el argumento mentalista.docx

8/16/2019 el argumento mentalista.docx

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El "argumento mentalista"

The Lucas-Penrose Argument about Gödel's Theorem

In 1961, J.R. Lucas published “Minds, Machines and Gödel,” in which he forula!ed a con!ro"ersial an!i#echanis

ar$uen!. %he ar$uen! clais !ha! Gödel&s firs! incople!eness !heore shows !ha! !he huan ind is no! a %urin$

achine, !ha! is, a copu!er. %he ar$uen! has $enera!ed a $rea! deal of discussion since !hen. %he influen!ial

'opu!a!ional %heor( of Mind, which clais !ha! !he human mind is a copu!er, is false if Lucas&s ar$uen!

succeeds. )ur!herore, if Lucas&s ar$uen! is correc!, !hen “s!ron$ ar!ificial in!elli$ence,” !he "iew !ha! i! is possible a!

leas! in principle !o cons!ruc! a achine !ha! has !he sae co$ni!i"e abili!ies as huans, is false. *owe"er, nuerous

ob+ec!ions !o Lucas&s ar$uen! ha"e been presen!ed. oe of !hese ob+ec!ions in"ol"e !he consis!enc( or inconsis!enc(

of !he huan ind- if we canno! es!ablish !ha! huan inds are consis!en!, or if we can es!ablish !ha! !he( are in fac!

inconsis!en!, !hen Lucas&s ar$uen! fails for reasons ade clear below/. 0!hers ob+ec! !o "arious idealia!ions !ha!

Lucas&s ar$uen! a2es. !ill o!hers find soe o!her faul! wi!h !he ar$uen!. Lucas&s ar$uen! was re+u"ena!ed when!he ph(sicis! R. 3enrose forula!ed and defended a "ersion of i! in !wo boo2s, 1949&s The Emperor's New Mind and

1995&s Shadows of the Mind. l!hou$h !here are siilari!ies be!ween Lucas&s and 3enrose&s ar$uen!s, !here are also

soe ipor!an! differences. 3enrose ar$ues !ha! !he Gödelian ar$uen! iplies a nuber of clais

concernin$consciousness and 7uan!u ph(sics- for e8aple, consciousness us! arise fro 7uan!u processes and i!

i$h! !a2e a re"olu!ion in ph(sics for us !o ob!ain a scien!ific e8plana!ion of consciousness. %here ha"e also been

ob+ec!ions raised !o 3enrose&s ar$uen! and !he "arious clais he infers fro i! soe 7ues!ion !he an!i#echanis

ar$uen! i!self, soe 7ues!ion whe!her i! en!ails !he clais abou! consciousness and ph(sics !ha! he !hin2s i! does,

while o!hers 7ues!ion his clais abou! consciousness and ph(sics, apar! fro his an!i#echanis ar$uen!.

ec!ion one discusses Lucas&s "ersion of !he ar$uen!. :uerous ob+ec!ions !o !he ar$uen! ; alon$ wi!h Lucas&s

responses !o !hese ob+ec!ions ; are discussed in sec!ion !wo. 3enrose&s "ersion of !he ar$uen!, his clais abou!

consciousness and 7uan!u ph(sics, and "arious ob+ec!ions !ha! are specific !o 3enrose&s clais are discussed in sec!ion

!hree. ec!ion four briefl( addresses !he 7ues!ion, “


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no! pro"able, so i! us! be !ha! we cannot prove i! in S. %he assup!ion !ha! !he Gödel sen!ence is pro"able in S leads

!o con!radic!ion, so if S is consis!en!, i! us! be !ha! !he Gödel sen!ence is unpro"able in S, and !herefore !rue, because

!he sen!ence clais !ha! i! is no! pro"able. In o!her words, if consis!en!, S is incople!e, as !here is a !rue a!hea!ical

clai !ha! canno! be pro"en in S. )or an in!roduc!ion !o Gödel&s !heore, see :a$el and :ewan 19A4/.

Gödel&s proof is a! !he core of Lucas&s 1961/ ar$uen!, which is rou$hl( !he followin$. 'onsider a achine cons!ruc!ed

!o produce !heores of ari!he!ic. Lucas ar$ues !ha! !he opera!ions of !his achine are analo$ous !o a foral s(s!e.

%o e8plain, “if !here are onl( a defini!e nuber of !(pes of opera!ion and ini!ial assup!ions buil! in!o !he BachineC, we

can represen! !he all b( sui!able s(bols wri!!en down on paper” Lucas 1961 11A/. %ha! is, we can associa!e specific

s(bols wi!h specific s!a!es of !he achine, and we can associa!e “rules of inference” wi!h !he opera!ions of !he achine

!ha! cause i! !o $o fro one s!a!e !o ano!her. In effec!, “$i"en enou$h !ie, paper, and pa!ience, Bwe couldC wri!e down

an analo$ue of !he achine&s opera!ions,” and “!his analo$ue would in fac! be a foral proof” ibid/. o essen!iall(, !he

ari!he!ical clais !ha! !he achine will produce as ou!pu!, !ha! is, !he clais !he achine pro"es !o be !rue, will

“correspond !o !he !heores !ha! can be pro"ed in !he correspondin$ foral s(s!e” ibid/. :ow suppose !ha! we

cons!ruc! !he Gödel sen!ence for !his foral s(s!e. ince !he Gödel sen!ence canno! be pro"en in !he s(s!e, !he

achine will be unable !o produce !his sen!ence as a !ru!h of ari!he!ic. *owe"er, a huan can loo2 and see !ha! !he

Gödel sen!ence is !rue. In o!her words, !here is a! leas! one !hin$ !ha! a huan ind can do !ha! no achine can.

%herefore, “a achine canno! be a cople!e and ade7ua!e odel of !he ind” Lucas 1961 11?/. In shor!, !he huan

ind is no! a achine.

*ere is how Lucas 199D para$raph ?/ describes !he ar$uen!

% do not o3er a sim4le 5noc5/do+n 4roof that minds are inherently better than machines6 but a schemafor constructing a dis4roof of any 4lausible mechanist thesis that might be 4ro4osed. "he dis4roof de4ends on the 4articular mechanist thesis being maintained6 and does not claim to sho+ that the mindis uniformly better than the 4ur4orted mechanist re4resentation of it6 but only that it is one res4ectbetter and therefore di3erent. "hat is enough to refute that 4articular mechanist thesis.

)ur!her, Lucas ibid/ belie"es !ha! a "arian! of his ar$uen! can be forula!ed !o refu!e an( fu!ure echanis! !hesis. %o

e8plain, Lucas sees !o en"ision !he followin$ scenario a echanis! forula!es a par!icular echanis!ic !hesis b(

claiin$, for e8aple, !ha! !he huan ind is a %urin$ achine wi!h a $i"en foral specifica!ion S. Lucas !hen refu!es

!his !hesis b( producin$ S&s Gödel sen!ence, which we can see is !rue, bu! !he %urin$ achine canno!. %hen, a echanis!

pu!s for!h a differen! !hesis b( claiin$, for e8aple, !ha! !he huan ind is a %urin$ achine wi!h foral

specifica!ion S’ . @u! !hen Lucas produces !he Gödel sen!ence for S&, and so on, un!il, presuabl(, !he echanis! sipl(

$i"es up.

0ne who has no! s!udied Gödel&s !heore in de!ail i$h! be wonderin$ wh( can&! we sipl( add !he Gödel sen!ence !o

!he lis! of !heores a $i"en achine “2nows” !hereb( $i"in$ !he achine !he abili!( Lucas clais i! does no! ha"e= In

Lucas&s ar$uen!, we consider soe par!icular %urin$ achine specifica!ion S, and !hen we no!e !ha! “S#achines”

!ha! is, !hose achines !ha! ha"e foral specifica!ion S/ canno! see !he !ru!h of !he Gödel sen!ence while we can, so

huan inds canno! be S#achines, a! leas!. @u! wh( can&! we sipl( add !he Gödel sen!ence !o !he lis! of !heores

!ha! S#achines can produce= Eoin$ so will presuabl( $i"e !he achines in 7ues!ion !he abili!( !ha! alle$edl(

separa!es !he fro huan inds, and Lucas&s ar$uen! fal!ers. %he proble wi!h !his response is !ha! e"en if we add

!he Gödel sen!ence !o S#achines, !hereb( producin$ %urin$ achines !ha! can produce !he ini!ial Gödel sen!ence as a

!ru!h of ari!he!ic, Lucas can sipl( produce a new Gödel sen!ence for !hese upda!ed achines, one which alle$edl( we

can see is !rue bu! !he new achines canno!, and so on ad infini!u. In su, as Lucas 199D para$raph 9/ s!a!es, “I! is

"er( na!uralF!o respond b( includin$ !he Gödelian sen!ence in !he achine, bu! of course !ha! a2es !he achine a

differen! achine wi!h a differen! Gödelian sen!ence all of i!s own.” %his issue is discussed fur!her below.

0ne reason Lucas&s ar$uen! has recei"ed so uch a!!en!ion is !ha! if !he ar$uen! succeeds, !he widel( influen!ial

'opu!a!ional %heor( of Mind is false. Li2ewise, if !he ar$uen! succeeds, !hen “s!ron$ ar!ificial in!elli$ence” is false- i!

is ipossible !o cons!ruc! a achine !ha! can perfec!l( iic our co$ni!i"e abili!ies. @u! !here are fur!her iplica!ions-

for e8aple, a "iew in philosoph( of ind 2nown as %urin$ achine functionalism clais !ha! !he huan ind is a

%urin$ achine, and of course, if Lucas is ri$h!, !his for of func!ionalis is false. )or ore on %urin$ achine

func!ionalis, see 3u!na 196D//. o clearl( !here is uch a! s!a2e.

. oe 3ossible 0b+ec!ions !o Lucas

http://www.iep.utm.edu/functism/http://www.iep.utm.edu/functism/http://www.iep.utm.edu/functism/http://www.iep.utm.edu/functism/


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Lucas&s ar$uen! has been, and s!ill is, "er( con!ro"ersial. oe ob+ec!ions !o !he ar$uen! in"ol"e consis!enc(- if we

canno! es!ablish our own consis!enc(, or if we are in fac! inconsis!en!, !hen Lucas&s ar$uen! fails for reasons ade

clear below/. )ur!herore, soe ha"e ob+ec!ed !ha! !he al$ori!h !he huan ind follows is so cople8 we i$h! be

fore"er unable !o forula!e our own Gödel sen!ence- if so, !hen a(be we canno! see !he !ru!h of our own Gödel

sen!ence and !herefore we i$h! no! be differen! fro achines af!er all. 0!hers ob+ec! !o "arious idealia!ions !ha!

Lucas&s ar$uen! a2es. !ill o!hers find soe o!her faul! wi!h !he ar$uen!. In !his sec!ion, soe of !he ore no!able

ob+ec!ions !o Lucas&s ar$uen! are discussed.

a. 'onsis!enc(

Lucas&s ar$uen! faces a nuber of ob+ec!ions in"ol"in$ !he issue of consis!enc(- !here are !wo rela!ed !hou$h dis!inc!

lines of ar$uen! on !his issue. )irs!, soe clai !ha! we canno! es!ablish our own consis!enc(, whe!her we are

consis!en! or no!. econd, soe clai !ha! we are in fac! inconsis!en!. %he success of ei!her of !hese ob+ec!ions would

be sufficien! !o defea! Lucas&s ar$uen!. @u! firs!, !o see wh( !hese ob+ec!ions if successful/ would defea! Lucas&s

ar$uen!, recall !ha! Gödel&s firs! incople!eness !heore s!a!es !ha! if a foral s(s!e in which we can pro"e a

sui!able aoun! of nuber !heor(/ is consis!en!, !he Gödel sen!ence is !rue bu! unpro"able in !he s(s!e. %ha! is, !he

Gödel sen!ence will be !rue and unpro"able onl( in consis!en! s(s!es. In an inconsis!en! s(s!e, one can pro"e an(

clai wha!soe"er because in classical lo$ic, an( and all clais follow fro a con!radic!ion- !ha! is, an inconsis!en!

s(s!e will no! be incople!e. :ow, suppose !ha! a echanis! clais !ha! we are %urin$ achines wi!h foral

specifica!ion S, and !his foral specifica!ion is inconsis!en! so !he echanis! is essen!iall( claiin$ !ha! we are

inconsis!en!/. Lucas&s ar$uen! sipl( does no! appl( in such a si!ua!ion- his ar$uen! canno! defea! !his echanis!.

Lucas clais !ha! an( achine will be such !ha! !here is a clai !ha! is !rue bu! unpro"able for !he achine, and since

we can see !he !ru!h of !he clai bu! !he achine canno!, we are no! achines. @u! if !he achine in 7ues!ion is

inconsis!en!, !he achine will be able !o pro"e !he Gödel sen!ence, and so will no! suffer fro !he deficienc( !ha! Lucas

uses !o separa!e achines fro us. In shor!, for Lucas&s ar$uen! !o succeed, huan inds us! be consis!en!.

'onse7uen!l(, if one clais !ha! we canno! es!ablish our own consis!enc(, !his is !an!aoun! !o claiin$ !ha! we canno!

es!ablish !he !ru!h of Lucas&s conclusion. )ur!herore, !here are soe $ood reasons for !hin2in$ !ha! e"en if we are

consis!en!, we canno! es!ablish !his. )or e8aple, Gödel&s second incople!eness !heore, which 7uic2l( follows fro

his firs! !heore, clais !ha! one canno! pro"e !he consis!enc( of a foral s(s!e S fro wi!hin !he s(s!e i!self, so, if

we are foral s(s!es, we canno! es!ablish our own consis!enc(. In o!her words, a echanis! can a"oid Lucas&sar$uen! b( sipl( claiin$ !ha! we are foral s(s!es and !herefore, in accordance wi!h Gödel&s second !heore,

canno! es!ablish our own consis!enc(. Man( ha"e ade !his ob+ec!ion !o Lucas&s ar$uen! o"er !he (ears- in fac!, Lucas

discusses !his ob+ec!ion in his ori$inal 1961/ and a!!ribu!es i! !o Ro$ers 19AH/ and 3u!na. 3u!na ade !he ob+ec!ion

in a con"ersa!ion wi!h Lucas e"en before Lucas&s 1961/ see also 3u!na 196D//. Li2ewise, *u!!on 19H6/ ar$ues fro

"arious considera!ions drawn fro 3robabili!( %heor( !o !he conclusion !ha! we canno! asser! our own consis!enc(. )or

e8aple, *u!!on clais !ha! !he probabili!( !ha! we are inconsis!en! is abo"e ero, and !ha! if we clai !ha! we are

consis!en!, !his “is a clai !o infallibili!( which is insensi!i"e !o coun!er#ar$uen!s !o !he poin! of irra!ionali!(” Lucas

19H6 15A/. In su, for Lucas&s ar$uen! !o succeed, we us! be assured !ha! huans are consis!en!, bu! "arious

considera!ions, includin$ Gödel&s second !heore, ipl( !ha! we can ne"er es!ablish our own consis!enc(, e"en if we are

consis!en!.

no!her possible response !o Lucas is sipl( !o clai !ha! huans are in fac! inconsis!en! %urin$ achines.


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wi!h our inconsis!encies, and would happil( affir bo!h hal"es of a con!radic!ion” ibid/. In effec!, we are no!

inconsis!en! achines e"en !hou$h we are soe!ies inconsis!en!- we are fallible bu! no! s(s!ea!icall( inconsis!en!.

)ur!herore, if we were inconsis!en! achines, we would po!en!iall( endorse an( proposi!ion wha!soe"er ibid/. s

en!ioned abo"e, one can pro"e an( clai wha!soe"er fro a con!radic!ion, so if we are inconsis!en! %urin$ achines,

we would po!en!iall( belie"e an(!hin$. @u! we do no! $enerall( belie"e an( clai wha!soe"er for e8aple, we do no!

belie"e !ha! we li"e on Mars/, so i! appears we are no! inconsis!en! %urin$ achines. 0ne possible coun!er !o Lucas is !o

clai !ha! we are inconsis!en! %urin$ achines !ha! reason in accordance wi!h soe for of 4araconsistent logic inparaconsis!en! lo$ic, !he inference fro a con!radic!ion !o an( clai wha!soe"er is bloc2ed/- if so, !his e8plains wh( we

do no! endorse an( clai wha!soe"er $i"en our inconsis!enc( see 3ries! DD?/ for ore on paraconsis!en! lo$ic/. 0ne

could also ar$ue !ha! perhaps !he inconsis!enc( in 7ues!ion is hidden, buried deep wi!hin our belief s(s!e- if we are no!

aware of !he inconsis!enc(, !hen perhaps we canno! use !he inconsis!enc( !o infer an(!hin$ a! all Lucas hiself

en!ions !his possibili!( in his 199D//.

Lucas also ar$ues !ha! e"en if we canno! pro"e !he consis!enc( of a s(s!e fro wi!hin !he s(s!e i!self, as Gödel&s

second !heore deons!ra!es, !here i$h! be o!her wa(s !o de!erine if a $i"en s(s!e is consis!en! or no!. Lucas

199D/ poin!s ou! !ha! !here are fini!ar( consis!enc( proofs for bo!h !he proposi!ional calculus and !he firs!#order

predica!e calculus, and !here is also Gen!en&s proof of !he consis!enc( of leen!ar( :uber %heor(. Eiscussin$

Gen!en&s proof in ore de!ail, Lucas 1996/ ar$ues !ha! while Gödels second !heore deons!ra!ed !ha! we canno!

pro"e !he consis!enc( of a s(s!e fro within !he s(s!e i!self, i! i$h! be !ha! we can pro"e !ha! a s(s!e is consis!en!

wi!h considera!ions drawn fro outside !he s(s!e. 0ne "er( serious proble wi!h Lucas&s response here, as Lucas

ibid/ hiself no!es, is !ha! !he wider considera!ions !ha! such a proof uses us! be consis!en! !oo, and !his can be

7ues!ioned. no!her possible response is !he followin$ a(be we can “s!ep ou!side” of, sa(, 3eano ari!he!ic and ar$ue

!ha! 3eano ari!he!ic is consis!en! b( appealin$ !o considera!ions !ha! are ou!side of 3eano ari!he!ic- howe"er, i! isn&!

clear !ha! we can “s!ep ou!side” of oursel"es !o show !ha! we are consis!en!.

Lucas 19H6 15H/ also a2es !he followin$ “7antian” poin!

84erha4s9 +e must assume our o+n consistency6 if thought is to be 4ossible at all. %t is6 4erha4s li5e the

uniformity of nature6 not something to be established at the end of a careful chain of argument6 butrather a necessary assum4tion +e must ma5e if +e are to start on any thin5ing at all.

possible repl( is !ha! assuin$ we are consis!en! because !his assup!ion is a necessar( precondi!ion for !hou$h!/

and our ac!uall( bein$ consis!en! are !wo differen! !hin$s, and e"en if we us! assue !ha! we are consis!en! !o $e!

!hou$h! off of !he $round, we i$h! be inconsis!en! ne"er!heless. )inall(,


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leas! accordin$ !o Lucas, i! i$h! be difficul!, bu! i! sees !ha! we could, a! leas! in principle, de!erine wha! !he

Gödelian forula is for an( $i"en s(s!e.

c. %he


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Eenne!! 19H/ has claied !here is soe!hin$ odd abou! Lucas&s ar$uen! insofar as i! sees !o !rea! huans as

crea!ures !ha! sipl( wander around asser!in$ !ru!hs of firs!#order ari!he!ic. Eenne!! 19H A?D/ rear2s,

0en do not sit around uttering theorems in a uniform &ocabulary6 but say things in earnest and jest6ma5es sli4s of the tongue6 s4ea5 se&eral languages:6 and ; most troublesome for this account ; utter all5inds of nonsense and contradictions:.

Lucas&s 199D para$raph H/ response is !ha! !hese differences be!ween huans and achines !ha! Eenne!! poin!s !o are

sufficien! for soe philosophers !o re+ec! echanis, and !ha! he BLucasC is sipl( $i"in$ echanis !he benefi! of !he

doub! b( assuin$ !ha! !he( can e8plain !hese differences. )ur!herore, huans can, and soe ac!uall( do, produce

!heores of eleen!ar( nuber !heor( as ou!pu!, so an( achine !ha! canno! produce all of !hese !heores canno! be

an ade7ua!e odel of !he huan ind.

e. Lewis&s 0b+ec!ion

Lewis 1969/ has also forula!ed an ob+ec!ion !o Lucas&s ar$uen!

Le+is argues that % 8that is6 Lucas9 ha&e established that there is a certain Lucas arithmetic+hich is

clearly true and cannot be the out4ut of some "uring machine. %f % could 4roduce the +hole of Lucasarithmetic6 then % +ould certainly not be a "uring machine. ut there is no reason to su44ose that % amable in general to &erify theoremhood in Lucas arithmetic ?@ 1$=.

%o clarif(, “3eano ari!he!ic” is !he ari!he!ic !ha! achines can produce and “Lucas ari!he!ic” is !he ari!he!ic !ha!

huans can produce, and Lucas ari!he!ic will con!ain Gödel sen!ences while 3eano ari!he!ic will no!, so huans are

no! achines, a! leas! accordin$ !o Lucas&s ar$uen!. @u! Lewis 1969/ clais !ha! Lucas has no! shown us !ha! he or

an(one else, for !ha! a!!er/ can in fac! produce Lucas ari!he!ic in i!s en!ire!(, which he us! do if his ar$uen! is !o

succeed, so Lucas&s ar$uen! is incople!e. Lucas responds !ha! he does no! need !o produce Lucas ari!he!ic in i!s

en!ire!( for his ar$uen! !o succeed. ll he needs !o do !o dispro"e echanis is produce a single !heore !ha! a

huan can see is !rue bu! a achine canno!- !his is sufficien!. Lucas 19HD 159/ holds !ha! “wha! I ha"e !o do is !o show

!ha! a ind can produce no! !he whole of Lucas ari!he!ic, bu! onl( a sall, rele"an! par!. nd !his I !hin2 I can show,

!han2s !o Gödels !heore.”

?. 3enrose&s :ew >ersion of !he r$uen!

3enrose has forula!ed and defended "ersions of !he Gödelian ar$uen! in !wo boo2s, 1949&s The Emperor’s New

Mind and 1995&s Shadows of the Mind. ince !he la!!er is a! leas! in par! an a!!ep! !o ipro"e upon !he forer, !his

discussion will focus on !he la!!er. 3enrose&s 1995/ consis!s of !wo ain par!s a/ a Gödelian ar$uen! !o show !ha!

huans inds are non#copu!able and b/ an a!!ep! !o infer a nuber of clais in"ol"in$ consciousness and ph(sics

fro a/. a/ and b/ are discussed in successi"e sec!ions.

a. 3enrose&s Gödelian r$uen!

3enrose has defended differen! "ersions of !he Gödelian ar$uen!. In his earlier wor2, he defended a "ersion of !he

ar$uen! !ha! was rela!i"el( siilar !o Lucas&s al!hou$h !here were soe inor differences for e8aple, in his

ar$uen!, 3enrose used %urin$&s !heore, which is closel( rela!ed !o Gödel&s firs! incople!eness !heore//. Insofar as

!his "ersion of !he ar$uen! o"erlaps wi!h Lucas&s, !his "ersion faces an( of !he sae ob+ec!ions as Lucas&s ar$uen!.

In his 1995/ !hou$h, 3enrose forula!es a "ersion of !he ar$uen! !ha! has soe ore si$nifican! differences fro

Lucas&s "ersion. 3enrose re$ards !his "ersion “as !he cen!ral new/ core ar$uen! a$ains! !he copu!a!ional odellin$

of a!hea!ical unders!andin$” offered in his 1995/ and no!es !ha! soe coen!a!ors see !o ha"e cople!el(

issed !he ar$uen! 3enrose 1996 1.?/.

*ere is a suar( of !he new ar$uen! !his suar( closel( follows !ha! $i"en in 'halers 199A ?./, as !his is !he

cleares! and os! succinc! forula!ion of !he ar$uen! I 2now of/ 1/ suppose !ha! “( reasonin$ powers are cap!ured

b( soe foral s(s!e ,” and, $i"en !his assup!ion, “consider !he class of s!a!een!s I can 2now !o be !rue.” /

ince I 2now !ha! I a sound, is sound, and so is &, which is sipl( plus !he assup!ion ade in 1// !ha! Ia inciden!all(, a sound foral s(s!e is one in which onl( "alid ar$uen!s can be pro"en/. @u! !hen ?/ “I 2now

!ha! G &/ is !rue, where !his is !he Gödel sen!ence of !he s(s!e &” ibid/. *owe"er, 5/ Gödel&s firs! incople!eness


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!heore shows !ha! & could no! see !ha! !he Gödel sen!ence is !rue. )ur!her, we can infer !ha! A/ I a & since & is

erel( plus !he assup!ion ade in 1/ !ha! I a /, and we can also infer !ha! I can see !he !ru!h of !he Gödel

sen!ence and !herefore $i"en !ha! we are &, & can see !he !ru!h of !he Gödel sen!ence/. %ha! is, 6/ we ha"e reached a

con!radic!ion & can bo!h see !he !ru!h of !he Gödel sen!ence and canno! see !he !ru!h of !he Gödel sen!ence/.

%herefore, H/ our ini!ial assup!ion us! be false, !ha! is, , or an( foral s(s!e wha!soe"er, canno! cap!ure (

reasonin$ powers.

'halers 199A ?.6/ !hin2s !he “$rea!es! "ulnerabili!(” wi!h !his "ersion of !he ar$uen! is s!ep /- specificall(, he

!hin2s !he clai !ha! we 2now !ha! we are sound is problea!ic he a!!ep!s !o show !ha! i! leads !o a con!radic!ion see

'halers 199A sec!ion ?//. 0!hers aside fro 'halers also re+ec! !he clai !ha! we 2now !ha! we are sound, or else

!he( re+ec! !he clai !ha! we are sound !o be$in wi!h in which case we do no! 2now !ha! we are sound ei!her since one

canno! 2now a falsehood/. )or e8aple, Mc'ullou$h 199A ?./ clais !ha! for 3enrose&s ar$uen! !o succeed, !wo

clais us! be !rue 1/ “*uan a!hea!ical reasonin$ is sound. %ha! is, e"er( s!a!een! !ha! a cope!en! huan

a!hea!ician considers !o be “unassailabl( !rue” ac!uall( is !rue,” and / “%he fac! !ha! huan a!hea!ical

reasonin$ is sound is i!self considered !o be “unassailabl( !rue.”” %hese clais see iplausible !o Mc'ullou$h 199A

?.5/ !hou$h, who rear2s, “)or people such as e/ who ha"e a ore rela8ed a!!i!ude !owards !he possibili!( !ha! !heir

reasonin$ i$h! be unsound, 3enroses ar$uen! doesn! carr( as uch wei$h!.” In shor!, Mc'ullou$h 199A/ !hin2s i!

is a! leas! possible !ha! a!hea!icians are unsound so we do no! defini!i"el( 2now !ha! a!hea!icians are sound.

McEero!! 199A/ also 7ues!ions !his aspec! aon$ o!hers/ of 3enrose&s ar$uen!. Loo2in$ a! !he wa( !ha!a!hea!icians ac!uall( wor2, he 199A ?.5/ clais, “i! is difficul! !o see how !hin2ers li2e !hese could e"en be reo!el(

appro8ia!ed b( an inference s(s!e !ha! chu$s !o a cer!ifiabl( sound conclusion, prin!s i! ou!, !hen !urns i!self off.”

)or e8aple, McEero!! poin!s ou! !ha! in 14H9 epe published a proof of !he four#color !heore which was no!

dispro"ed un!il 149D b( *eawood- !ha! is, i! appears !here was an 11 (ear period where an( cope!en! a!hea!icians

were unsound.

3enrose a!!ep!s !o o"ercoe such difficul!ies b( dis!in$uishin$ be!ween indi"idual, correc!able is!a2es !ha!

a!hea!icians soe!ies a2e and !hin$s !he( 2now are “unassailabl(” !rue. *e 1995 1AH/ clais “If BaC robo! isF

li2e a $enuine a!hea!ician, al!hou$h i! will s!ill a2e is!a2es fro !ie !o !ie, !hese is!a2es will be correc!ableF

accordin$ !o i!s own in!ernal cri!eria of “unassailable !ru!h.”” In o!her words, while a!hea!icians are fallible, !he( are

s!ill sound because !heir is!a2es can be dis!in$uished fro !hin$s !he( 2now are unassailabl( !rue and can also be

correc!ed and an( achine, if i! is !o iic a!hea!ical reasonin$, us! be !he sae wa(/. %he basic idea is !ha!a!hea!icians can a2e is!a2es and s!ill be sound because onl( !he unassailable !ru!hs are wha! a!!er- !hese !ru!hs

are !he ou!pu! of a sound s(s!e, and we need no! worr( abou! !he res! of !he ou!pu! of a!hea!icians. McEero!!

199A/ reains uncon"inced- for e8aple, he wonders wha! “unassailabili!(” eans in !his con!e8! and !hin2s 3enrose is

far !oo "a$ue on !he sub+ec!. )or ore on !hese issues, includin$ fur!her responses !o !hese ob+ec!ions fro 3enrose, see

3enrose 1996/.

b. Consciousness and Physics0ne si$nifican! difference be!ween Lucas&s and 3enrose&s discussions of !he Gödelian ar$uen! is !ha!, as alluded !o

abo"e, 3enrose infers a nuber of fur!her clais fro !he ar$uen! concernin$ consciousness and ph(sics. 3enrose

!hin2s !he Gödelian ar$uen! iplies, for e8aple, !ha! consciousness us! soehow arise fro !he 7uan!u real

specificall(, fro !he 7uan!u proper!ies of “icro!ubules”/ and !ha! we “will ha"e no chanceFBof unders!andin$

consciousnessCF un!il we ha"e a uch ore profound apprecia!ion of !he "er( na!ure of !ie, space, and !he laws !ha!

$o"ern !he” 3enrose 1995 ?9A/. Man( cri!ics focus !heir a!!en!ion on defea!in$ 3enrose&s Gödelian ar$uen!,

!hin2in$ !ha! if i! fails, we ha"e li!!le or no reason !o endorse 3enrose&s clais abou! consciousness and ph(sics.

McEero!! 199A ./ rear2s, “all !he plausibili!( of 3enroses !heor( of “7uan!u consciousness” in 3ar! II of !he

boo2 depends on !he Gödel ar$uen! bein$ sound,” so, if we can refu!e !he Gödelian ar$uen!, we can easil( re+ec! !he

res!. Li2ewise, 'halers 199A 5.1/ clais !ha! !he “reader who is no! con"inced b( 3enrose&s Gödelian ar$uen!s is

lef! wi!h li!!le reason !o accep! his clais !ha! ph(sics is non#copu!able and !ha! 7uan!u processes are essen!ial !o

co$ni!ion...”


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oe ha"e e8pressed doub!s o"er whe!her 7uan!u effec!s can influence neural processes. lein 199A ?.5/ s!a!es “i!

will be difficul! !o find 7uan!u effec!s in pre#firin$ neural ac!i"i!(” because !he brain opera!es a! !oo hi$h of

!epera!ure and “is ade of flopp( a!erial !he neural pro!eins can under$o an enorousl( lar$e nuber of differen!

!(pes of "ibra!ion/.” )ur!herore, 3enrose “discusses how icro!ubules can al!er s(nap!ic s!ren$!hsFbu! nowhere is

!here an( discussion of !he na!ure of s(nap!ic odula!ions !ha! can be achie"ed 7uan!u#echanicall( bu! no!

classicall(” lein 199A ?.6/. lso, “!he 7uan!u na!ure of neural ac!i"i!( across !he brain us! be se"erel( res!ric!ed,

since 3enrose concedes !ha! neural firin$ is occurrin$ classicall(” lein 199A ?.6/. In su, a! leas! $i"en wha! we 2now

a! presen!, i! is far fro clear !ha! e"en!s occurrin$ a! !he 7uan!u le"el can ha"e an( effec!, or a! leas! uch of an

effec!, on e"en!s occurrin$ a! !he neural le"el. 3enrose 1995/ hopes !ha! !he specific proper!ies of icro!ubules can help

o"ercoe such issues.

s en!ioned abo"e, !he Gödelian ar$uen!, if successful, would show !ha! s!ron$ artiBcial intelligence is false, and

of course 3enrose !hin2s s!ron$ .I. is false. *owe"er, 'halers 199A 5./ ar$ues !ha! 3enrose&s s2ep!icis abou!

ar!ificial in!elli$ence is dri"en lar$el( b( !he fac! !ha! “i! is so hard !o see how !he ere enac!ion of a copu!a!ion should

$i"e rise !o an inner sub+ec!i"e life.” @u! i! isn&! clear how loca!in$ !he ori$in of consciousness in 7uan!u processes !ha!

occur in icro!ubules is supposed !o help “


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$. %e&erences and urther %eading• enacerraf6 P. . '-od6 the Fe&il6 and -del6) Monist *1@=/!2.• Makes a number of objections to Lucas’s argument; for example, the complexity of the human mind implies that we might be

unable to formulate our own !del sentence

• oyer6 F. • Fennett6 F.C. 2. 'e&ie+ of "he reedom of the #ill6) The #ournal of Philosoph" E=@ *2>/!1.• *iscusses Lucas’s The reedom of the $ill, and specifically his !delian argument

• eferman6 S. 2.

• &enrose appeals to Libet to show that classical physics cannot account for consciousness

• Lucas6 H. .


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• #hiteley6 C.

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