concurrently submitted
elsewhere.}\\ ~\\}

\author{{\em Varol Akman}\\ Department of Computer Engineering and
Information Science\\ Faculty of Engineering, Room EA--503\\ Bilkent
University, Bilkent, Ankara 06533, Turkey\\ ~\\ E-mail: {\tt
akman@cs.bilkent.edu.tr}\\ Phone/Fax: +90 312 266--4133/--4126\\}

\date{\today}

\maketitle

\newpage
\section*{\huge \bf ORACLES AND NOTIONS}

\vspace*{0.5in}
\hrule
\smallskip

\em
Mark Crimmins and John Perry have recently put forward a particularly
illuminating theory of propositional attitude ascription.  On their
account (1989), beliefs are concrete cognitive
structures---particulars---that belong to an agent, and contain ideas
and notions as constituents.

In this paper, I concentrate on notions and offer a synthesis,
inspired by Keith Devlin (1991b), according to which notions can be
regarded as (partial and not necessarily faithful) mental counterparts
of oracles in situation semantics.  This might help answer some of the
worries of Jennifer Saul who suggests (1993: p.~248) that ``Crimmins
and Perry must provide further information about the sorts of things
notions are, about what makes something one notion rather than
another, besides being the one referred to in a certain belief
report.''
\rm
\smallskip
\hrule

\section{Notions}

The highlight of the Crimmins-Perry theory is that notions (and ideas
for that matter), like beliefs, are concrete particulars (``things in
the head''): they belong only to single agents. While agents can have
similar representations, they cannot share them. As in the well-known
Cicero-Tully example, an agent may have two notions of a single
individual. This can happen essentially in two ways---see Crimmins and
Perry (1989: p.~256)---but the one which is more problematic for
belief reports is basically the following. Due to mix-up and
``failure to place,'' an agent may have several notions of an
individual, which he does not associate. On the Crimmins-Perry theory,
such an agent would not be blamed of entertaining internally
inconsistent beliefs. True, the agent may have (as in the renowned
scenarios of Saul Kripke's puzzle about the Frenchman Pierre, or Mark
Richard's puzzle about the lady in the phone booth) two beliefs with
completely opposite contents, but since these beliefs involve
different notions, there is no salient causal relation between
them. In short, ``there is nothing particularly puzzling about [such]
examples [$\ldots$] so long as we simply consider the beliefs, and not
the reporting of them,'' Crimmins and Perry state (1989:
p.~260).\footnote{The reader is referred to pp.~260--261 of the cited
reference for details of how the Crimmins-Perry semantic account
attends to such puzzles. Here is the Pierre situation in a
nutshell. He has one notion of London, which is linked to his
background reading on the city and to his use of the word ``Londres,''
and another, disjoint notion of London, which is caused as a result of
his stay there and which thus influences his use of the word
``London.'' He associates the Londres-notion with his idea of being
bonny and the London-notion with his idea of being dingy.}

To recap, Crimmins and Perry posit that a belief report (whose
$t$-clause determines a Russellian structured proposition) stipulates
not only the proposition that an agent believes, but also a cognitive
particular (viz. the agent's belief in the proposition). The notions
involved in the report are the so-called {\em unarticulated
constituents\/} of the proposition expounded by the report.

\section{Oracles}

I follow Devlin's exposition (1991a \& b) closely.  Let $\Gamma$ be a
collection of parametric infons. $\Gamma$ will make a {\em set of
issues\/}, or a {\em sei\/} in short. A sei provides one with a
framework for conversing about some part of the world or the whole
world. The important thing here is that by anchoring the parameters in
an infon in the sei, an item of information is obtained.

Given an individual or a situation $a$, the $\Gamma$-{\em oracle\/} of
$a$, denoted as $\otwo \Gamma a$, is the situation comprising that
part of the world and the entire `body of knowledge' that concerns
$a$. This is relativized to a sei, i.e., it is understood to be
meaningful within the framework provided by $\Gamma$. Thus, different
seis will enable one to discourse---and reap information---about
different aspects of the world. For example, if $a=Perry$ then by
choosing $\Gamma$ suitably one can study any of the following: the
philosophical papers of John Perry, his competence as a tennis player,
his childhood in Nebraska, his collaboration with Fran\c{c}ois
Recanati, etc.

Let $\Gamma$-{\em infon\/} denote any infon that results from
anchoring the parameters in an infon in $\Gamma$. $\otwo \Gamma a$ is
the minimal situation $s$ such that $s \models \sigma$ for any
factual, parameter-free $\Gamma$-infon $\sigma$ that genuinely
involves $a$. It follows that for any $\Gamma$-infon $\sigma$ in which
only objects that are constituents of $\otwo \Gamma a$ occur, $\otwo
\Gamma a \models \sigma$ if and only if $\omega \models
\sigma$. ($\omega$ is known as the {\em world\/}.) One particularly
natural way to understand this is as follows. If the only kind of
information available to one is that supplied by $\Gamma$, then $\otwo
\Gamma a$ cannot be distinguished from $\omega$.

For example, consider the Fodor situation, $s_f = \otwo \Gamma
{Fodor}$, for an appropriate sei $\Gamma$. Stretching back in time to
include among others, his notorious Granny and forward in time to
include his grandchildren (if any) $s_f$ will contain Fodor's
birthplace, his favorite books (including A.~A.~Milne's {\em The House
at Pooh Corner\/}, of course!), offices he has held, students he has
taught, and so on.  One important observation has to do with the
extent of $s_f$. Different people at different times may have access
to radically different information about $s_f$. Daniel Dennett must
surely know more about $s_f$ than I do, for I never met the man but am
just familiar, in some degree, with the recent Fodor-Lepore {\em
Shopper's Guide\/} and a couple of earlier works. Fodor himself will
know considerably more about $s_f$, though a future biographer of this
thought-provoking philosopher may unearth facts which could be news
even to Fodor. Similarly, the Granny had access to information about
$s_f$ quite different from that known to Fodor's colleagues, Fodor's
parents, or Fodor himself.

\section{Notions as mental counterparts of oracles}

It was stated in \S2 that oracles are situations. This, in turn,
implies that they are highly intensional objects and cannot be
completely described.  For example, the oracle associated with Fodor
is rich; one cannot, in general, hope to list all the facts that make
up $\otwo \Gamma {Fodor}$, even for a seemingly trivial $\Gamma$.
However, a mathematical approximation is feasible.  Considering an
oracle $s$ (some real situation), an abstract counterpart can be
constructed, namely the set $\{\sigma \mid s \models
\sigma\}$.\footnote{In its most interesting instances, $s$ would not
be {\em static\/} (involving one or more contemporary spatial
locations) but {\em dynamic\/} (spread over a time-sequence of
locations), e.g., Fodor from his very early childhood to the present.}

The simple groundwork to give a characterization of Crimmins-Perry
notions is now laid out. For a given person, let his $\Gamma$-{\em
notion\/} of an individual $a$ be the reflection in this person's mind
of $\otwo \Gamma a$. When $\Gamma$ is taken, following Devlin, to be
the set of all parametric infons in the informational ontology of any
of the people who have heard of $a$, it may be omitted (and thus we
simply write $\oone a$) and one can talk about a {\em notion\/} of $a$
without any qualifiers.

To possess a notion of an individual is to bear the appropriate
ownership relation to a mental counterpart that is culled from the
oracle of that individual.  Notions are not entirely faithful
reflections of oracles; they are tainted with misinformation,
inconsistency, distortion, exaggeration, fabrication, $\ldots$---plain
wrong stuff in short. It is this aspect of notions that usually leads
one to talk about {\em bona fide\/} vs. {\em lousy\/} notions.  Perry,
while explaining {\em files\/}, a forerunner of notions, says (1980:
p.~87):

\begin{quotation}
\noindent
Now each file card offers me, at each seminar, a profile, a
set of predicates. Whom does this profile stand for? We clearly must
make a distinction between the persons, if any, of whom the profile is
true, and the source of the profile. The source is the student my
perception of whom led to the establishment of the file (it need not
have been perception, though, as far as I can see).  The predicates on
the file may or may not be true of her. I update the cards after each
class. Old entries are changed, new entries are made, the writing
fades, I may have made mistakes recording the data, and so forth.
\end{quotation}

Oracles are idealized devices. Being actual situations they reflect
the reality with the highest fidelity conceivable. Notions, when
possessed by a rational, regular agent, should also be reasonably
accurate (albeit partial) reflections of oracles, if they are going to
be of any use to the agent's mental well-being. Consider one's notion
of Fodor. If this is a fairly good counterpart of $\oone {Fodor}$,
then it would be useful in many circumstances. For example, most of
the statements one would make using his (bona fide) notion of Fodor
would likely be true, e.g., ``Fodor wrote a book jointly with
Lepore.'' On the other hand, there might be, in general, some
misinformation in one's notion, viz. ``Fodor has two titles published
by the MIT Press.'' (He has four.) Depending upon the amount of
misinformation, a particular notion may simply disintegrate and lose
its applicability.  Consider a perplexed philosophy student's (lousy)
notion of George Lakoff, which he---for one reason or another---takes
to be a notion of Fodor.  It is safe to predict that this befuddled
notion would be of no use whatsoever to him.

Whereas oracles are public in a very real sense (objects about which
it is possible to acquire and/or pass information), notions are
strictly private. Agents may have notions with the same content, but
they cannot have the same notion. In other words, for agents
$\alpha_1$ and $\alpha_2$, there exist two notions $n_1$ and $n_2$,
respectively, of an individual $a$. Each of these notions carry some
relationship to $\oone a$ but in general there is no way to compare
$n_1$ and $n_2$ in precise terms. In most useful instances, what makes
$n_1$ and $n_2$ suitable notions of $a$ is that (i) they have
considerable similarity---obviously under a properly chosen similarity
metric---to each other (denoted as $n_1 \approx n_2$), and more
importantly, (ii) they have considerable overlaps with $\oone
a$.\footnote{One is reminded of Gilbert Harman's observation in his
{\em Thought\/}: ``The only sort of sameness of meaning we know is
similarity in meaning, not exact sameness of meaning.''}

The outlined proposal to regard Crimmins-Perry notions as mental
counterparts of oracles can be traced back to Devlin (1991a,
pp.~234--235):

\begin{quotation}
\noindent
[A]ssociated to this guy Keith [$k$] is a certain situation
$r_k$ [$= \oone k$], and as the occasion demands, different people can
draw on various items of information about $r_k$ (in terms of our
ontology, we might say they can utilize various compound infons,
$\sigma$, such that $r_k \models \sigma$). The situation $r_k$ remains
constant here, a fixed situation, part physical and part abstract,
intimately associated with Keith. [$\ldots$] There is obviously a
relationship between the oracle $r_k$ and Jan's {\em notion\/} of
Keith [$\ldots$]. Indeed, under ideal circumstances Jan's [Devlin's
wife] notion of the person $k$ will amount to a mental aggregate of
infons supported by $r_k$, and so too will the listener's (perhaps
much leaner) notion about the person Jan refers to. Indeed, any
information (infons), $\sigma$, about $k$ that Jan uses will be part
of her notion of $k$.  [$\ldots$] And likewise for the listener.
\end{quotation}

There is a slight catch, by the way. Devlin's notion, while strikingly
similar to the Crimmins-Perry one, is arrived at independently.
(Devlin does not cite the Crimmins-Perry paper in his book.) His
definition goes along the following lines (1991a: p.~162). If $a$ is
an object individuated by an agent $\alpha$, then the $a$-representing
cognitive structure realized in the brain of $\alpha$ as a result of
that individuation or identification, is called a notion of $a$. While
this interpretation does not employ the terminology of Crimmins-Perry
theory (e.g., particulars) it is unmistakably in the precise spirit of
their account.

\section{Saul's objections}

In this detailed abstract, I will only take up Saul's first criticism
which has to do with what she calls {\em excessive specificity\/},
i.e., her view that the Crimmins-Perry approach to belief reporting
requires more specificity than is called for by commonsense
intuitions. In order to make her alleged point, Saul considers the
following report:
 
\begin{equation}
{\rm Edna~believes~that~Jones~is~bald.}
\end{equation}

She assumes that the context in which (1) is uttered furnishes a {\em
normal\/} notion of Jones.\footnote{According to Saul (1992: p.~425) a
notion is normal ``if it is involved in normal sorts of beliefs,
relative to the community of which the agent is considered a member by
the participants in a discourse.''  Crimmins and Perry (1989: p.~270,
n.~15) add that ``other aspects of the background of the discourse,
including facts about what is relevant to the goals of the discourse''
need to be considered. Finally, Crimmins (1992: p.~95) cautions:
``Certainly, what counts as [normal] is a vague, society-relative {\em
and\/} purpose-dependent matter.''} The proposition expressed by (1)
attributes to Edna a belief that Jones is bald, a belief involving a
particular normal notion $n$ of Jones. In the actual world $\omega$,
this proposition is true.
 
Then Saul imagines a possible world $\omega'$ which resembles to
$\omega$ in every respect except one: Edna has now a belief with
the same content that involves a notion $n'$, another normal notion of
Jones in which his nose, in Saul's words, ``receives a bit more
emphasis.''  Saul asserts that (1) is false in $\omega'$. Since the
way $\omega'$ differs from $\omega$ should not affect the truth value
of (1) it looks like there is a problem.
 
Underlying this analysis of Saul is the following assumption of hers
(1993: p.~427):

\begin{quotation}
\noindent
If a notion---an actual concrete cognitive particular---is
part of the proposition expressed by a true belief report, then that
particular is \undertext{essential} to the truth of the report. In a
world in which the agent has not {\em that\/} particular, but a
\undertext{slightly different} one, the report will be false. [my
underlines]
\end{quotation}
 
To my best knowledge, this assumption is nowhere to be found in the
original Crimmins-Perry account. As a matter of fact, Saul comes to
question her strong presupposition immediately (1993: p.~428):
 
\begin{quotation}
\noindent
It might be objected that notions simply can't be as fragile
as I have suggested. Surely notions persist across possible worlds
just as people do. It is perfectly sensible to talk about Jones having
a bigger nose in another world, so why isn't it reasonable to suppose
that Edna's $\omega'$ notion of Jones is the {\em same\/} one, but
with greater emphasis on his nose size? In order to make such a move,
Crimmins and Perry need to provide an account of cross-world identity
for notions. It's certainly not obvious that $n'$ is still $n$, and in
fact it seems more likely that it is not. But we really don't know
about this, and lack intuitions on the subject altogether---because we
lack intuitions about notions. They are theoretical entities
introduced simply to account for our intuitions about propositional
attitude puzzles.
\end{quotation}

Saul then adds that ``it would be difficult to do this in a
non-question-begging manner.''

According to the present discussion, there is a rather straightforward
explanation which captures pretheoretic intuitions properly, namely,
our oracle-based account. First, consider $s_j = \otwo \Gamma {Jones}$
in $\omega$. We take it for granted that $\Gamma$ here is an
appropriate sei which includes those parametric infons that have
something to do with the baldness of Jones.  Since nose size cannot
play, by its nature, a determining role in this context, it would
simply be irrelevant. While the equivalent of $s_j$ in $\omega'$,
i.e., ${s'}_j$, would include an infon to take care of the bigger
nose, the mental counterpart (reflection) $n'$ of ${s'}_j$ would be
`blind' to such a feature vis-\`{a}-vis (1).  This means that we can
take $n' \approx n$ and thus (1) would still turn out to be true in
$\omega'$.

Finally, note that things would work out as expected when (1) is
replaced by

\begin{equation}
{\rm Edna~believes~that~Jones~has~a~longish~nose.}
\end{equation}

That is, (2) would normally be false in $\omega$ and true in
$\omega'$.  This is due to the fact that nose size is now relevant.

\section{Postscript}

In the final version of the paper, I'll provide a more detailed
analysis.  I'll also attend to Saul's other intricate arguments re the
Crimmins-Perry approach and explain why they do not carry much force
once one takes an oracle-based stance towards notions. (See Akman and
Surav (1995) for another demonstration of the use of oracles in
artificial intelligence problems, e.g., modeling relevance to a
context.)

\section{References}

\begin{itemize}

\item Akman, Varol, and Surav, Mehmet, 1995, `Contexts, Oracles, and
Relevance,' in {\em Working Notes of the AAAI--95 Fall Symposium on
``Formalizing Context''\/}, Buva\v{c}, Sa\v{s}a, and Fikes, Richard
(organizers), Cambridge, Mass.: MIT, pp.~23--30.

\item Crimmins, Mark, 1992, {\em Talk About Belief\/}, Cambridge,
Mass.: MIT Press.

\item Crimmins, Mark, and Perry, John, 1989, `The Prince and the Phone
Booth: Reporting Puzzling Beliefs,' {\em Journal of Philosophy\/},
Vol.~86, pp.~685--711. Reprinted with a postscript in Perry (1993:
pp.~249--278).  [Page references in the text are to the Perry volume.]

\item Devlin, Keith, 1991a, {\em Logic and Information\/}, New York:
Cambridge University Press.

\item Devlin, Keith, 1991b, `Oracles in Situation Semantics,' in {\em
Situation Theory and Its Applications\/}, Vol.~2, Barwise, Jon,
Gawron, Jean Mark, Plotkin, Gordon, and Tutiya, Syun (eds.), CSLI
Lecture Notes No.~26, Stanford, Calif.: Center for the Study of
Language and Information, pp.~41--49.

\item Perry, John, 1980, `A Problem About Continued Belief,' {\em
Pacific Philosophical Quarterly\/}, Vol.~61, pp.~317--332. Reprinted
with a postscript in Perry (1993: pp.~69--90). [Page references in the
text are to the Perry volume.]

\item Perry, John, 1993, {\em The Problem of the Essential Indexical
(and Other Essays)\/}, New York: Oxford University Press.

\item Saul, Jennifer M., 1993, `Still an Attitude Problem,' {\em
Linguistics and Philosophy\/}, Vol.~16, pp.~423--435.

\end{itemize}
\end{document}
