Does Klein's Infinitism Offer a Response to Agrippa's Trilemma?

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DOES KLEIN’S INFINITISM OFFER A RESPONSE TO AGRIPPA’S TRILEMMA?
STEPHENWRIGHT
A. Theregressofreasonsthreatensanepistemicagent’srighttoclaimthat
anybeliefsarejustified.Inresponse,PeterKlein’sinfinitismarguesthataninfinite
seriesofsupportingreasonsoftherighttypenotonlyisnotviciousbutcanmake
forepistemicjustification.Inordertoresistthesceptic,infinitismneedstoprovide
reasontothinkthatthereisatleastonejustifiedbeliefintheworld. Underan
infinitistconceptionthisinvolvesshowingthatatleastonebeliefissupportedby
aninfiniteseriesofsupportingreasons.Thispaperarguesthatshowingthismakes
problemsfortheinfinitist. Thefinitemindsproblemthatpreventscompletionof
aninfiniteseriesiswelldocumented. Thispaperexaminesalternativeattemptsto
provideevidenceofinfinitythattheinfinitistmighttake,whetherbyusinganotion
of justification without infinite reasons or by altering the notion of evidence. It
concludesthatbothofthesefailandconsequentlyinfinitismisunabletooffera
solutiontoAgrippa’strilemma.
1. I
The very idea of a workable infinitist solution to Agrippa’s trilemma is a rela-
tively recent development in epistemology. Traditionally, attempted solutions to
the problem have focused on foundationalist and coherentist accounts.1 Peter Klein
dragsinfinitismintothespotlightandarguesthatthetacitrejectionofinfinitismis
unwarranted.2 Thispaperexamineshisdefenceofinfinitismandclaimsthatheis
rightthatthereasonableepistemologistshouldnotdismissinfinitismwithoutargu-
ment. Despitethis,theultimateconclusionisthatinfinitismdoesnotofferaviable
solutiontoAgrippa’strilemma. Grantingtheinfinitist’sclaimthatajustifiedbelief
is supported by an infinite, non-repeating series of reasons does not, contra Klein,
yieldaresponsetothescepticalproblemattheheartofthetrilemma.
This paper proceeds as follows: In Sect. 2 I set out Klein’s infinitism in terms
of its claims and motivations. I also explain the finite minds problem—which I use
later in my own argument—and outline how Klein defends infinitism against this.
Iwouldliketoexpressmythankstoallthosewhohavereadandcommentedonearlierdraftsof
thispaper.MostsignificantlyIhavebeenfortunateenoughtohavebenefittedfrominputanddirection
fromDavidGalloway,butfurtherintellectualdebtsareowedtoPeterKlein,forhissuggestedpossible
responsestotheoriginalevidenceofinfinityproblemaswellasJohnCallanan,andAndrewCling. My
thanksalsototheanonymousreviewersforSynthese.
1MichaelWilliamspointsoutthatfoundationalistsandcoherentistsoftenattempttosimplyargue
againsttheoppositepositioninordertomotivatetheirown—asthoughthechoiceissimplybetween
foundationalismandcoherentism(Williams,2005,pp.204-205).
2ThoughKleinisthemostprominentcontemporarydefenderofinfinitism,itwouldbemisleadingto
presenthimastheonlyinfinitist.OtherdefencesofinfinitismaresetoutinFantl(2003).Fantldiscusses
aninfinitistaccountofpropositional ratherthandoxastic justification. ScottAikinalsodiscussesvarious
differentaccountsthatmightreasonablybeconsideredspeciesofinfinitism(Aikin,2008,2005). This
paperhoweverisdevelopedandpresentedasarguingagainsttheversionofinfinitismofferedbyKlein,
whothinksthatargumentsforinfinitismcanovercomethescepticalchallenge.
1
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 2
InSect. 3Ifocusonadifferentproblem—theevidenceofinfinityproblem,whichItake
tobeanalternativethoughrelatedchallengetoKlein’sposition. Section4outlines
a strategy that the infinitist might take in order to defend against the evidence of
infinityproblem. Thisemploysbothamodifiedversionofwhatitistohaveevidence
forsomethingandalsoanotionofbeingprovisionally justified. InSect. 5however
I argue that this fails. Lastly, in Sect. 6 I consider the possibility of arguing for
infinitismbyexclusion. Iarguethatthistypeofargumentcanbemadetoworkonly
iftheinfinitistisalsoabletoexcludethescepticaloption. IclaimthatKleinneeds
anargumentagainstscepticisminordertoavoidviolatingtheprinciplesupporting
hisrejectionoffoundationalism.
2. IS
The infinitist attempts to respond to the problem known either as the regress of
reasons orasAgrippa’strilemma.3 Itisatruismthatsomebeliefsareinferredfrom
others. Inordertomapouttheinferentialrelationsbetweenbeliefs,onemightstart
withb—thebeliefthatacertainshapehasfourrightangles. Whenpressedwiththe
question of ‘why do you believe that b?’ one might provide r —the belief that the
1
shape is a square as a reason. The question might then be asked ‘why believe r ?’
1
andsoon. Ultimatelyoneofthreethingsmusthappen:
(1): Theprocessendswithareasonr thatisnotsupportedbyanotherreason.
n
(2): Theseriesofreasonsbecomescircular—areasonusedearlierintheseries
isusedagain.
(3): Theseriescontinuesforeverwithnewreasons.
Thefoundationalistthinksbeliefsoftherightsortaremembersofaseriesofthetype
describedin(1). Thecoherentistarguesthatbeliefsoftherightsortaremembers
ofaseriesthatresemblesthestructuresetoutin(2). Theinfinitistarguesthatthe
right sort of belief is a member of an infinite set of the type outlined in (3). For
thepur-posesofthispaperIfollowKlein(1971)inholdingthatbeliefs‘oftheright
type’aredoxasticallyjustified.
The sceptical conclusion is that no agent is justified in believing one particular
proposition rather than its negation. Since the three options are exhaustive and
exclusive and each is problematic the sceptic concludes that no belief is justified.
Withthisinmind,aresponsemustdotwothings. Firstly,itmustclaimthatmembers
ofastructureofacertaintypeare,atleastsometimes,justified. Callthisastructural
claim.
Secondlyitmustalsooffersomereasontothinkthattherearesomebeliefsthat
are members of this type of series. This I will call the anti-sceptical claim.4 If the
infinitist is able to show how its structural claim does not lead to scepticism, then
infinitismoffersasolutiontoAgrippa’strilemma. Kleinthinksthatitcan.
Distinguishing between these two claims supposes a distinction between meta-
epistemologyandnormativeepistemology. Thestructuralclaim,whichIproposetogrant
totheinfinitist,concernsmeta-epistemology,whereastheanti-scepticalclaim,which
3Themorenormalnameistheregressofreasons. TheproblemissetoutasAgrippa’sTrilemmain
Williams(1996;2001;2005).FortheproblemsetoutastheregressofreasonsseeCling(2008).
4Thisiscertainlytrueofbothcoherentismandinfinitism, whichbothholdthatonlyabeliefcan
provideareasonforabelief(Davidson,1989).Laterwewillseethatfoundationalistsarenotasobviously
committedtothis.
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 3
Ithinkisaproblemgiventheinfinitist’sstructuralclaim,isaclaimaboutnormative
epistemology.
Klein’sinfinitismstatesthat:
[I]norderforaperson,S,tobejustifiedinbelievingaproposition,
p,theremustbeaninfinitesetofpropositionsavailabletoSthatcan
bearrangedinanon-repeatingseriessuchthatthefirstmemberr
1
isareasonforp,andthesecondmember,r isareasonforr ,and
2 1
r isareasonforr ,etc.,andnor repeatsintheseries(Klein,2003,
3 2 i
p. 718).
The use of the phrase ‘available to S’ here draws suspicion. If ‘available to S’ is
supposed to mean that consciously holding all of the beliefs in the infinite series
isnecessaryforjustification,thenthisrapidlyleadstotheconclusionthatnofinite
mindedagenthasanyjustifiedbeliefs.
Assumingthatallhumanbeingshavefiniteminds,thisseemsliketheendofthe
infinitist’santi-scepticism. ThereasonforthisissimpleandpointedoutbyRichard
Fumerton—noindividualcouldevercompleteaninfiniteseriesofreasoningsince
a finite mind cannot hold an infinite number of beliefs and as a result infinitism
does not permit justified beliefs (Fumerton, 1995, p. 57). The problem of having
aninfiniteseriesofbeliefscontainedwithinafinitemindiscalledthe‘finiteminds
problem.’5
Klein’sinfinitismisnotsupposedtobearapidargumenttowardscepticismhow-
ever. Thisistheanti-scepticalclaimthatKleinmakes. Rather,itisintendedtoavoid
theconclusionthatnoneofushasajustifiedbeliefwhilstarguingthatsuchabelief
isamemberofaninfinitenon-repeatingseries. Withthisinmindratherthantake
‘availabletoS’tomean‘containedwithinthemindofS’Kleinholdsthatareason
mightbeavailabletoanagentiftheagenthasadispositiontoformthebeliefinthe
appropriatecircumstances(Klein,1998,p. 920).6
Klein also employs a notion of being provisionally justified. Whilst he acknowl-
edgesthatthefinitemindsproblemdemonstratesthatthequestionofwhetheror
not a belief is justified cannot be settled easily, he holds that a belief can be dox-
astically justified for an agent if every time the agent has searched for a reason in
supportofabelief,therehasbeenoneavailable.
Naturallyoneisjustifiedonlyifonehasdone‘enough’reasoningtolicensethe
claimthattherewillbeaninfiniteseriesofreasons. Howmuchisenoughistaken
to be ‘a matter of the pragmatic features of the epistemic context’ (Klein, 2007a,
p. 10).7 Kleinpointsouttheextantproblemsoffoundationalismandcoherentism
to motivate his structural claim. Since these do not apply to infinitism, he claims
itprovidesadefensibleaccountofthestructureofjustifiedbeliefs. Contemporary
5The finite minds problem is also discussed by John Williams, who states that ‘[o]nly God could
entertainaninfinitenumberofbeliefs.ButsurelyGodisnottheonlyjustifiedbeliever’(Williams,1981,
p.85).ForadevelopmentonthetraditionalfinitemindsproblemseePodlaskowskiandSmith(2011).
6OfcourseifKleinwassimplyinterestedinthestructuralclaim,thefinitemindsproblemwouldnot
matter. Iftheclaimwassimplythatjustifiedbeliefs(ifthereareany)formaninfiniteseries,thenthere
wouldbenoproblemwithsayingtherearenone—whichisjusttheconsequenceofthefiniteminds
argument. AninfinitistofAikin’s(2005)stripe,whoalmostseemstoendorsethatinfinitismleadsto
scepticism,doesnotneedtoworryaboutthescepticalconsequence.
7Itisworthnotingthatfoundationalismandcoherentismdonotfacesimilarproblems—whilstthere
maybefoundationalchainsofreasoningthathaven+1members,theremaywellbechainswithn−1
members.Thisisnottrueofanyinfiniteseries.
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 4
criticsoffoundationalismarguethatfoundationalistsstruggletoarticulateconvinc-
ingly why foundational beliefs are justified yet basic.8 The moral of this according
toKleinisthatarbitrariness(understoodasabeliefunsupportedbyanotherbelief)
ought to be avoided. He expresses this in the Principle of Avoiding Arbitrariness
(PAA).9
Principle of Avoiding Arbitrariness: For all x, if a person, S, has a
justificationforx,thenthereissomereason,r ,availabletoSforx;
1
andthereissomereason,r ,availabletoSforr ;etc(Klein,1999,
2 1
p. 299).
Klein’sattackoncoherentismtargetstwoversionsofcoherentism. Thesedisagree
about the nature of justification (or ‘warrant’ as Klein calls it). One coherentist
approach is to say that justification is transmitted from one belief to another as the
foundationalist does. Such a position involves endorsing circular reasoning how-
ever.10 Klein, like many, takes circular reasoning to be undesirable and offers the
PrincipleofAvoidingCircularity(PAC)toavoidtheproblemsfacedbycoherentist
accountsofthistype.11
Principle of Avoiding Circularity: For all x, if a person, S, has a
justificationforx,thenforally,ifyisintheevidentialancestryofx
forS,thenx isnotintheevidentialancestryofyforS.
These two principles provide a reason to adopt an infinitist position. PAA rules
outfoundationalismandthecombinationofPAAandPACrulesoutcoherentism.12
Sinceinfinitismistheonlyremainingstructuralclaim,onemighttakethistobean
argument by exclusion to an infinitist position. Klein also thinks however that in-
finitismhasanumberofattractivefeaturesindependentlyoftheargumentsagainst
foundationalismandcoherentism.
Onesuchreasonisthat,unlikefoundationalism,infinitismcanmakesenseofthe
ideathathavingmorereasonsinsupportofabeliefleavesanindividualwithmore
8ForastatementofsomeoftheproblemsseeBonJour(1985),Davidson(1989)andSellars(1963).In
defenceoftheideathatproperlybasicbeliefscanbearticulatedseeChisholm(1982),Goldman(1979),
andPryor(2005).
9OfcourseifKleinwassimplyinterestedinthestructuralclaim,thefinitemindsproblemwouldnot
matter. Iftheclaimwassimplythatjustifiedbeliefs(ifthereareany)formaninfiniteseries,thenthere
wouldbenoproblemwithsayingtherearenone—whichisjusttheconsequenceofthefiniteminds
argument. An infinitist of Aikin (2005) stripe, who almost seems to endorse that infinitism leads to
scepticism,doesnotneedtoworryaboutthescepticalconsequence.
1010AnotherversionofcoherentismiswhatKleindescribesas‘warrantemergent’coherentism.Ac-
cordingtothisview,themoremembersthereareinacoherentset,thegreaterthejustificationoftheset
asawhole.Kleinrejectsthispositionhoweversinceheregardsitasaone-stepversionoffoundationalism
(Klein,2006,p.134).
11KleindescribesPACas‘anobviouspresuppositionofgoodreasoning’(Klein,1999,p.298).Whya
coherentistshouldnotregardtheavoidanceofaninfiniteseriesasapresuppositionofgoodreasoning
isanothermatter.
12ItmightbeagoodthingthatKleinchallengescoherentismusingthecircularityproblemrather
thantheproblemofatruthconnectionasdiscussedinOlsson(2005). Onemightthinkthatthereis
noclearconnectionbetweenaninfiniteseriesandtruth—mybeliefthatitiswetseemsnomorelikely
tobetruegivenmybeliefthatitisverywetthanwithoutthisbelief. Thismeansthatinfinitismstillhas
worktodoinrespondingtoChisholm’s‘ProblemoftheCriterion’(Chisholm,1982). Inresponseto
theproblemofthetruthconnectionseePeijnenburg(2007). Klein’saccountarguesforthenecessity,
butnotsufficiencyofaninfiniteseriesofsupportingreasons. Thequestionofwhatitisthatmakesan
infiniteseriessufficientistakenupinCling(2004).
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 5
justification. Thereasonforthisisbecauseafoundationalist(unlikeaninfinitist)is
committedtotheviewthatjustificationinvolvesafinitenumberofreasons. Thisis
importantsinceKleinthinksthatonceanindividualreachesacertainpointinthe
reasoning,thebeliefqualifiesasknowledge.
Basedonthis, Kleinthinksthattheinfinitistisbetterpositionedthanthefoun-
dationalisttoaccountfortherelationshipbetweenjustificationandknowledge. In
responsetothis,JohnTurrisuggeststhatafoundationalistcanalsohaveaninfinity
ofreasons—mybeliefthatthetimeis11:43issupportedbymybeliefthatitislater
than11:42andalsobymybeliefthatitisearlierthan11:41andsoon(Turri,2009,
pp. 162-163). The emergent nature of justification in Klein’s account makes the
difference here though. Klein borrows this notion of emergent justification from
coherentism.
Sincethejustificationofthesetisgreaterthemoremembersithas,theinfinitist
canmakesenseofanagenthavingincreasingjustificationashe/sheuncoversmore
reasons. Ultimately of course, infinite structures are of the same length and as a
result the agent’s justification rather than the objective justification of the belief
changes.
The foundationalist on the other hand takes the individual’s justification to be
no stronger than the justification he/she has for the basic beliefs since it is from
these that the other beliefs are inferred. The idea of increased justification is also
setoutbyKleinelsewhere.13 Hestatesthat‘Iammakingprogressinincreasingthe
doxasticjustificationoftheoriginalbeliefwhenIlocatemoreandmorereasonsfor
it’ (Klein, 2007b, p. 28). The reason that this claim is important to this paper is
becauseitshowsfurtherthatKlein’sinfinitismissupposedtohaveananti-sceptical
component to it. Klein thinks that the merit of infinitism is not just as the best of
three accounts of justification—it is also to show that there can be such justified
beliefs.
3. T‘EIP’DI
The infinitist therefore holds that a justified belief is one that is supported by
an infinite number of non-repeating reasons. In this section I argue that, unlike
foundationalismandcoherentism,thereisnodistinctive‘mark’orsuigenerischar-
acteristicofamemberofaninfiniteseriesthatcanbeidentified. Lateron,Iargue
thatthisgivestheinfinitistaproblem.
SupposeweundertaketheAgrippanprojectandexamineourbeliefstoascertain
the structure of the supporting reasons. In support of our belief b, which we take
tobejustified,wediscoverthatwehaveareasonr whichisinturnsupportedbyr
1 2
andthisissupportedbyr . Supposealsothatwecontinuegoingthroughmoreand
3
morenon-repeatingreasonsuntilwearriveatreasonrnatwhichpointwestop. If
theinfinitistaccountofthestructureofdoxasticjustificationiscorrectandweare
correct in thinking that b is a justified belief, then it must be the case that r has
n
neither:
(1): Beenusedintheseriesofreasonsbefore.
Nor
(2): Isonethatisnotsupportedbyotherreasons.
13MichaelBergmannarguesthatKlein’spositionisnotaninfinitistone(Bergmann,2007). Inre-
sponsetothisKleinpointsouttheideaofincreasedjustificationinaninfinitistaccount(Klein,2007b).
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 6
OfcourseKleindoesnotclaimthatweneedtohavedonethereasoningtouncover
aconclusivereasonforthetruthof(2)—asecond-orderdispositionwillsuffice,but
theremustbeanotherreasontobediscoveredshouldwelookforit.
Thismeansthatiftheinfinitisthastherightstructuralclaimaboutjustification
andwearerightintakingb tobejustified,r willhavenodistinctivecharacterthat
n
marksitoutasamemberofthetypeofseriescorrespondingtothestructuralclaim
ofeitherthefoundationalistorthecoherentist. Thequestionthenthatweshould
ask the infinitist is why is it reasonable for us to believe that the series is in fact infinite?
If it is not, then infinitism leads to scepticism. It needs to be the case that beliefs
areobjectivelyjustified,sinceanobjectivelyunjustifiedbeliefbeingjustifiedforthe
agentdoesnotofferasolutiontoAgrippa’strilemma.
Foundationalistswouldcertainlyexpectthesupportingreasonsforsomejustified
beliefs to be long. They are not committed to saying that for any justified belief,
tracingthereasonsinsupportofitwillquicklyandeasilyyieldafoundationalbelief.
Itseemslikelythattheywouldadmitthatr isnotabasicbelief,butifbisjustifiedthe
n
seriesofsupportwillendwithabasicbelief. Thecircularityendorsingcoherentist
hasasimilarmoveavailable. Whilstfoundationalistsandcoherentistseachcommit
toaparticularstructureofjustifiedbeliefs,neithercommittoaclaimregardingthe
maximum size of the structure. This means one cannot exclude the possibility of
foundationalismbasedonthepresenceofmanynon-basicreasons.
Callthistheevidenceofinfinityproblem. Theproblemworksagainsttheclaim
that an agent has a reason to take one particular belief to be justified rather than
the claim that there are any beliefs that are in fact justified. Unlike the infinitist,
thefoun-dationalistandthecoherentistcanprovideconclusivereasons—thefoun-
dationalistbyarrivingatabeliefwithacertainpropertythatmakesitappropriately
basic and the coherentist by arriving at a belief that has already been used in the
series. Theonlywayinwhichtheinfinityofaseriesmightbeshownconclusivelyis
bycompletion. Thereisno‘shortcut’toestablishingtheinfinitenatureofaseriesin
thewaythatbasicbeliefsestablishthataseriesisofthefoundationalisttype. Whilst
itisnotevenclearthatthecompletionofaninfiniteseriesofbeliefsispossiblelet
usleavethisasideandsimplysaythatonlycompletioncouldshowconclusivelythe
infinite nature of a series. In advance of completion, we certainly cannot know a
beliefisamemberofaninfiniteseries.
Theacceptanceoftheclaimmadeinthefinitemindsproblemthatafinitemind
cannot contain an infinite series means the infinitist cannot demonstrate the exis-
tenceofjustifiedbeliefsinthesamewayasafoundationalistorcoherentist. Klein
circum-ventsthisbyarguingthatwedonotneedcompletionsinceasecond-order
dispositiontoadoptthenextbeliefwillsuffice. Withoutcompletionhowever, one
might wonder what sort of evidence of infinity there could be. The finite minds
problem is there-fore particularly forceful alongside the evidence of infinity prob-
lem. Couplingthetwoproblemscreatesadifficultdilemmafortheinfinitist.14 This
isbecausethetwoproblemspullindifferentdirections. Thefinitemindsproblem
forces the infinitist to accept that completion of an infinite series is not necessary
forjustification. Ontheotherhand,theevidenceofinfinityproblempressesforthe
claimthatwedoneedtocompleteaninfiniteseriesofreasoningtoyieldareason
14TheclaimthatinfinitismfacesatroublingdilemmaisalsothestrategysetoutinBergmann(2007)
argumentagainstinfinitism.ThedilemmathatBergmannthinkstheinfinitistfaceshoweverisdifferent
totheonethatispresentedhere.
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 7
tothinkthatanybeliefispartofa(truthconducive)infinitesetandreasontothink
infinitismdoesnotleadtoscepticism.15
Ofcourseananalogouspointmightbemadeaboutthereliabilistfoundationalist.
Ishowlaterhoweverthattheproblemisamorepressingonefortheinfinitistsince
thereliabilisthasalineofresponseavailablethattheinfinitistdoesnotduetothe
infinitistsubscribingtoPAAwherethefoundationalistdoesnot.
Iftheinfinitistacceptsthatthereisnoevidenceofinfinity,theclaimthatabelief
isjustifiedwillbeatbestevidentiallyunderdetermined. Thisisbecauseofthelack
of a distinctive character to individual beliefs in an infinite series. The series may
howeverbeconclusivelyshowntobefinitebyturningouttobeeitherafoundation-
alistoneoracoherentistoneandthereforeunjustifiedaccordingtotheinfinitist’s
structuralclaim. Thisisthepointoftheevidenceofinfinityproblem. Thefactthat
an agent has no evidence of infinity does not change whether or not the belief is
actuallyinfinitelysupported. Inordertojustifiablyclaimthattherearejustifiedbe-
liefsinresponsetotheAgrippansceptichowever,theinfinitistdoesneedevidence
ofinfinity. Otherwisetheinfinitistisleftwiththepossibilityofobjectivelyunjustified
beliefsthatarejustifiedfortheagentorvice-versaneitherofwhichamountstoare-
sponsetothetrilemma.16 Specifically,theevidenceofinfinityproblemaimstoshow
that an infinitist structural claim is unable to support an anti-sceptical claim. Like
the finite minds problem, the evidence of infinity problem allows a critic to grant
theinfinitistthestructuralclaimandallowthat‘someinfiniteregressesofreasons
are not vicious’ (Klein, 2004, p. 116). The problem is that even if not all infinite
regressesofreasonsarevicious,givingevidencefortheclaimthatabeliefispartof
avirtuousinfiniteseriesisbeyondtheinfinitist.
Assuming possibility is to be understood as quantification over possible worlds
and an infinite series of reasons is possible, showing that any beliefs are actually
justifiedinvolvesshowingthatintheactualworld,thesupportingreasonsforman
infiniteseries. Showingthatitismerelypossible forbeliefstoformaninfinitenon-
repeating series is not sufficient to show that anyone’s beliefs actually form such a
set. Thescepticalconclusioncannotbeavoidedbythemerepossibilityofaninfinite
seriessinceitsaysnothingaboutactuality. Whatisneededisevidenceforaninfinite
seriesofreasonsintheactualworld.
Theevidenceofinfinityproblemhasanothermodalcomponent. Italsoclaims
thatitisimpossibleforanagentwithafinitemindtohaveevidenceoftheinfinite
natureofaseriesofbeliefs. Theclaimisnotthatthereisnopossibleworldinwhich
there is an infinite series of beliefs reasons available (in the dispositional way) in
supportofabelief—itistodowiththeagenthavingevidenceofthis. Inshort,the
modalclaimmadebytheevidenceofinfinityproblemisthatevenifwepermitthe
infinitist’sstructuralclaimandthataninfiniteseriesofbeliefsispossible,thereisno
possibilityofanagentwithafinitemindeverestablishingconclusivelythatabelief
isjustified.17
15Anotherargumentwiththeconsequencethatifinfinitismisthecorrectaccountofthestructureof
justifiedbeliefs,thenthereisreasontothinkanybeliefjustifiedissetoutinCling(2009).
16ThisissetoutinmoredetailinSect.5.
17Onemightthinkthattheinfinitistneednotactuallyshowthataseriesofbeliefsisinfinite.Itakeit
howeverthatbelievingaseriesofsupportingreasonstobeinfinite(ajustifiedbelief)inthiswaytoviolate
PAA—usedbyKleininhisrejectionoffoundationalism.Thisargumentismadelater.
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 8
Thisistheevidenceofinfinityproblem. Whencoupledtothefinitemindsprob-
lemtocreatethedilemmaitrepresentsagenuinechallengethattheinfinitistdoes
nothaveareadyresponseto. InthenextsectionIsetouthowtheinfinitistmight
seektoavoidtheevidenceofinfinityproblembymakingtwocounterclaims. The
response covers possible infinitist rejections of both the premises supporting the
evidenceofinfinityproblem.
4. APIREIP
Thewaythattheevidenceofinfinityproblemisconstructedagainsttheinfinitist
isinanargumentofthefollowingstructure:
(P1): For an infinitist to think that a belief is doxastically justified, he must
thinkthatitissupportedbyaninfinitenumberofreasons.
(P2): Therecouldbenoevidencetosupporttheclaimthatthereasonsavail-
abletosupportabeliefareinfiniteasopposedtonumerousbutfinite.
Therefore
(Conclusion): Theinfinitisthasnoreasontothinkthatanybeliefthatsome-
oneholdsisdoxasticallyjustified.
Thisamountstoafailureoftheanti-scepticalclaim. InthissectionIconsiderways
inwhichtheinfinitistmightseektodenytheproblematicresultarticulatedinCon-
clusionbydenyingeither(P1),(P2)orboth.
Letusbeginwith(P2). Theargumentationgivenaboveinthemotivationofthe
evidenceofinfinityproblemappearssound. Afterall,thereasoningbehindtheevi-
denceofinfinityproblemissupposedtousepremisesthattheinfinitistacceptsand,
from these, show that there is no evidence of infinity that could be available to an
agent with a finite mind. Klein’s response to the finite minds problem shows that
completionisoutofthequestion. Furthermore, theinfinitistrejectionoffounda-
tionalism uses the claim that immediate justification is problematic, which means
thatthemembersoftheinfinitesetbearnodistinctivefeaturesintheirownright.
The infinitist might seek to argue for an amended conception of what it is for
somethingtobeevidenceforaparticularhypothesis. Theevidenceofinfinityprob-
lemtradesontheideathatsomethingisevidenceforahypothesisifthathypothesis
is the only one that is compatible with the evidence. For instance the discovery of
anepistemicallybasicbeliefqualifiesasevidenceforthehypothesisthatthebelief
structureisbuiltonbasicbeliefs. Thisisbecauseonlythehypothesisinquestionis
compatible with the evidence. Undoubtedly this kind of conclusive reason, which
isdiscussedbyDretske, isonewaythatsomethingcanbeevidenceinsupportofa
hypothesis (Dretske, 1971). The infinitist might hold however that there is more
thanonewayinwhichsomethingcanbeevidence.
Theinfinitistmight arguethat something isevidence fora hypothesisif thehy-
pothesisisthebestexplanationoftheevidence.18 Thiscontrastswiththeaccountof
evidenceabovewherebythehypothesisistheonlyexplanationoftheevidence. Us-
ingthisideaofwhatitisforsomethingtobeevidence,onecouldstillclaimevidence
for a hypothesis even though there is more than one hypothesis that the evidence
islogicallycompatiblewith. Appliedtotheevidenceofinfinityproblemthismeans
thatthepresenceofmanynon-foundationalbeliefsinaseriescouldbeevidenceof
18IamgratefulheretoPeterKleinforsuggestingthislineofdefencetome.
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 9
theinfinityoftheseries.19 Ofcoursetheideaofa‘bestexplanation’hassomething
of a pragmatic character. What makes an explanation the best is not always clear,
butonethoughtisthatanexplanationisthebestifitinvolvesthebestcombination
ofsimplicityandcoveringthedata. Forthisreasonthereneedstobesomeaccount
ofwhyinferencetobestexplanationdirectsonetowardstheepistemicgoaloftruth.
Assumingtwohypothesesexplainthedataequallywell,thequestioniswhyasimpler
oneshouldbemorelikelytobetrue. InthispaperIproposetogranttotheinfinitist
thatthereissomereasontothinksimplicitytruthconduciveinordertoadvancethe
discussion.
Theideaofevidencedespitelogicalunderdeterminationseemsreasonableenough.
Certainlytheinitialaccountofevidenceseemsverystrongandmeanswerarelyhave
evidenceforanything. Ordinarilywetakeourselvestohaveevidenceforcertainevi-
dentiallyunderdeterminedhypotheses. Whatthismeansfortheinfinitististhatthe
argumentationinsupportof (P2)mightfallshortofsupportingthestrongmodal
conclusion that there could never be any evidence of infinity. This is because the
premiseandthesupportingargumentationinvokeafalseassumption—thattheonly
wayforsomethingtobeevidenceforahypothesisisifthehypothesisistheonlyone
compatible with it. One might also accuse the infinitist’s critic of artificially align-
ingthenotionsof‘evidence’and‘conclusivereason.’Thecriticmightseemtobase
(P2)ontheclaimthatsomethingisevidenceforahypothesisifandonlyifitisalso
aconclusivereasoninsupportofthehypothesis.
This represents a problem since the notions of evidence and conclusive reason
can be wedged apart and there can be evidence that is not a conclusive reason.
Takingtheideaofaconclusivereasontobeeithersomesortofdeductiveargument
fromeitheraprioriorposterioripremisesoralternativelyanexistentialproofmeans
thatitseemsthereoughttobeapossibilityofevidencethatisnotaconclusivereason.
Ifitiscorrectthattherecanbeevidencethatisnotaconclusivereasonthenthe
infinitistcanholdthattheargumentsupporting(P2)issufficienttoshowthatthere
isnopossibilityofaconclusivereasoninsupportofaninfiniteseries,butinsufficient
to refute the claim that there is a possibility of evidence of infinity. The infinitist
mightthereforedevelopanargumentagainstthesecondpremisegroundedonthe
implausibility of the notion of evidence that it uses. Furthermore, this rejection
squareswithoureverydayunderstandingaboutevidence.
Itispossiblehoweverthattheinfinitistmaynotbesatisfiedwithsimplyrejecting
thesecondpremiseoftheattack. Rejectingthesecondpremiseissufficienttoresist
theanti-infinitistconclusion,oratanyratemaketheargumentlogicallyinvalid. As
well as this though there is a possibility that the infinitist might also argue against
(P1). Whilsttheinfinitistdoesclaimthatajustifiedbeliefisonethatissupported
byaninfinitenumberofreasons,hemaystillsuggestthat(P1)asithasbeensetout
isfartoostrong.
How could the infinitist claim there something problematic about the wording
in(P1)? Onewayusestheclaimthatanindividualisprovisionallyjustifiedifitisthe
casethat, wheneverhe/she has sought supportingreasons, theyhave been found.
Indeedtheinfinitistmightholdthatthiskindofprovisionaljustificationisthebest
19Exactlyhowinfinityisgoingtobeshowntobethebestexplanationweshallsee. Itakeitinthis
paperthatapplyingsimpleinductiontoextrapolatefromtheevidencethat‘allsupportingreasonshave
beensupportedbyreasons’totheclaimthat‘allsupportingreasonswillbesupportedbyreasons’isonly
aswelljustifiedasinductioningeneral.OnthejustificationofinductionseeSkyrms(2000).
(2013)Synthese,Vol.190,No.6,pp.1113-1130. 10
afinitemindcouldeverhaveaccessto(PodlaskowskiandSmithforthcoming,p. 1).
OnthissubjectKleinsays:
The infinitist will take the belief that p to be doxastically justified
forSjustincaseShasengagedinproviding‘enough’reasonsalong
anendlesspathofreasons. Swouldbecompletelydoxasticallyjusti-
fiedifeveryreasoninthepathwereprovided. Butassumingittakes
some time to provide reasons, even though a proposition might be
completely justified (if there is a suitable path of reasons), no be-
lief couldeverbecompletelydoxasticallyjustified. Nothingisever
completelysettled,butasSengagesintheprocessofprovidingrea-
sonsforherbeliefstheybecomebetterjustified—notbecauseSis
gettingclosertocompletingthetask,butratherbecauseShaspro-
vided more reasons for her belief. How far for-ward in providing
reasons S need go seems to me to be a matter of the pragmatic
features of the epistemic context—just as which beliefs are being
questionedorwhichcanbetakenasreasonsiscontextuallydeter-
mined(Klein,2007b,p. 10).
The claim that a belief is doxastically justified for an individual if the individual
has found reasons in support up to a certain point works against the finite minds
problem. Ifalltheevidenceneededisthatallthebeliefsuptoacertainpointare
supportedbyreasons(orhavereasonsavailabletosupportthem)thenthesetmight
becontainedwithinafinitemind. Atanyratetheinfinitistisnoworseoffthanthe
foundationalist. Thisideaofastoppingpointmightappearfoundationalist. Indeed
it might even violate PAA—wielded by the infinitist against foundationalism. This
neednotbethough, sincetheinfinitisttakesthesupportingreasonstobeinfinite
and as a result accepts that whether or not the belief is objectively justified is not
clearifreasonshaveonlybeenfounduptoafinitepoint.
Addingthistothe‘bestexplanation’conceptionofevidencecreatesaresponse
tobothevidenceofinfinityproblemandfinitemindsproblems. Theinfinitistcan
holdthatwearejustifiedinbelievingthatthereisaninfinitenumberofsupporting
reasons since the best explanation for the fact that every time a reason has been
sought in support of a belief there has been one. Using the weakened sense of
evidencethismightprovideevidenceofinfinity. Themodifiedversionof (P1)also
claimsthatthisisenoughforabelieftobedoxasticallyjustifiedforanagent. Asa
resultofthis, wecanseethatprovidedaninfiniteseriesofsupportingreasonsisa
possibility,theinfinitistcanclaimjustificationfortheclaimthatthereisatleastone
justifiedbeliefsincealltheavailablereasonsareasonewouldexpectofaninfinite
series.
Theinfinitistappearstohavearesponsetothedilemmathatrejectsbothpremises
used in the evidence of infinity problem. Modifying the premises as the infinitist
doesmeansthescepticalconclusionnolongerfollows. InthenextsectionIevaluate
thisresponseandarguethatitfacessignificantproblems.
5. AIREIP
ThereisadegreeofplausibilitytotheideathatH beingthebestexplanationofx
meansxisevidenceforH.Wemightbeabletoacceptthatevidenceneednotprovide
conclusive reasons in support of a hypothesis. The response to (P2) is therefore