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␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓α␈↓ ∧iLOCKE - THE UNFINISHED BUSINESS

␈↓ α∧␈↓␈↓ αTJohn␈α↔Locke's␈α↔␈↓↓Essay␈α↔Concerning␈α↔Human␈α↔Understanding␈↓,␈α↔published␈α↔in␈α↔1690,␈α⊗founded
␈↓ α∧␈↓empiricism␈α∞by␈α
proposing␈α∞that␈α
all␈α∞human␈α
knowledge␈α∞is␈α
obtained␈α∞either␈α
through␈α∞the␈α
senses␈α∞or␈α
by
␈↓ α∧␈↓␈↓↓internal␈αsense␈↓␈α
or␈αreflection␈α
on␈αthe␈α
person's␈αmental␈αprocesses.␈α
 This␈αwas␈α
in␈αopposition␈α
to␈αprevious
␈↓ α∧␈↓philosophical␈α
doctrines␈α
of␈α␈↓↓innate␈α
ideas␈↓.␈α
 In␈αthis␈α
paper␈α
we␈α
shall␈αconsider␈α
the␈α
analogous␈αquestion␈α
for
␈↓ α∧␈↓machines;␈αcan␈αwe␈αmake␈αa␈α
computer␈αprogram␈α"without␈αinnate␈αideas"␈α
that␈αgets␈αall␈αits␈αinformation␈α
as
␈↓ α∧␈↓proposed by Locke.

␈↓ α∧␈↓␈↓ αTThe␈α⊂issue␈α⊂to␈α⊂be␈α⊂tested,␈α⊂whether␈α⊂it␈α⊂is␈α⊂possible␈α⊂for␈α⊂a␈α⊂system␈α⊂to␈α⊂learn␈α⊂by␈α⊂observation␈α⊂and
␈↓ α∧␈↓reflection␈αwhat␈αa␈αhuman␈αknows,␈αstarting␈αwithout␈αinnate␈αideas,␈αis␈αapproximately␈αsemi-decidable␈αby
␈↓ α∧␈↓computer␈α⊂experiment.␈α⊃ (By␈α⊂semi-decidable␈α⊃we␈α⊂mean␈α⊃that␈α⊂a␈α⊃computer␈α⊂program␈α⊃that␈α⊂performed
␈↓ α∧␈↓adequately␈α∃would␈α∀vindicate␈α∃Locke,␈α∀but␈α∃failure␈α∀to␈α∃find␈α∀one␈α∃wouldn't␈α∀prove␈α∃that␈α∃a␈α∀smarter
␈↓ α∧␈↓cognologist␈αmightn't␈αdo␈αbetter.␈α By␈αapproximately␈αwe␈αmean␈αthat␈αthere␈αmight␈αremain␈αa␈αcontroversy
␈↓ α∧␈↓as␈αto␈αwhether␈αthe␈αprogram␈αwas␈αsufficiently␈αLockean).␈α If␈αthe␈αprogram␈αsucceeded,␈αthere␈αwould␈αalso
␈↓ α∧␈↓remain the issue of whether it approximated human behavior.

␈↓ α∧␈↓␈↓ αTWe␈α
don't␈αhave␈α
a␈αcandidate␈α
Lockean␈αprogram␈α
and␈α
are␈αnot␈α
about␈αto␈α
write␈αone.␈α
 In␈αthis␈α
article
␈↓ α∧␈↓we␈α∂only␈α∂discuss␈α∂such␈α∂a␈α∂program␈α∂in␈α⊂the␈α∂hope␈α∂that␈α∂the␈α∂discussion␈α∂will␈α∂be␈α∂illuminating␈α⊂both␈α∂for
␈↓ α∧␈↓artificial intelligence and for epistemology.

␈↓ α∧␈↓␈↓ αTLocke␈α
does␈α
not␈α
discuss␈α
mechanisms,␈α
and␈α
the␈α
tools␈α
for␈α
dicussing␈α
intellectual␈αmechanisms␈α
have
␈↓ α∧␈↓only␈αbegun␈α
to␈αbe␈αcreated␈α
since␈αthe␈α
advent␈αof␈αmathematical␈α
logic,␈αcomputers,␈α
articicial␈αintelligence
␈↓ α∧␈↓research␈α∂and␈α∞the␈α∂study␈α∞of␈α∂the␈α∞epistemological␈α∂problems␈α∞of␈α∂cognology␈α∞(AI).␈α∂ Therefore,␈α∂we␈α∞must
␈↓ α∧␈↓begin␈αby␈αmaking␈αLocke's␈αproblem␈αmore␈αprecise␈αat␈αthe␈αcost␈αof␈αmodernizing␈αhis␈αformulations.␈α Here
␈↓ α∧␈↓are some considerations:

␈↓ α∧␈↓␈↓ αT1.␈αWe␈αshall␈αsuppose␈αthat␈αthe␈αprogram␈αmanipulates␈αsentences␈αin␈αa␈αsuitable␈αformal␈αlanguage.
␈↓ α∧␈↓Inputs␈α∂from␈α∂the␈α∂outside␈α∂produce␈α∂sentences␈α∂in␈α∞memory,␈α∂and␈α∂so␈α∂do␈α∂Locke's␈α∂␈↓↓internal␈α∂sensation␈↓␈α∞or
␈↓ α∧␈↓␈↓↓reflection␈↓.␈α Besides␈α␈↓↓internal␈αsensation␈↓,␈αwe␈αalso␈αhave␈αprocesses␈αof␈αlogical␈αinference,␈αand␈αmaybe␈αalso
␈↓ α∧␈↓non-monotonic␈α∩reasoning␈α⊃(McCarthy␈α∩1979).␈α⊃ Inference␈α∩generates␈α⊃new␈α∩sentences␈α∩from␈α⊃previous
␈↓ α∧␈↓sentences␈αaccording␈αto␈αthe␈αrules␈αof␈αinference␈αof␈αa␈αsuitable␈αlogical␈αsystem.␈α Reflection␈αgenerates␈αnew
␈↓ α∧␈↓sentences␈α⊂by␈α⊂looking␈α⊃at␈α⊂the␈α⊂collection␈α⊃of␈α⊂sentences␈α⊂already␈α⊃present.␈α⊂ One␈α⊂product␈α⊃of␈α⊂reflection
␈↓ α∧␈↓might␈αbe␈αa␈αformal␈αsentence␈αcorresponding␈αto␈αthe␈αEnglish,␈α␈↓↓"I␈αdon't␈αhave␈αenough␈αfacts␈αto␈αdecide␈αthe
␈↓ α∧␈↓↓best␈α∞way␈α
to␈α∞get␈α
to␈α∞the␈α
meeting␈α∞in␈α
Chicago"␈↓.␈α∞ It␈α
is␈α∞amusing␈α
that␈α∞the␈α
logical␈α∞notion␈α
of␈α∞a␈α
"reflection
␈↓ α∧␈↓principle"␈α∞which␈α∞from␈α∞the␈α∞sentence␈α∞␈↓↓"Snow␈α∞is␈α
white"␈↓␈α∞gives␈α∞the␈α∞sentence␈α∞␈↓↓"'Snow␈α∞is␈α∞white'␈α∞is␈α
true"
␈↓ α∧␈↓↓satisfies␈αLocke's␈αnotion␈αof␈αreflection.␈α The␈αabove␈αexamples␈αof␈αreflection␈αare␈αa␈αbit␈αfeeble;␈αwe␈αwill␈αneed
␈↓ α∧␈↓↓much more than that in order to vindicate Locke.

␈↓ α∧␈↓Other examples of reflection
␈↓ α∧␈↓I never saw a purple cow.

␈↓ α∧␈↓Is non-monotonic reasoning a form of reflection?


␈↓ α∧␈↓␈↓ αT2.␈αLocke␈αargues␈αabout␈αwhether␈αthe␈αprinciple␈α␈↓↓"What␈αis,␈αis"␈↓␈αis␈αinnate␈αand␈αargues␈αthat␈αit␈αisn't
␈↓ α∧␈↓on␈α
the␈α
ground␈α
that␈α
children␈α
and␈α
idiots␈α
don't␈α
assent␈α
to␈α
it.␈α
 Let␈α
us␈α
modernize␈α
the␈α
principle␈α
to␈αthe
␈↓ α∧␈↓tautology␈α⊂␈↓↓p ⊃ p␈↓,␈α⊂and␈α∂suppose␈α⊂that␈α⊂among␈α⊂the␈α∂capabilities␈α⊂of␈α⊂our␈α⊂program␈α∂is␈α⊂the␈α⊂ability␈α⊂to␈α∂do
␈↓ α∧␈↓deductive␈αpropositional␈αcalculus␈αreasoning.␈α Someone␈αmight␈αthen␈αclaim␈αthat␈αany␈αprogram␈αthat␈α
can
␈↓ α∧␈↓␈↓ u2


␈↓ α∧␈↓do␈αpropositional␈αcalculus␈αhas␈α␈↓↓p ⊃ p␈↓␈αinnately␈αpresent,␈αi.e.␈αbuilt␈αinto␈αthe␈αprogram,␈αbut␈αwe␈αwon't␈α
take
␈↓ α∧␈↓that as our sense of innate presence.

␈↓ α∧␈↓␈↓ αTInstead␈α⊂we␈α⊂will␈α⊂distinguish␈α⊃between␈α⊂the␈α⊂ideas␈α⊂that␈α⊃the␈α⊂programmer␈α⊂used␈α⊂in␈α⊃writing␈α⊂the
␈↓ α∧␈↓program␈α∞and␈α∞the␈α∞sentences␈α∞that␈α∞are␈α∞explicitly␈α∞present␈α∞in␈α∞the␈α∞machine␈α∞and␈α∞count␈α∞only␈α∂an␈α∞initial
␈↓ α∧␈↓stock␈α⊂of␈α⊃the␈α⊂latter␈α⊂as␈α⊃innate␈α⊂ideas.␈α⊂ This␈α⊃corresponds␈α⊂to␈α⊂Locke's␈α⊃exclusion␈α⊂of␈α⊂children␈α⊃on␈α⊂the
␈↓ α∧␈↓grounds␈αthat␈αthey␈αcannot␈αunderstand␈αthe␈αexplicit␈αstatement␈αof␈α␈↓↓"What␈αis,␈αis"␈↓␈αwell␈αenough␈αto␈α
assent
␈↓ α∧␈↓to␈α∀it␈α∀even␈α∀though␈α∀their␈α∀thinking␈α∀doesn't␈α∀controvert␈α∀it.␈α∀ It␈α∀also␈α∀corresponds␈α∀to␈α∀the␈α∪modern
␈↓ α∧␈↓mathematical␈αpractice␈αof␈αdistinguishing␈αthe␈αsentences␈αof␈αsystem␈αfrom␈αsentences␈αin␈αa␈αmetalanguage.
␈↓ α∧␈↓From the programming point of view the distinction is also desirable.

␈↓ α∧␈↓␈↓ αTUnfortunately,␈αthis␈αallows␈αthe␈αskeptic␈αto␈αargue␈αthat␈αthis␈αpermits␈αsneaking␈αin␈αany␈αinnate␈α
idea
␈↓ α∧␈↓by␈αbuilding␈αit␈αinto␈αthe␈αprogram,␈αbut␈αwe␈αpromise␈αnot␈αto␈αdo␈αthat,␈αand␈αhope␈αto␈αconvince␈αthe␈αskeptic
␈↓ α∧␈↓later␈α
when␈α
he␈α
sees␈α
the␈α
system␈α
that␈α
we␈α
haven't␈α
cheated.␈α
 Perhaps␈α
Locke's␈α
␈↓↓p ⊃ p␈↓␈α
example␈αwill␈α
always
␈↓ α∧␈↓be␈αcontroversial,␈α
and␈αconsidering␈α
Kant's␈αcontention␈αthat␈α
Euclidean␈αgeometry␈α
must␈αbe␈α
innate␈αmay
␈↓ α∧␈↓be␈α⊃more␈α⊃illuminating.␈α∩ Of␈α⊃course,␈α⊃the␈α⊃discovery␈α∩of␈α⊃non-Euclidean␈α⊃geometry␈α∩weakened␈α⊃Kant's
␈↓ α∧␈↓contentions,␈α∀but␈α∀perhaps␈α∀they␈α∪could␈α∀be␈α∀rehabilitated␈α∀by␈α∪modifying␈α∀it␈α∀to␈α∀some␈α∪approximate
␈↓ α∧␈↓geometry.

␈↓ α∧␈↓␈↓ αT3.␈αPerhaps␈αLocke␈α
can␈αbe␈αsufficiently␈α
vindicated␈αby␈αa␈α"Missouri␈α
program"␈αrather␈αthan␈α
by␈αa
␈↓ α∧␈↓full␈αreasoning␈αprogram.␈α A␈αMissouri␈αprogram␈αis␈α
more␈αlike␈αa␈αproof-checker␈αthan␈αa␈αproblem␈α
solver.
␈↓ α∧␈↓It␈α∞accepts␈α∞proposals␈α∞from␈α∂the␈α∞outside␈α∞to␈α∞perform␈α∂reasoning␈α∞and␈α∞checks␈α∞whether␈α∂these␈α∞proposals
␈↓ α∧␈↓lead␈αto␈αthe␈αdesired␈αconclusion.␈α In␈αthis␈α
case,␈αthe␈αMissouri␈αprogram␈αwould␈αhave␈αto␈αaccept␈α
proposals
␈↓ α∧␈↓to␈α
observe␈α
the␈α
outside␈α
world␈α
and␈α
its␈α
own␈α
memory.␈α
 Naturally,␈α
a␈α
Missouri␈α
program␈α
could␈α
be␈α
written
␈↓ α∧␈↓to␈α∪accept␈α∪any␈α∪conclusion,␈α∪but␈α∪it␈α∪a␈α∪correct␈α∪Missouri␈α∪program␈α∪cannot␈α∪be␈α∪led␈α∀to␈α∪unwarranted
␈↓ α∧␈↓conclusions␈αand␈αespecially␈αcan't␈α
be␈αled␈αto␈αlogical␈α
contradictions.␈α The␈αtechnical␈αadvantage␈α
thinking
␈↓ α∧␈↓in␈αterms␈αof␈αthe␈α
Missouri␈αprogram␈αis␈αthat␈αit␈α
bypasses␈αthe␈αproblem␈αof␈α
heuristics␈α(as␈αthe␈αterm␈αis␈α
used
␈↓ α∧␈↓in␈α∂AI),␈α∞since␈α∂the␈α∂outside␈α∞user␈α∂supplies␈α∂all␈α∞necessary␈α∂cleverness.␈α∞ It␈α∂seems␈α∂to␈α∞me␈α∂that␈α∂Locke␈α∞and
␈↓ α∧␈↓other␈α∞philosophers␈α∞haven't␈α∂been␈α∞concerned␈α∞with␈α∞heuristics␈α∂anyway,␈α∞and␈α∞splitting␈α∂cognology␈α∞into
␈↓ α∧␈↓epistemology and heuristics (I have always claimed) is worthwhile even for AI research.

␈↓ α∧␈↓␈↓ αT4.␈αAn␈αarea␈αin␈αwhich␈α
Locke␈αand␈αother␈αphilosophers␈αhave␈α
been␈αweak␈αis␈αin␈αtheir␈αdiscussion␈α
of
␈↓ α∧␈↓visual␈α∪perception.␈α∪ They␈α∪write␈α∪as␈α∪though␈α∪visual␈α∪perception␈α∪consisted␈α∪in␈α∪assigning␈α∪values␈α∪to
␈↓ α∧␈↓variables␈α⊂representing␈α⊂size,␈α∂color␈α⊂etc,,␈α⊂i.e.␈α⊂as␈α∂though␈α⊂the␈α⊂result␈α⊂of␈α∂an␈α⊂observation␈α⊂could␈α⊂be␈α∂the
␈↓ α∧␈↓execution␈α⊂of␈α∂the␈α⊂Algol␈α∂statement␈α⊂␈↓αbegin␈↓␈α∂size␈α⊂←␈α⊂10;␈α∂color␈α⊂←␈α∂red␈α⊂␈↓αend␈↓.␈α∂ Unfortunately,␈α⊂this␈α⊂is␈α∂too
␈↓ α∧␈↓simple,␈α
and␈α
the␈α
result␈α
of␈α
an␈α
observation␈α
has␈α
to␈α
be␈α
the␈α
creation␈α
of␈α
some␈α
kind␈α
of␈α
internal␈αnetwork␈α
or
␈↓ α∧␈↓perhaps␈α
a␈α∞whole␈α
collection␈α
of␈α∞sentences␈α
giving␈α
names␈α∞to␈α
parts␈α
of␈α∞the␈α
scene␈α
and␈α∞expressing␈α
their
␈↓ α∧␈↓relationships.␈α As␈αRussell␈α(1946)␈αpoints␈αout,␈αuntil␈αrecently␈αphilosophers␈αhave␈αwritten␈αas␈αthough␈αall
␈↓ α∧␈↓ideas␈α⊂could␈α⊂be␈α⊃written␈α⊂with␈α⊂unary␈α⊃predicates␈α⊂only␈α⊂and␈α⊂have␈α⊃ignored␈α⊂the␈α⊂necessity␈α⊃of␈α⊂treating
␈↓ α∧␈↓relations.␈α On␈αthe␈αone␈αhand,␈αthis␈αhas␈αled␈αto␈αoversimplifying␈αthe␈αproblems,␈αand␈αon␈αthe␈αother␈αhand,
␈↓ α∧␈↓it␈αhas␈αled␈αto␈αunjustified␈αconclusions␈αthat␈αcertain␈αkinds␈αof␈αreasoning␈α(that␈αhappen␈αto␈αrequire␈αmany
␈↓ α∧␈↓place relations) are impossible.

␈↓ α∧␈↓␈↓αRussell, Bertrand (1946)␈↓: ␈↓↓History of Western Philosophy␈↓,
␈↓ α∧␈↓Allen and Unwin, London.


␈↓ α∧␈↓␈↓ αTWe␈α∞aren't␈α
prepared␈α∞to␈α∞say␈α
what␈α∞kinds␈α∞of␈α
sentences␈α∞observations␈α∞might␈α
lead␈α∞to␈α∞in␈α
general,
␈↓ α∧␈↓but␈α∞here␈α∞is␈α∞a␈α∞step␈α∂beyond␈α∞what␈α∞is␈α∞implicit␈α∞in␈α∂Locke␈α∞and␈α∞other␈α∞philosophers.␈α∞ Suppose␈α∂that␈α∞the
␈↓ α∧␈↓␈↓ u3


␈↓ α∧␈↓letter␈α∂E␈α∂is␈α∞observed␈α∂in␈α∂the␈α∞middle␈α∂of␈α∂an␈α∂English␈α∞text␈α∂by␈α∂a␈α∞Chinese␈α∂unfamiliar␈α∂with␈α∂the␈α∞Latin
␈↓ α∧␈↓alphabet.  Calling the given occurrence of E by the name ␈↓↓E1,␈↓ we might have the sentence

␈↓ α∧␈↓␈↓↓in(E1,Scene1)␈α≡∧␈α∨ispart(X1,E1)␈α≡∧␈α≡ispart(X2,E1)␈α∨∧␈α≡ispart(X3,E1)␈α≡∧␈α∨ispart(X4,E1)␈α≡∧
␈↓ α∧␈↓↓ishorizontalsegment(X1)␈α?␈α↓∧␈α?␈α↓ishorizontalsegment(X2)␈α?␈α↓∧␈α?␈α↓ishorizontalsegment(X3)␈α?␈α↓∧
␈↓ α∧␈↓↓isverticalsegement(X4)␈α∧␈αlength(X1)␈α=␈α1␈α∧␈αlength(X2)␈α=␈α0.8␈α∧␈αlength(X3)␈α=␈α1␈α∧␈αlength(X4)␈α=␈α1.2␈α∧
␈↓ α∧␈↓↓top(X4) = left(X1) ∧ middle(X4) = left(X2) ∧ bottom(X4) = left(X3)␈↓

␈↓ α∧␈↓giving␈α⊃part␈α⊂of␈α⊃the␈α⊃result␈α⊂of␈α⊃the␈α⊂observation.␈α⊃ Perhaps␈α⊃more␈α⊂of␈α⊃the␈α⊂same␈α⊃would␈α⊃complete␈α⊂the
␈↓ α∧␈↓observation,␈αbut␈αmaybe␈α
further␈αelaboration␈αis␈αrequired.␈α
 Note␈αthat␈αwe␈α
have␈αhad␈αto␈αinvent␈α
internal
␈↓ α∧␈↓names␈αfor␈αthe␈αparts␈αof␈α
the␈αfigure␈αin␈αorder␈αto␈α
write␈αthe␈αsentence.␈α An␈αinternal␈αrepresentation␈α
might
␈↓ α∧␈↓make do with pointers to parts of an actual image.

␈↓ α∧␈↓␈↓ αT5.␈αIn␈αone␈αplace␈αLocke␈αseems␈αto␈αimply␈αthat␈αreflection␈αoperates␈αonly␈αon␈αinformation␈αproduced
␈↓ α∧␈↓from␈αthe␈αsenses␈αand␈αnot␈αon␈αinformation␈αproduced␈αby␈αreflection␈αitself.␈α In␈αother␈αplaces␈αhe␈αseems␈αto
␈↓ α∧␈↓allow␈αreflection␈αon␈αthe␈αresults␈αof␈αreflection.␈α We␈αshall␈αallow␈αit␈αin␈αthe␈αstrong␈αsense␈αof␈αeven␈αallowing
␈↓ α∧␈↓sentences that refer to themselves.