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↓ α∧↓↓ u1


↓ α∧↓α↓ ∧6A PROGRAMME FOR META-EPISTEMOLOGY

↓ α∧↓↓ αTMeta-epistemologyα
willα∞beα
toα∞epistemologyα
asα
metamathematicsα∞isα
toα∞mathematics.α
 Taking
↓ α∧↓epistemologyα
asα
theα
theoryα
ofα
knowledgeαandα
howα
itα
isα
obtained,α
meta-epistemologyαstudiesα
systems
↓ α∧↓thatα∂seekα⊂knowledgeα∂inα⊂aα∂world.α∂ Anα⊂epistemologicalα∂systemα⊂isα∂thenα∂aα⊂worldα∂andα⊂aα∂knowledge
↓ α∧↓seeker in that world.

↓ α∧↓↓ αTOurα
ultimateα
goalα
isα
toα
studyα
epistemologicalα
systemsα
technically.α
 Thusα
weα
mayα
considerα
a
↓ α∧↓knowledgeα⊃seekingα⊂computerα⊃programα⊂connectedα⊃toα⊂aα⊃systemα⊂ofα⊃finiteα⊂stateα⊃automataα⊃andα⊂ask
↓ α∧↓whetherα
aα
givenα
knowledgeαseekingα
strategyα
canα
learnα
certainαfactsα
aboutα
theα
"externalαworld".α
 To
↓ α∧↓theαextentαthatαepistemologicalαquestionsαcanαbeαputαinαsuchαaαtechnicalαform,αtheirαanswersα
areαto
↓ α∧↓beα∂obtainedα∂byα∞mathematics.α∂ Theα∂philosophicalα∞issuesα∂willα∂thenα∞concernα∂whetherα∂theα∞technical
↓ α∧↓formα
ofαtheα
questionαproperlyα
representsαtheα
originalαphilosophicalα
problem.α Ifα
theα
experienceαof
↓ α∧↓metamathematicsα⊃isα⊃aα∩portent,α⊃theα⊃mathematicalα⊃answersα∩won'tα⊃beα⊃acceptedα∩asα⊃philosophically
↓ α∧↓conclusiveα∀butα∀willα∀neverthelessα∀transformα∀theα∀wayα∀inα∀whichα∀philosophersα∀thinkα∀aboutα∪the
↓ α∧↓problems.α
 Iα
haveα
inα
mindα
Goedel'sα
incompletenessα
theorems,α
Gentzen'sα
resultsα
onα
theα
consistency
↓ α∧↓of arithmetic and the result that intuitionist and classical arithmetic are equiconsistent.

↓ α∧↓↓ αTIα
mustα
confessα
thatαIα
cannotα
yetα
giveα
technicalαformsα
ofα
epistemologicalα
questionsα
thatαseem
↓ α∧↓ripe for mathematical attack.  However, I have some ideas that may be helpful.

↓ α∧↓1.α
Avoidingα
heuristicα
problems.α
 Workα
inα
artificialα
intelligenceα
suggestsα
thatα
findα
outα
theα
factsα
of
↓ α∧↓theα∂worldα∞hasα∂twoα∞components.α∂ Oneα∂componentα∞isα∂aα∞generalα∂frameworkα∞orα∂languageα∂inα∞which
↓ α∧↓hypothesesα
andα
factsα
canα
beα
expressed,α
andα
theα
otherα
isα
aα
strategyα
ofα
searchα
andα
experiment.α
 In
↓ α∧↓artificial intelligence, the first is called epistemology, and the second is called heuristics.

↓ α∧↓↓ αTItα∞isα∞ourα
hopeα∞thatα∞theα
heuristicα∞problemα∞canα
beα∞avoidedα∞inα
studyingα∞epistemologyα∞inα
the
↓ α∧↓followingα∂way.α∂ Insteadα∂ofα∂imaginingα∂aα∂computerα∂programα∂thatα∂seeksα∂knowledge,α∂weα∂imagineα∂a
↓ α∧↓programα
thatα
isα
ledα
towardsα
theα
truthα
byα
aα
Socraticα
tutor.α
 Itsα
tutorα
suppliesα
noα
knowledgeα
toα
be
↓ α∧↓acceptedα∞onα∞theα∞tutor'sα∞authority,α∞butα∞merelyα∞proposesα∞observations,α∞experimentsα∞andα∞inferences.
↓ α∧↓Theα⊃studentα⊃programα⊃acceptsα⊃orα⊃rejectsα⊃theseα⊃stepsα⊃accordingα⊃toα⊃itsα⊃built-inα⊃epistemology,α⊃i.e.
↓ α∧↓knowledge,αrulesα
ofαinference,αandα
rulesαofαreasonableα
conjecture.α Weαrequireα
thatαtheα
studentαbe
↓ α∧↓consistentα
inα
thatα
noα
Socratesα
canα
leadα
itα
intoα
aα
contradiction.α
 (Laterα
weα
shallα
haveα
toα
relaxα
this
↓ α∧↓strictureα
aα
little).α
 Ifα
theα
Socraticα
tutorα
canα
leadα
itα
toα
discoverα
aα
certainα
factα
aboutα
itsα
world,α
then
↓ α∧↓weαshallαsayαthatα
itsαepistemologyαisαadequateα
forαobtainingαthisαfact.α
 Sinceαwe,αtheαcreatorsαofα
the
↓ α∧↓epistemologicalα∞system,α
alsoα∞createdα
theα∞worldα∞inα
whichα∞knowledgeα
isα∞sought,α
weα∞knowα∞whatα
the
↓ α∧↓facts are, so it is a definite question as to whether the program has discovered them.

↓ α∧↓↓ αTWeα
mustαhopeα
thatαavoidingα
heuristicsα
isαsuccessful,α
becauseαstudyingα
systemsα
thatαcombine
↓ α∧↓epistemology and heuristics will be very difficult.

↓ α∧↓↓ αTConsiderα
firstαKant'sα
ideaαthatα
ourαabilityα
toα
understandαtheα
worldαdependsα
onαhavingα
some
↓ α∧↓innateα
ideas.α Manyα
ofαhisα
originalαproposalsα
asα
toαwhatα
modesαofα
perceivingαtheα
worldαareα
innate,
↓ α∧↓e.g.αEuclideanα
geometry,αhaven'tαsurvivedα
intact,αandαothersα
areαinsufficientlyα
definitelyαdescribed,
↓ α∧↓butα
somethingα
alongα
thisα∞lineα
isα
stillα
defended.α
 Hereα∞isα
anα
attemptα
atα
aα∞correspondingα
technical
↓ α∧↓question.

↓ α∧↓↓ αTLetα
theα
worldα
beα
aα
systemα
withα
aα
stateα
thatα
variesα
asα
aα
functionα
ofα
aα
realα
variableα
↓↓t↓α
called
↓ α∧↓time.α⊂ Letα⊂theα⊂"student"α⊂beα⊂computerα⊃programα⊂withα⊂senseα⊂andα⊂motorα⊂organsα⊂connectedα⊃toα⊂this
↓ α∧↓↓ u2


↓ α∧↓"outsideαworld".α Weαsupposeαthatα
theαwayαtheαstateαofαtheα
outsideαworldαchangesαasαaα
functionαof
↓ α∧↓itsα∞previousα∞historyα∞andα∞itsα∞motorα∞inputsα∂isα∞describedα∞byα∞aα∞collectionα∞ofα∞sentencesα∞ofα∂setα∞theory.
↓ α∧↓Supposeα∂furtherα∂thatα∞theα∂particularα∂"outsideα∂world"α∞isα∂anα∂arbitraryα∂memberα∞ofα∂aα∂certainα∂setα∞of
↓ α∧↓"possible outside worlds" - this set also being defined by a sentence of set theory.

↓ α∧↓↓ αTNowα
weα
canα
tryα∞toα
embodyα
differentα
epistemologicalα∞strategiesα
inα
theα
studentα∞program.α
 A
↓ α∧↓ratherα⊂strongα⊂empiricistα⊂strategyα⊂wouldα⊂allowα∂onlyα⊂hypothesesα⊂thatα⊂wereα⊂expressedα⊂inα⊂termsα∂of
↓ α∧↓sensory-motorα
relationsαinα
someαrestrictedα
language.α Aα
Kantianαprogramα
wouldα
allowαhypotheses
↓ α∧↓thatα∂conformedα⊂toα∂someα∂preferredα⊂↓↓syntheticα∂aα⊂priori↓α∂ideas.α∂ Itα⊂seemsα∂toα∂meα⊂thatα∂aα⊂setα∂theoretic
↓ α∧↓epistemologyαcorrespondingαtoα
modernαscientificαpracticeα
wouldαallowαtheα
tutorαtoαproposeα
newαset
↓ α∧↓theoreticα∂constantsα∂withoutα∂havingα∂toα∂defineα∂themα∂andα∂proposeα∂sentencesα∂ofα∂setα∂theoryα⊂asα∂laws
↓ α∧↓connectingαthem.α
 Dependingαonαwhatα
wasαproposedα
andαwhatαtheα
worldαisα
like,αtheαstudentα
might
↓ α∧↓beα∞ableα
toα∞decideα
onα∞theseα
proposedα∞laws,α
butα∞noα
aα∞prioriα
requirementα∞wouldα
beα∞madeα∞thatα
the
↓ α∧↓proposed laws be decidable experimentally.

↓ α∧↓↓ αTWeα∞shouldα∞compareα∞theα∂efficacyα∞ofα∞manyα∞specificα∂innateα∞modesα∞ofα∞perception,α∂e.g.α∞spatial
↓ α∧↓andα
temporal,α
withα∞theα
generalα
modeα
thatα∞saysα
thatα
theα
worldα∞isα
aα
causalα∞systemα
mathematically
↓ α∧↓describable,αe.g.αbyαsentencesαofαZermelo-Fraenkelαsetαtheory.α Theαlatterαpresumablyαhasα
aαcertain
↓ α∧↓universality.α
 Anyα
specificα
modeα
ofα
perception,α
e.g.α
theα
tendencyα
toα
interpretα
sensationsα
asα
arising
↓ α∧↓fromα
persistentα
objectsα
locatedα
inα
three-dimensionalα
space,α
canα
beα
formulatedα
asα
aα
hypothesisα
in
↓ α∧↓set theory.

↓ α∧↓↓ αTSystemsα∞ofα
theα∞typeα
describedα∞aboveα∞separateα
theα∞knowerα
fromα∞theα
outsideα∞world.α∞ Atα
the
↓ α∧↓costα
ofα
elaborationα∞thatα
mayα
makeα
theoremsα∞harderα
toα
formulateα
andα∞prove,α
weα
canα∞removeα
the
↓ α∧↓separation.α∂ Considerα∂aα∂twoα∞orα∂threeα∂dimensionalα∂cellularα∞automatonα∂system.α∂ Inα∂suchα∂aα∞system,
↓ α∧↓eachα
cellα
isα
aα∞finiteα
automatonα
whoseα
stateα
atα∞timeα
↓↓t+1↓α
dependsα
onα
itsα∞stateα
andα
theα
statesα∞ofα
its
↓ α∧↓immediateαneighborsαatαtimeα↓↓t.↓αAαgoodαexampleαisαConway'sαLifeαautomatonαthatαusesα
anαinfinite
↓ α∧↓twoαdimensionalαarrayαofαtwoαstateαautomataα-αoneαlocatedαatαeachαpointαofαtheαplaneαwithαinteger
↓ α∧↓co-ordinates.α
 Theαstateα
ofαaα
cellαatα
timeα↓↓t+1↓α
isα0α
ifαtheα
numberαofα
itsαeightα
neigborsαinα
stateαoneα
is
↓ α∧↓lessαthanα
2αorα
moreαthanα3.α
 Ifα2α
neighborsαareαinα
stateα1,α
itαretainsαitsα
stateαandα
ifα3αneighborsα
are
↓ α∧↓inα∞stateα
1,α∞itα∞goesα
toα∞stateα∞1.α
 Itα∞hasα
beenα∞shownα∞thatα
theα∞Lifeα∞cellularα
automatonα∞isα∞aα
universal
↓ α∧↓computerα∂andα∂constructor.α⊂ Inα∂particular,α∂self-reproducingα∂arraysα⊂ofα∂Lifeα∂cellsα∂thatα⊂canα∂execute
↓ α∧↓arbitraryα∪computerα∀programsα∪areα∪possible.α∀ Weα∪canα∪imagineα∀equippingα∪suchα∪anα∀arrayα∪with
↓ α∧↓differentα
epistemologicalα
programsα
andα
askα
whatα
programsα
wouldα
doα
formulateα
andα
confirmα
the
↓ α∧↓hypothesisα
thatα
theα
fundamentalα
physicsα
ofα
theirα
worldα
wasα
theα
Lifeα
cellularα
automaton.α
 Ifαthere
↓ α∧↓wereα
manyαofα
them,α
whatαhypothesesα
wouldαtheyα
formulateα
aboutαotherα
minds,α
consciousness,αetc?
↓ α∧↓Wouldα
theyα
discriminateα
properlyαbetweenα
theirα
programsα
(minds)αandα
theα
configurationsα
ofαcells
↓ α∧↓(brains)α⊗constitutingα⊗theα↔computerα⊗executingα⊗theα⊗program?α↔ Indeed,α⊗isα⊗thisα↔theα⊗interesting
↓ α∧↓distinction?