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meta[e85,jmc]		Meta-epistemology

Meta-epistemology in philosophy and artificial intelligence

	This paper introduces a notion of meta-epistemology and argues its
importance for philosophy and for artificial intelligence.

Definition: Meta-epistemology is the study of the relation between
the structure of a world with an imbedded knowledge-seeker
and what that seeker can know about it.

We abbreviate knowledge-seeker to ks.

	What a ks can know depends on its opportunities to observe the
world, its ability to act in it, the language it uses to express its
beliefs, its prior knowledge and the principles by which it derives new
beliefs from its old beliefs and experience.  All these relations are the
subject matter of meta-epistemology.  We propose the theoretical study of
meta-epistemology involving axiomatization of the properties of the world
and the position of the ks in it.

	Part of our goal is to separate the meta-epistemological problem
from the problem of what our own world is like, although our ultimate
objective is to apply the theory to knowledge-seeking computer programs in
our own common sense world.  We also want to separate the epistemology
from the heuristics as advocated in (McCarthy and Hayes 1969).  For
this reason we emphasize what the ks will accept rather than an
active knowledge-seeking strategy.  We can imagine it as a critical
reader of a scientific paper rather than an original researcher.

	Meta-epistemology is analogous to metamathematics in that
it studies knowledge-seeking systems from the outside the world.
Some of its theorems will have the following form: If a
world has such and such a structure, then a knowledge-seeker with a
certain language, certain prior beliefs, a certain interaction with the
rest of the world and certain rules for adopting new beliefs
will be able to accept fact A about the world but will not come to
accept B.

	We believe that meta-epistemology should be studied formally
apart from the more usual question of the epistemology of the real
world.  The reason is that the common sense real world is more complex
than is apparent to superficial thinking.  A good ks
will have a more complex strategy than merely discovering individual
new facts by discrete experiments and expressing them in a pre-determined
language.  The knowledge-seeker's approach to the common sense world
needs to be more like that of the physicist to the physical world.
The physicist is prepared for the fact that the fundamental
structure of the world is quite far from immediate
observation.  He doesn't expect to be able to support each axiom
by a single decisive experiment.  Instead he has to contemplate
complex structures that predict the results of new experiments
while continuing to agree with the old experiments.  Moreover,
experiments are devised to test theories about the world
as often as theories are devised to account for previous experiments.

	The common sense world is also very complex, although
in a different way from the physicists' world.  The main difference is that
the physicist uses what we may call ``complete models'' in which the
evolution of the system is determined (perhaps statistically) by an
initial state belonging to a state space defined by his theory.  Thus
modern physics is concerned with Schr\:odinger equations that describe
how the state evolves.  On the other hand common sense reasoning
deals with systems in which we cannot isolate a state space
that covers the phenomenon we are interested in.  During the course
of reasoning and action, new phenomena often arise, and the formalism
has to admit this.  When the physicist is confronted with an
unexpected phenomenon, he reverts to common sense and constructs
a new model.  This process of constructing a new model is not part
of the formal theory of physics.  Physicists do it informally, and
philosophers of science study how they do it.

	I have been thinking about the need for meta-epistemology
for some years, but I decided to refrain from writing about it
for publication until I had some mathematical results.  Such
a result would be a theorem about what strategies would discover
what knowledge in what kind of world.  Unfortunately, I still have
no such results but have decided to publish anyway in the hopes that
others will solve some of the problems that have so far been too
difficult for me.

	There is at least one paper that needs to be mentioned in
connection with E. F. Moore's 1956 ``Gedanken Experiments with
Sequential Machines''.  Moore's problem is determining the structure
of an automaton by experiment --- observing the outputs that
result from sequences of inputs.  He discusses, with the aid of
examples, how what can be determined depends on the structure of
the automaton.  This is certainly relevant to meta-epistemology
even though his results refer to experiments with a number of
steps that can be large compared to the number of states of the
automaton being investigated so that repetitions can be expected.
Moreover, the knowledge-seeker is external to the automaton
being investigated.

	An example which embodies more of the structure that
meta-epistemology should study may be called the problem of
``the life world physicist''.  {\it Life} is a two dimensional
cellular automaton invented by the mathematician J. H. Conway.
It is well described in (Berlekamp, et. al. 1982).  This simple
automaton system admits very complex structures, and they show
that self-reproducing computers can exist as large configurations
of activated life-cells.  We define a life-world physicist as
such a configuration programmed to find out the physics of its
world.  A successful life-world physicist would make experiments
leading to the conclusion that the fundamental physics of its
world was the life cellular automaton.  A successful life-world
biologist would discover the structure of the class of automata
to which it belonged.  The relevant meta-epistemological questions
concerns what languages, presumptions and strategies are needed
for the succesful life-world scientist.  There may also be
theorems of a negative character.  For example, I suspect that it
might be proved that an extreme operationalist language and
strategy might be unable to even formulate the proposition that
its fundamental physics is that of the life cellular automaton.
Unfortunately, I have no idea how to proceed with this example
beyond such conjectures.

	We can proceed somewhat further informally with meta-epistemology
by considering the way a child forms concepts.  Our observation
of such concepts is through the child's use of language, but let's
keep an open mind and admit the possibility that the concepts
themselves are not necessarily in one-to-one correspondence with
words of the language.  At least the epistemological structure
is not represented by a collection of sentences in the language
used for communication.  Indeed I believe that when we succeed in
designing intelligent robots, we will need to make the internal
``mentalese'' language different from any external language.  This
is because an internal language can use pointer structures that
cannot be exported without dumping the whole of memory.  Therefore,
external communication requires the use of words as discrete objects.

	The human capability most directly observable in a child
is that of successfully using concepts while in possession of
far less than the standard amount of knowledge of them.  Consider
the concept of mother.  It begins as something like a proper name.
Then it becomes a predicate denoting an adult woman with children,
although it may sometimes cover all adult women.  In this state it
is often used where the child will later learn to use the word wife.
  Finally it becomes
a function from a child to its female parent and also the relation
of a child and female parent.  The distinction between biological
mother and a woman who takes care of a child comes later.  Even
our adult use of the word mother is susceptible to further
evolution.  Thus if the implantation of ova from one woman in the
uterus of another becomes a common practice, the usage of the
word mother will require adjustment.

	Consider a child hearing ``The lion and the unicorn were
fighting for the crown''.  The fact that lions are real beasts
and unicorns are mythical beasts doesn't enter for a small child.
Indeed the distinction isn't clear to the child.  When the child is read
the poem and perhaps sees a picture, the question of whether it may ever
encounter a lion or a unicorn may not even arise.  There may not
even be an implicit commitment on the question in the mental structure of
the child.

	One might suppose that adults are better off and that the concepts
we use have definite meanings, but examples of ambiguity provide
counterexamples.  Consider Barbara Partee's sentence ``Tom wanted to have
an affair with Bill's wife''.  Most people don't see this sentence as
ambiguous and in most real life contexts it isn't.  However, we can ask
whether it applies in case we know that the woman Tom wants to have an
affair with is Bill's wife but Tom doesn't know that.  We can also ask
about the case where Tom has mistakenly heard that Bill has a beautiful
wife, but in fact Bill isn't even married.  We see these ambiguities once
they are pointed out but we require an ad hoc decision to determine
whether the concept of Tom wanting an affair with Bill's wife applies in
these cases.  I will argue that it isn't merely a case of there being
clear concepts and the only question being whether the phrase applies to a
concept.  I'll argue that the {\it de re} and {\it de dicto} concepts
don't exist in a person's mind until he becomes aware of the problem.
Perhaps AI provides a firmer ground for the matter.  Namely, when we
design a robot, we cannot hope to make it use only unambiguous concepts.
To do so would require solving too many of the problems of linguistic
philosophy before we could start on AI.  To use a term introduced rather
ambiguously by Hubert Dreyfus (196x), robots need ``ambiguity tolerance''.

An example from Moli\'ere

	Moli\'ere's play {\it La Malade Imaginaire} is about
a doctor who explains that sleeping potions work because they contain
``dormitive virtue''.  Moli\'ere's doctor is a fool, and this is taken
as an example of pompous nonsense.

	However, suppose there existed a substance with the following
properties.  The ability of a concoction to put a person to sleep
depended on the amount of the substance in the potion.  Suppose that
when a potion was heated the substance passed into the vapor at
a certain temperature could be condensed and was conserved.  Suppose,
however, that the substance was never isolated in pure form, e.g.
because it decomposed when too concentrated.  If the doctor knew of
such experiments, then the concept of dormitive virtue would have
considerable explanatory power and could be at the basis of a technology
for making sleeping potions.
	For example, separating the dormitive
virtue from certain other parts of a crude potion might avoid
unpleasant side-effects.

	Therefore, the doctor's sin is not an absolute one; rather it is
analogous to writing a check on insufficient funds.  Moreover, before any
of the above experiments have been made, thinking of the possibility of
dormitive virtue may be a requirement for making them.

	For close to a hundred years between Dalton and (say)
Einstein's determining the Avogadro number from Brownian motion,
the concept of atom was regarded by many as like dormitive virtue.
It explained many phenomena, but they believed that atoms should
not be regarded as real.  However, the main proponent of this view,
Ostwald, was convinced in the early twentieth century that atoms
are real.

	Now perhaps we can make a meta-epistemological conjecture.
Namely, in certain worlds, a knowledge-seeker must be able to
conjecture entities that are not definable in terms of previous
experience in order to think of experiments that will discover
certain aspects of the world.  I don't presently know how to
express this conjecture in a more formal way.