Coherence and Truth Conducive Justification
Author(s): Charles B. Cross
Source: Analysis, Vol. 59, No. 3 (Jul., 1999), pp. 186-193
Published by: Oxford University Press on behalf of The Analysis Committee
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Coherenceand truth conducivejustification
B. CROSS
CHARLES
Does epistemicjustificationturn out to be truthconduciveundera coherence theory of epistemicjustification?PeterKlein and Ted Warfieldargue
that it does not:
... coherence, per se, is not truth conducive; that is, ... by increasing
the coherenceof a set of beliefs,the new, more coherentset of beliefs
is often less likely to be truethan the original,less coherentset. (Klein
and Warfield1994: 129)
What they show is that a more coherentset of beliefsmay have a smaller
unconditionalprobability of joint truth than some of its less coherent
subsets. Responding to objections raised by Trenton Merricks (1995),
Kleinand Warfield(1996) affirman even strongerconclusion:
... if justificationis both truthconduciveand as coherentistscharacterize it (namely as coherence, a property of sets of beliefs) then
systemsof beliefscannot possiblybecomemore justifiedas they grow
in logicallyindependentbeliefs. (Kleinand Warfield1996: 120)
SinceKlein and Warfield(1996) insist that it is coherentiststhat they are
addressing,and since the coherencetheory of justificationadvanced by
LaurenceBonJour(1985) seemsto be the theorythat most influencestheir
own discussion,one would expect theirargumentagainstthe truthconducivenessof coherentistjustificationto apply,if at all, to BonJour'stheory.
In what follows I will show that this is not the case. I will also show that
an important premiss is omitted from Klein's and Warfield'sargument
against the truth conduciveness of justification as understood in the
versionof coherentismthey explicitlyconsider,which I will call the Naive
CoherenceTheory.Accordingto the Naive CoherenceTheory,an agent's
beliefset is justifiediff that set is epistemicallycoherent,the degreeof justification of the belief set being defined as the degree of its coherence.
Fortunately,the premiss that Klein and Warfieldomit can be defended
without begging the question against the Naive CoherenceTheory. The
samecannot be said of an analogouspremissthat would make Klein'sand
Warfield'sargumenteffectiveagainstBonJour'stheory.
In BonJour'sversion of coherentism,as BonJourtakes pains to point
out, the coherenceof an agent'sbeliefsat a particularmomentis not a sufficient conditionfor their beingjustified.BonJourwrites:
... the force of a coherentistjustificationdependsultimatelyon the
fact that the system of beliefs in question is not only coherent at a
59.3, July 1999, pp. 186-93. 0 Charles B. Cross
ANALYSIS
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COHERENCE AND TRUTH CONDUCIVE JUSTIFICATION
187
moment(a resultwhich could be achievedby arbitraryfiat), but
remainscoherentin the longrun.It is onlysuchlong-runcoherence
whichprovidesanycompellingreasonforthinkingthatthe beliefsof
the systemarelikelyto be true.Butthe ideaof long-runcoherenceis
only genuinelyapplicableto a systemof beliefswhich is actuallyheld
by someone.(BonJour1985:153)
Long-runcoherenceis not a matterof how well a singleset of propositions
hang together:it is a matterof whethera sufficientlyhigh degreeof hanging-togetheris preservedacross times in the belief history of an actual
agent, which history consists of a temporallyindexed sequenceof sets of
of long-runcoherencefall out
propositions.How does the requirement
fromBonJour's
theory?First,BonJour(1985:153)stipulatesthatin order
to count as empiricallyjustifiedan agent'scontingentbeliefsmust belong
to a systemof beliefsthatsatisfieshis Observation
In order
Requirement.
to satisfythe ObservationRequirementa systemof beliefs
... must containlaws attributinga high degreeof reliabilityto a
reasonablevarietyof cognitivelyspontaneousbeliefs(includingin
thosekindsof introspective
beliefswhicharerequiredfor
particular
the recognition of other cognitively spontaneous beliefs). (BonJour
1985: 141)
BonJourlater observes:
... a coherencetheorywhich incorporatesthe indicatedconceptionof
observationbases justificationnot on the static coherenceof a system
of beliefsconsideredin the abstractbut ratheron the dynamiccoherence of an ongoing systemof beliefswhich someone actuallyaccepts.
(BonJour1985: 144)
BonJourgoes on to arguefor the truthconducivenessof justificationunder
his versionof the coherencetheoryby defendingthe following conclusion,
in which by 'stability'he means the degree to which the belief sets in a
given belief history tend to convergeto a single view of the world, which
view changeslittle except to reflectchangesin the world over time:
A system of beliefs which (a) remainscoherent (and stable) over the
long run and (b) continuesto satisfythe ObservationRequirementis
likely, to a degree which is proportionalto the degree of coherence
(and stability)and the longness of the run, to correspondclosely to
independentreality.(BonJour1985: 171)
If we are to use the resourcesof probabilitytheoryto describethis claim,
then we must interpret it as a claim about conditional probability. Suppose
that B is the conjunction of the members of some set of propositions.' The
claim of the passage just quoted is not a claim about the unconditional
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188
CHARLESB. CROSS
probabilityof B; if it were, it would be a claim about 'a system of beliefs
consideredin the abstract'.BonJour'struthconducivenessthesis is instead
a claim about the probabilityof B given that B is the conjunctionof the
currentbeliefsof an actualagentwhose beliefhistoryconsists of belief sets
that have remainedcoherent and stable while continuing to satisfy the
Observation Requirement.The truth conduciveness claim is that this
conditionalprobabilityis positivelycorrelatedwith the degreeof stability
of the agent'sbelief history,its lengthof run, and the degreeto which the
agent'sbeliefshave remainedcoherent.Let us take a momentto formulate
this claim more carefully.
A set of propositionsis justified,on BonJour'stheory,if it is the current
belief set of an agent whose belief history has exhibited stability and
remainedcoherent while continuingto satisfy the ObservationRequirement. But justificationis a matterof degree,and the passagequoted above
indicates that degrees of justificationare to be measured along three
dimensions.One of these dimensionsis level of coherencepreservedacross
times:other things being equal, the more coherentan agent'sbeliefs have
remained throughout the agent's belief history, the more justified her
currentbeliefs. A second dimensionis stability:other things being equal,
the more nearlythe beliefsets in an agent'sbeliefhistorytend to converge
upon a stable view of the world, the more justifiedher current beliefs.
Finally we have length of run: other things being equal, the longer an
agent's belief history, the more justifiedher current beliefs.2The threedimensional notion of degree of justificationassumed in the passage
quoted above is captured if degrees of justificationare representedas
vectors of the form (c, s, r) and if overallcomparisonsof degreeof justification are measuredaccordingto the following definition:
(DEF1) (c2,s2, r2) representsa greater degree of justificationthan
iff c2 > c1 and s 2 s, and r2> r, and eitherc2> c, or
(c1, s1,
or r2> r1.
s, > s, rm)
1 We will assume for the sake of this discussionthat belief sets are finite, but the probability of a set of propositions can be defined even if the set is infinite and the algebra
of propositions does not allow infinite conjunctions. Elsewhere (see Cross 1995) I
have endorsed a way of doing this that defines the probability of an infinite set {A1,
..., A, ...} of propositions as lim,,,.Pr(A1& ... & A,). I no longer favour this way
of handling probabilities of infinite sets but now prefer an approach endorsed by
Field (1977) that takes the probabilitiesof infinite sets as primitive.
2 It might be objected that a correlation between length of run and degree of justification is plausible only if agents are continuously subjectto observational input, which
they are not. BonJourcould answer this objection by adjustinghow length of run is
measured:Periods of time when an agent is temporarilyshut off from observational
input (e.g. periods of unconsciousness)but during which her beliefs do not change
should simply be deducted from a belief history's length of run.
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COHERENCE AND TRUTH CONDUCIVE JUSTIFICATION
189
Sincedegreeof justificationis measuredalong threedimensions,the justificationcondition in termsof which truthconducivenessis evaluatedmust
also reflectthis:
(DEF2) B is justified to a degree defined by (c, s, r) [symbolically
J(B,c, s, r)] iff B is the conjunctionof the members of the
currentbelief set of an actualagent whose belief historyhas
length r and consists of belief sets that have remainedcoherent to degree c and stable to degree s while satisfying the
ObservationRequirement.
Then, where Pr is a measure of objective probability,BonJour'struth
conduciveness claim can be formulated as follows, assuming that
0 <Pr(B1)< 1 and 0 <Pr(B2)<1 and Pr(J(B1,
cl, sl, rl)) # 0 Pr(J(B2,
c2,s2,r2)):
a greaterdegreeof justification
than
(TC1) If (c2, s2, r2) represents
> Pr(B1IJ(B1,cl, si, r1)).
(cl, s1, r1), then Pr(B21J(B2,c2,s2,
rx))
That is, for BonJour'stheory (as for any theory of justification)truth
conducivenessmeans that the probabilityof B2given that B2is justifiedto
a greaterdegreeexceedsthe probabilityof B1giventhat B1is justifiedto a
lesserdegree.
BonJour defends the truth conduciveness claim quoted earlier and
formalizedabove as (TC1) on the basis of an argumentthat correspondence to reality would be the best explanation of why an ongoing belief
system that continued to satisfy the Observation Requirementwould
remaincoherentand stableover the long run (see Bonjour1985: 171-79).
It is not my aim here to assess BonJour'sargument,but regardlessof the
meritsof that argument,it is clear,as I will presentlyshow, that Klein'sand
Warfield'scritiqueof coherentismdoes not underminethe truthconduciveness claim that BonJourdefends.
ConsiderKlein'sand Warfield'sDunnit case, in which an agent'sinitial
belief set (the conjunctionof whose membersis B) is expanded, with no
initialbelief being dropped,to becomea new and more coherentbelief set
(the conjunctionof whose membersis B*) by the mere additionof a new
belief b that improves the degree to which the agent's beliefs 'hang
together'.3Kleinand Warfieldcorrectlypoint out that if b is logicallyindependentof B and B*= B & b and Pr(B)> 0 and Pr(b)< 1 (as in the Dunnit
3
Merricks(1995: 308) provides the following succinct formulation of the example:
Now consider two belief sets. The first, B, includes the following beliefs:
b1 Dunnit had a motive for the murder.
b2 Witnesses claim to have seen Dunnit do it.
b3 A credible witness claims to have seen Dunnit two hundred miles from
the scene of the crime at the time of the murder.
b4 Dunnit committed the murder.
(continued)
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190
CHARLES B. CROSS
case), then, even though the belief set representedby B* may be more
coherentthan the belief set representedby B, still it must turn out that
Pr(B*)< Pr(B).But what mattersabout this example if we are evaluating
the truthconducivenessof justificationon BonJour'stheory is not the relation between the unconditionalprobabilityof B* and the unconditional
probabilityof B. Instead,what mattersis the relationbetweenthe probabilityof B* given that B* is justifiedto a greaterdegree(represented,let us
say,by the triple(c*,s*,r*)) and the probabilityof B given that B is justified
to some lesser degree (represented,let us say, by the triple (c, s, r)). The
Dunnit examplefails as a counterexampleto (TC1) becausefrom the fact
that Pr(B*)<Pr(B) we cannot infer that Pr(B*IJ(B*c*s*r*))?<
Pr(BIJ(B, c, s, r)). That is, Pr(B*IJ(B*,c*,s*,r*)) may well be greaterthan
Pr(BIJ(B, c, s, r)), just as (TC1) requires,despitethe fact that the beliefset
representedby B* is a supersetof the belief set representedby B. This
possibility exists because the distinctnessof B* and B (as well as the
distinctness of (c*,s*,r*) and (c,s,r)) ensures that J(B*,c*,s*,r*) and
J(B,c, s, r) are distinctpropositions,so that the conditionalprobabilityof
B* and the conditional probability of B are computed using different
conditions.
The argumentof the precedingparagraphturnson its beingpossiblefor
Pr(B*IJ(B*,c*,s*,r*))to be greater than Pr(BIJ(B,c,s,r)) even when
Pr(B*)<Pr(B),but we would be able to rule out this possibilityif we were
entitledto assumenot only that Pr(B*)< Pr(B)but also that B* is probabilistically independent of J(B*,c*,s*,r*) and that B is probabilistically
independent of J(B,c,s,r), for in that case it would follow that
Pr(B*IJ(B*,c*,s*,r*)) = Pr(B*) < Pr(B)= Pr(BIJ(B,c, s, r)), and the Dunnit
examplewould be a counterexampleto (TC1) afterall. But to make these
independenceassumptionswould beg the question againstBonJour:part
of what his truthconducivenessclaimmeansis preciselythat the jointtruth
of the propositionsin an agent'sbeliefset is not probabilisticallyindependent of the justificationstatus of the agent'sbelief set, assumingthat the
justificationstatus of an agent'sbelief set is determinedby how the agent's
belief history stands with respect to certain requirementsof coherence,
stability, and observationalinput. Thus, Klein's and Warfield'sanalysis
notwithstanding,the Dunnit example presentsno obstacle to its turning
out that justificationas defined on BonJour'scoherence theory is truth
conducive.
Now consider B* which has the membersof B, plus the following:
b Dunnit has an identical twin which was seen by the credible witness two
hundred miles from the scene of the crime during the murder.
B* is more coherent than B.
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COHERENCE AND TRUTH CONDUCIVE JUSTIFICATION
191
But if Klein'sand Warfield's
Dunnitexampledoes not show that
of
is nottruthconducive,doesit at least
conception justification
BonJour's
show that justificationis not truthconduciveon the Naive Coherence
Theexampledoesshowthis,
Theory,theexplicittargetof theirargument?
butourdiscussionhasexposeda gapin Klein'sandWarfield's
on
argument
thispoint.Fortunately,
thegapcanbe filled.
Recallthat on the Naive CoherenceTheory,what makesa beliefset
of the
coherent,thedegreeof justification
justifiedis its beingepistemically
beliefset beingdefinedas its degreeof epistemiccoherence.Accordingly,
theappropriate
conditionto usein evaluating
thetruthcondujustification
civenessof justification
is
fortheNaiveCoherence
Theory the following:
(DEF3) B is justifiedto degreec [symbolically
j(B,c)] iff B is the
the
membersof a set of propositionswhose
conjunctionof
degreeof coherenceis c.
Sincetruthconduciveness
is foranytheoryof justification
a matterof how
is to betruegivenhowjustifiedit is,thetruth
likelya bearerof justification
conduciveness
claimfortheNaiveCoherence
as
Theorycanbeformulated
follows:
(TC2) If c,> c1, thenPr(B2Ij(B2,c2)) > Pr(B1Ij(B1,cl)).
Thatis, the probabilityof B2giventhatB2 is justifiedto a greaterdegree
exceedsthe probabilityof B, giventhatB, is justifiedto a lesserdegree.
Now, recallthatin the Dunnitexample,B* is morecoherentthanB, yet
Pr(B*)< Pr(B).Lettingc* representthe degreeof coherenceof B* and
lettingc representthe degreeof coherenceof B, does it follow that the
Dunnitexampleis a counterexample
to (TC2)?Thisdependson whether
it followsfromPr(B*)< Pr(B)thatPr(B*Ij(B*,c*))? Pr(BIj(B,c)), butthe
latterdoesnot followgivenonlythatPr(B*)< Pr(B).Onceagainwe are
computingconditionalprobabilities
usingdifferentconditions.Thedifferenceis thatinthecaseof theNaiveCoherence
Theory,a movefromPr(B*)
< Pr(B)to Pr(B*Ij(B*,c*)) ? Pr(BIj(B,c)) can be justifiedin a non-question-begging
waygivenanadditional
premiss.Letusconsiderhowthiscan
be done.
Wenotedin ourdiscussionof (TC1)thatthe Dunnitexampleis a counto (TC1)if certainprobabilistic
are
terexample
independence
assumptions
true.TheDunnitexampleis a counterexample
to (TC2)if analogousprobabilisticindependence
holdconcerning
truthandjustification
assumptions
as analysedby the NaiveCoherence
Theory:
In
(PrInd) theDunnitexample,B* andj(B*,c*)areprobabilistically
indeindependent,and B and j(B,c) are probabilistically
pendent.
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192
CHARLES B. CROSS
The Dunnit example does refute (TC2) if (PrInd)holds, for in that case
c*)) > 0) Pr(B*Ij(B*,c*)) = Pr(B*)
(assumingthat Pr(j(B,c)) > 0 and Pr(j(B*,
< Pr(B)= Pr(BIj(B,c)) even though c* > c. But, in giving a critiqueof the
Naive CoherenceTheory,is it fair to assume(PrInd)?
In our discussionof (TC1) and (TC2) we noted that it would beg the
question against BonJourto assumethat the joint truth of a given set of
propositionsis probabilisticallyindependentof its beingthe currentbelief
set of an actual agent whose belief history meets certain requirementsof
coherence,stability,and observationalinput. By contrast, it does not beg
the question against the Naive CoherenceTheory to assume (PrInd),or
indeedto assumethat in general,the joint truthof a set of propositionsis
probabilisticallyindependentof its degree of coherence, taken in the
abstract.Indeed,the following (non-question-begging)argumentis sufficientto establish(PrInd):if c* and c arethe degreesof coherenceof B* and
B, respectively,consideredin the abstract,then it is not a contingentmatter
that B* and B have these respectivedegreesof coherence.Thus, if true at
all, j(Bn,c*)and j(B, c) are necessarilytrue, and if j(B*,c*) and j(B,c) are
necessarilytrue,then each has unit unconditionalobjectiveprobability,i.e.
Pr(j(B*,c*)) = Pr(j(B, c)) = 1, in which case Pr(B* Ij(B,c*))
= Pr(B*) and
Pr(B)= Pr(BIj(B, c)).4This argumentdoes not beg the questionagainstthe
Naive CoherenceTheorybecauseit does not beg the questionagainstthat
theoryto supposethat degreeof coherenceis a non-contingentpropertyof
sets of propositionsconsideredin the abstract.
A final question arises:if when the Naive CoherenceTheory is applied
to the Dunnit example it can be arguedthat Pr(j(B*,c*)) = Pr(j(B,c)) = 1,
then perhaps it can be argued in the context of BonJour'stheory that
Pr(J(B, c~,s*, r*)) = Pr(J(B,c, s, r)) = 1, so that justification and truth are
probabilisticallyindependentin that context after all. Nothing doing. A
claimof the formJ(B,c, s, r) reportsthe existenceof an actualagentwhose
currentbelief set is representedby B and whose actualbelief historysatisfies requirementsof coherence,stability,and observationalinput.s Since
I include below the independencecalculation for the belief set representedby B. The
other calculation is similar. Assume Pr(j(B,c)) = 1; then we have Pr(B & j(B, c)) =
Pr(B)and hence the following:
Pr(B& j(B, c))
Pr(B)
- 1
Pr(BIj(B,(B,c)
Pr(B).
1
Pr(j(B,c))
s By contrast, a claim of the form j(B, c) does not assertthe existence of an actual agent
whose belief set is representedby B. That is, being the belief set of an actual agent is
not part of what makes a belief set justifiedon the Naive CoherenceTheory. It is true
that when consideringclaims of the form j(B, c) we normally restrict the range of B
to conjunctionsof belief sets of agents, but this does not mean that j(B, c) itself asserts
that B representsthe belief set of an actual agent.
4
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COHERENCE AND TRUTH CONDUCIVE JUSTIFICATION
193
the existenceof an agent with such a belief history is a contingentmatter,
no claimof the formJ(B,c, s, r) can plausiblybe saidto haveunitunconditionalobjectiveprobability.
Klein and Warfieldwere therefore right about the Naive Coherence
Theory,though, as we have seen, their argumentwas incomplete:it omitted an important premiss, namely (PrInd).The situation is different as
regards BonJour'stheory: the truth conduciveness of justification on
BonJour'stheoryis not refutedby the Dunnitexampleor,in general,by the
fact that a coherentset of beliefs will often turn out to be more likely to
contain a falsehoodthan some of its less coherentsubsets.Sincethis latter
fact does not constitute a reason to reject BonJour'stheory, it does not
constitute a reason to reject the very idea of a coherence theory of
justification.6
The Universityof Georgia
Athens, GA 30602-1627, USA
[email protected]
References
BonJour,L. 1985. The Structureof EmpiricalKnowledge. Cambridge,Mass.: Harvard
UniversityPress.
Cross, C. 1995. Probability, evidence, and the coherence of the whole truth.
Synthese 103: 153-70.
Field, H. 1977. Logic, meaning, and conceptual role. Journal of Philosophy 74: 379409.
Klein, P. and T. Warfield.1994. What price coherence?Analysis 54: 129-32.
Klein, P. and T. Warfield.1996. No help for the coherentist. Analysis 56: 118-21.
Merricks,T. 1995. On behalf of the coherentist. Analysis 55: 306-309.
6 This researchwas
supported in part by the Universityof Georgia Research Foundation. The author would like to thank Peter Smith, Stephen Hetherington, and an
anonymous refereefor comments leading to improvementsin this essay.
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