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.cb LOCKE - THE UNFINISHED BUSINESS


	John Locke's %2Essay Concerning Human Understanding%1, published
in 1690, founded empiricism by proposing that all human knowledge is
obtained either through the senses or by %2internal sense%1 or reflection
on the person's mental processes.  This was in opposition to previous
philosophical doctrines of %2innate ideas%1.  In this paper we shall consider
the analogous question for machines; can we make a computer program
"without innate ideas" that gets all its information as proposed by
Locke.

	The issue to be tested, whether it is possible for a system to
learn by observation and reflection what a human knows, starting without
innate ideas, is approximately semi-decidable by computer experiment.  (By
semi-decidable we mean that a computer program that performed adequately
would vindicate Locke, but failure to find one wouldn't prove that a
smarter cognologist mightn't do better.  By approximately we mean that
there might remain a controversy as to whether the program was
sufficiently Lockean).  If the program succeeded, there would also
remain the issue of whether it approximated human behavior.

	We don't have a candidate Lockean program and are not about
to write one.  In this article we only discuss such a program in the
hope that the discussion will be illuminating both for artificial
intelligence and for epistemology.

	Locke does not discuss mechanisms, and the tools for dicussing
intellectual mechanisms have only begun to be created since the
advent of mathematical logic, computers, articicial intelligence research
and the study of the epistemological problems of cognology (AI).
Therefore, we must begin by making Locke's problem more precise at
the cost of modernizing his formulations.
Here are some considerations:
.item←0

	#. We shall suppose that the program manipulates sentences
in a suitable formal language.  Inputs from the outside produce
sentences in memory, and so do Locke's
%2internal sensation%1 or %2reflection%1.
Besides %2internal sensation%1, we also
have processes of logical inference, and maybe also non-monotonic
reasoning (McCarthy 1979).
Inference
generates new sentences from previous sentences according to
the rules of inference of a suitable logical system.  Reflection
generates new sentences by looking at the collection of sentences
already present.  One product of reflection might be a
formal sentence corresponding to the English, %2"I don't have
enough facts to decide the best way to get to the meeting in Chicago"%1.
It is amusing that the logical notion of a "reflection principle"
which from the sentence %2"Snow is white"%1 gives the
sentence %2"'Snow is white' is true" satisfies Locke's notion
of reflection.  The above examples of reflection are a bit feeble;
we will need much more than that in order to vindicate Locke.

.foo←true
.if foo then begin
.nofill

Other examples of reflection
I never saw a purple cow.

Is non-monotonic reasoning a form of reflection?

.end

	#. Locke argues about whether the principle %2"What is, is"%1
is innate and argues that it isn't on the ground that children and
idiots don't assent to it.  Let us modernize the principle to the
tautology %2p_⊃_p%1, and suppose that among the capabilities
of our program is the ability to do deductive
propositional calculus reasoning.  Someone might then claim that
any program that can do propositional calculus has %2p_⊃_p%1 innately
present, i.e. built into the program,
but we won't take that as our sense of innate presence.

	Instead we will distinguish between the ideas that the programmer
used in writing the program and the sentences that are explicitly
present in the machine and count only an initial stock of the
latter as innate ideas.  This corresponds to Locke's exclusion
of children on the grounds that they cannot understand the
explicit statement of %2"What is, is"%1 well enough to assent to
it even though their thinking doesn't controvert it.  It also
corresponds to the modern mathematical practice of distinguishing
the sentences of system from sentences in a metalanguage.  From
the programming point of view the distinction is also desirable.

	Unfortunately, this allows the skeptic to argue that this
permits sneaking in any innate idea by building it into the
program, but we promise not to do that, and hope to convince the
skeptic later when he sees the system that we haven't cheated.
Perhaps Locke's %2p_⊃_p%1 example will always be controversial,
and considering Kant's contention that Euclidean geometry must
be innate may be more illuminating.  Of course,
the discovery of non-Euclidean geometry weakened Kant's contentions,
but perhaps they could be rehabilitated by modifying it to some
approximate geometry.

	#. Perhaps Locke can be sufficiently vindicated by a
"Missouri program" rather than by a full reasoning program.  A
Missouri program is more like a proof-checker than a problem
solver.  It accepts proposals from the outside to perform reasoning
and checks whether these proposals lead to the desired conclusion.
In this case, the Missouri program would have to accept proposals
to observe the outside world and its own memory.  Naturally, a
Missouri program could be written to accept any conclusion, but
it a correct Missouri program cannot be led to unwarranted conclusions
and especially can't be led to logical contradictions.  The
technical advantage thinking in terms of the Missouri program is
that it bypasses the problem of heuristics (as the term is
used in AI), since the outside user supplies all necessary
cleverness.  It seems to me that Locke and other philosophers
haven't been concerned with heuristics anyway, and splitting
cognology into epistemology and heuristics (I have always claimed)
is worthwhile even for AI research.

	#. An area in which Locke and other philosophers have been weak is
in their discussion of visual perception.  They write as though visual
perception consisted in assigning values to variables representing size,
color etc,, i.e. as though the result of an observation could be the
execution of the Algol statement %3begin%1 size ← 10; color ← red %3end%1.
Unfortunately, this is too simple, and the result of an observation
has to be the creation of some kind of internal network or perhaps 
a whole collection of sentences giving names to parts of the scene
and expressing their relationships.  As Russell (1946) points out,
until recently philosophers have written as though all ideas could
be written with unary predicates only and have ignored the necessity
of treating relations.  On the one hand, this has led to oversimplifying
the problems, and on the other hand, it has led to unjustified conclusions
that certain kinds of reasoning (that happen to require many place
relations) are impossible.

.if foo then begin nofill

%3Russell, Bertrand (1946)%1: %2History of Western Philosophy%1,
Allen and Unwin, London.

.end

	We aren't prepared to say what kinds of sentences
observations might lead to in general, but here is a step beyond
what is implicit in Locke and other philosophers.
Suppose that the letter E is observed in the middle of an English
text by a Chinese unfamiliar with the Latin alphabet.  Calling
the given occurrence of E by the name ⊗E1, we might have the
sentence

%2in(E1,Scene1) ∧ ispart(X1,E1) ∧ ispart(X2,E1) ∧ ispart(X3,E1)
∧ ispart(X4,E1) ∧ ishorizontalsegment(X1) ∧ ishorizontalsegment(X2)
∧ ishorizontalsegment(X3) ∧ isverticalsegement(X4) ∧ length(X1) = 1
∧ length(X2) = 0.8 ∧ length(X3) = 1 ∧ length(X4) = 1.2
∧ top(X4) = left(X1) ∧ middle(X4) = left(X2) ∧ bottom(X4) = left(X3)%1

giving part of the result of the observation.  Perhaps more of the
same would complete the observation, but maybe further elaboration
is required.  Note that we have had to invent internal names for
the parts of the figure in order to write the sentence.  An
internal representation might make do with pointers to parts of
an actual image.

	#. In one place Locke seems to imply that reflection
operates only on information produced from the senses and not
on information produced by reflection itself.  In other places
he seems to allow reflection on the results of reflection.  We
shall allow it in the strong sense of even allowing sentences
that refer to themselves.