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.cb A PROGRAMME FOR META-EPISTEMOLOGY


	Meta-epistemology should be to epistemology as metamathematics is
to mathematics.  Taking epistemology as the theory of knowledge
and how it is obtained, meta-epistemology studies systems that
seek knowledge in a world.  An epistemological system is then a
world and a knowledge-seeker in that world.  If the world, the
knowledge-seeker, and the criterion for deciding whether the
knowledge-seeker knows a fact are given mathematically, then
what the knowledge-seeker will discover is a mathematical question.
The advantage of meta-epistemology is that knowing the world in which
knowledge is sought makes the evaluation of epistemological methods
mathematical.

	Our goal is to study epistemological systems technically.
Thus we may consider a knowledge seeking computer program connected to a
system of finite state automata and ask whether a given knowledge seeking
strategy can learn certain facts about the "external world".  To the
extent that epistemological questions can be put in such a technical form,
their answers may be obtained by mathematics.  The remaining philosophical
issues will then concern whether the technical form of the question
properly represents the original philosophical problem.  If the experience
of metamathematics is a portent, the mathematical answers won't be
accepted as philosophically conclusive but will nevertheless transform the
way in which philosophers think about the problems.  I have in mind
Goedel's incompleteness theorems, Gentzen's results on the consistency of
arithmetic and the result that intuitionist and classical arithmetic are
equiconsistent.

	I must confess that I cannot yet give technical forms
of epistemological questions that seem ripe for mathematical
attack.  However, here are some ideas that may be helpful.
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#. Avoiding heuristic problems.  Work in artificial intelligence
suggests that finding out the facts of the world has two components.
One component is a general framework or language in which hypotheses
and facts can be expressed, and the other is a strategy of search
and experiment.  In artificial intelligence, the first is called
epistemology, and the second is called heuristics.

It is our hope that the heuristic problem can be avoided in studying
epistemology in the following way.  Instead of imagining a computer
program that seeks knowledge, we imagine a program that is led towards the
truth by a Socratic tutor.  Its tutor supplies no knowledge to be accepted
on the tutor's authority, but merely proposes observations, conjectures,
experiments and inferences.  The student program accepts or rejects these
steps according to its built-in epistemology, i.e.  knowledge, rules of
inference, and rules of reasonable conjecture.  We require that the
student be consistent in that no Socrates can lead it into a
contradiction.  (Later we may relax this stricture a little).

	If the Socratic tutor can lead it to discover a certain fact about its
world, then we shall say that its epistemology is adequate for obtaining
this fact.  Since we, the creators of the epistemological system, also
created the world in which knowledge is sought, we know what the facts
are, so it is a definite question as to whether the program has discovered
them.  Deciding whether an epistemological theory is adequate to obtain
knowledge of a world about which we know everything should be easier than
deciding whether it is adequate for our own mostly unknown world.

	We must hope that avoiding heuristics is successful, because
studying systems that combine epistemology and heuristics will be
very difficult.

	Consider first Kant's idea that our ability to understand the
world depends on having some innate ideas.  Many of his original proposals
as to what modes of perceiving the world are innate, e.g. Euclidean
geometry, haven't survived intact, and others are insufficiently
definitely described, but something along this line is often still defended.
Here is an attempt at a corresponding technical question.

	Let the world be a system with a state that varies as a
function of a real variable ⊗t called time.  Let the "student"
be computer program with sense and motor organs connected to
this "outside world".  We suppose that
the way the state of the outside world changes as a function of
its previous history and its motor inputs is described by a collection
of sentences of set theory.  Suppose further that the particular
"outside world" is an arbitrary member of a certain set of "possible
outside worlds" - this set also being defined by a sentence of
set theory.

	Now we can try to embody different epistemological strategies
in the student program.  A rather strong empiricist strategy would
allow only hypotheses that were expressed in terms of sensory-motor
relations in some restricted language.  A Kantian program would
allow hypotheses that conformed to some preferred %2synthetic a priori%1
ideas.  It seems to me that a set theoretic epistemology corresponding
to modern scientific practice would allow the tutor
to propose new set theoretic constants without having to define
them and propose sentences of set theory as laws connecting them.
Depending on what was proposed and what the world is like, the student
might be able to decide on these proposed laws, but no a priori
requirement would be made that the proposed laws be decidable
experimentally.  If Kant were right, his %2synthetic a priori%1
notions would have to be part of the axioms, because the system
would be unable to guess them.

	We should compare the efficacy of many specific innate modes of
perception, e.g. spatial and temporal, with the general mode that
says that the world is a causal system mathematically describable,
e.g. by sentences of Zermelo-Fraenkel set theory.  The latter
presumably has a certain universality.  Any specific mode of
perception, e.g. the tendency to interpret sensations as arising
from persistent objects located in three-dimensional space, can
be formulated as a hypothesis in set theory.

	Systems of the type described above separate the knower
from the outside world.  At the cost of elaboration that may make theorems
harder to formulate and prove, we can remove the separation.  Consider
a two or three dimensional cellular automaton system.  In such a
system, each cell is a finite automaton whose state at time ⊗t+1 
depends on its state and the states of its immediate neighbors
at time ⊗t.  

	A good example is Conway's Life automaton that uses
an infinite two dimensional array of two state automata - one located
at each point of the plane with integer co-ordinates.  The state
of a cell at time ⊗t+1 is 0 if the number of its eight neigbors in
state one is less than 2 or more than 3.  If 2 neighbors are in state
1, it retains its state and if 3 neighbors are in state 1, it goes to
state 1.  

	It has been shown that the Life cellular automaton is a
universal computer and constructor.  In particular, self-reproducing
arrays of Life cells that can execute arbitrary computer programs
are possible.  We can imagine equipping such an array with different
epistemological programs and ask what programs would do formulate
and confirm the hypothesis that the fundamental physics of their
world was the Life cellular automaton.  If there were many of them,
what hypotheses would they formulate about other minds, consciousness,
etc?  Would they discriminate properly between their programs (minds)
and the configurations of cells (brains) constituting the computer
executing the program?  Indeed, is this the interesting distinction?

	Just accepting the idea of studying epistemological systems
from the outside already leads to some epistemological conclusions.
For example, it is often questioned whether it makes sense to ask
whether there are unknowable facts about the world.  The coresponding
question about an epistemological system certainly makes sense.
The knowledge-seeker may be too weakly connected to the world to
get certain information.  Moreover, as E.F. Moore (1956) showed,
two questions may each be answerable but not jointly, because a necessary
action to answer one of them may destroy the possibility of answering
the other and conversely.

.bb Possible Frustration Theorems

	While the main content of meta-epistemology had better not be
frustration theorems, the inadequacy of some philosophical points of
view might be made extremely plausible by proving some frustration
theorems.

	The theorems should have an epistemological rather than a
heuristic character.  They concern whether certain information about
the world to which a KS is connected can be expressed in a given
language.

	For example, suppose that EN consists of several interconnected
parts, and only some of these parts interact directly with KS, but that
the general structure is known, i.e. the diagram of parts.  Can we
express the fact that the connections between part A and part B all
have information flowing from A to B and never vice versa?
It does seem that an S-R language should have severe limitations
in expressing such information, or other general infhαmation about
the structure of the external world.  However, it may be that such
information can be expressed as propensities to behave, but maybe
something can be said about the complexity of such expressions.

	The opposite of assertions that behavioral languages can't
express facts about the interconnections of the external world would
be a set of rules for translating statements about interconnections
into behavioral language.
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	Maybe we could make something out of the hypothesis of
virtuus dormitiva.

We can regard the negative Minsky-Papert results on perceptrons
as meta-epistemological.

The life creatures learning that their fundamental physics is the
life plane.

Gedanken experiments with sequential machines.


.end