THE IRREDUCIBILITY O F KNOWL EDGE
L. S. CARRIER
I a im to sh o w the imp o ssib ility o f g ivin g a re d u ctive analysis o f knowledge. M y argument w i l l depend u p o n ch a ra cterizing th e concept o f knowledge a s a n e p iste mic concept.
Other e p iste mic concepts besides kn o win g in clu d e p e rce iving and remembering such concepts introduce a propositional
clause o f t h e f o r m t h a t p ' . A lth o u g h I b e lie ve t h a t m y
argument ca n a lso b e extended t o t h e e p iste mic concepts
of perceiving and remembering, I shall concentrate e xclu sive ly
on the concept o f knowledge articulated in the sentence f o rm
'A kn o ws th a t p'. B u t f irst I mu st stipulate as t o wh a t co n stitutes a n e p iste mic concept, a n d w h a t co n stitu te s a r e ductive analysis.
One ma rk o f a n e p iste mic co n ce p t i s t h a t t h e sentence
expressing i t is o n ly a p a rtia l tru th -fu n ctio n o f the sentence
embedded i n t h e p ro p o sitio n a l clause. I t s b e in g t ru e t h a t
p te lls u s nothing about th e tru th -va lu e o f ' A kn o ws th a t p '
(KAp); whereas, i t s b e in g fa lse t h a t p does d e te rmin e t h e
falsity o f KAp . Th e difference between a non-epistemic co n cept lik e negation and a n epistemic concept lik e knowledge
is sh o wn b y th e f o llo win g truth-tables:
(1)
(
—,p
2
)
p
K A p
F
F
F
Having a 'mixe d truth-table' l ik e (2 ) i s s t ill o n ly a necessary co n d itio n f o r b e in g a n e p iste mic concept, sin ce K A p
shares t h is same tru th -ta b le wit h th e concept o f lo g ica l n e -
168
L
.
S. CARRI ER
cessity. So t o distinguish ' A kn o ws th a t p ' f ro m ' I t is necessary th a t p ' w e mu st f u rt h e r re q u ire e p iste mic concepts t o
include a p u re ly psychological component which, i n the case
of knowledge, i s n o rma lly t a ke n t o b e t h e 'p ro p o sitio n a l
attitude' of belief.
A n y re d u ctive a n a lysis o f a n e p iste mic concept mu st re duce t h is concept t o o t h e r concepts,none o f wh ic h i s it se lf
epistemic. B u t these o t h e r concepts mu s t b e non-epistemic
in t h e d iffe re n t wa ys t h a t re fle ct t h e lo g ica l difference b e tween t h e t ru t h co mp o n e n t a n d t h e p u re ly p sych o lo g ica l
component. Sin ce K A p e n ta ils I t i s t ru e t h a t p ' (Tp ), t h e
truth component is g ive n b y the id e n tity fu n ctio n in (3) b e low. Tru t h is thus a non-epistemic concept b y reason o f it s
being, l i k e negation, a n extensional concept, o r o n e t h a t i s
completely truth-functional.
(
3 P
)
T
F
T p
T
F
Since e p iste mic concepts in clu d e a p u re ly p sych o lo g ica l
component, t h is component mu st also b e non-epistemic. B u t
purely psychological concepts l i k e b e lie f a re non-epistemic
by v irt u e o f t h e ir b e in g in te n tio n a l concepts. Th a t is, t h e
truth-value o f th e sentence expressing such a psychological
concept w i l l be co mp le te ly undetermined b y th e tru th -va lu e
of th e sentence embedded i n t h e p ro p o sitio n a l clause. Th is
feature is present i n ' A believes th a t p ' (BAp ), a s sh o wn in
(4) b e lo w, b u t i t i s a ls o sh a re d b y sentences e xp re ssin g
wishes, hopes, fears, and a ll o th e r non-epistemic propositional attitudes:
(4)
p
T
F
B A p
?
?
THE IRREDUCIBILITY O F KNO WLEDG E
1
6
9
A re d u ctive analysis o f an epistemic concept, then, is one
which wo u ld in clu d e a t least o n e component th a t is e xte n sional, a t least one th a t is intentional, and none th a t is epistemic. Th e g o a l o f a re d u ctive a n a lysis o f knowledge i s t o
split th is concept in to concepts wh ich include those expressed b y (3) and (4). Bu t since mere tru e b e lie f is n o t sufficient
for knowledge, so me o t h e r concept mu st a lso b e included .
II
Since Plato's Me n o , attempts h a ve been ma d e t o f o rmu late t h is a d d itio n a l co n ce p t i n t e rms o f A ' s h a vin g g o o d
reasons f o r h is b e lie f th a t p. B u t there is some co n tro ve rsy
concerning wh e th e r o f n o t t h e h a vin g o f good reasons f o r
belief is itse lf an intentional concept. Suppose that it is, wit h
'reasons' s i m p l y d e n o tin g o t h e r su p p o rtin g b e lie fs t h a t A
has f o r h is belief that p. Then (5) b e lo w gives the tru th -fu n ctional re la tio n between p a n d ' A has g o o d reasons f o r b e lie vin g that p' (RAp):
(
5 P R A p
)
T
?
F
?
The concepts expressed b y (3 ), (4 ), a n d (5 ) n o w p ro vid e
a candidate f o r a re d u ctive analysis o f knowledge. B u t i t is
not a via b le candidate. Counterexamples f irs t ra ise d b y Be rtrand Ru sse ll (
show
th a t t ru e b e lie f wit h good reasons i s s t i l l in su fficie n t
1
for
knowledge.
Th e counterexamples succeed because o f the
) a n d
intentional
l a t e rinterpretation of 'good reasons'. Th is interpretation
p o p u
(
i z1912), p. 132.
vl ers
1aity rPress,
e () d
(1963),
b 2B 121-123.
y )e
r
EE
d
d
t
mm
u
r
n ua
d
Gn
e
d
t
t
R
i G
e
E
r U
T
S
(
170
L
.
S. CARRI ER
creates a lo g ica l gap between Tp and RAp , so th a t one can
always in tro d u ce cases i n wh ich A s reasons f o r belief, a l though good ones, a re irre le va n t to th e t ru t h o f wh a t is b e lieved.
For example, suppose th a t in J u ly 1974 A came t o th e belief t h a t N i x o n wo u ld le a ve o f f ice p re ma t u re ly, b e lie vin g
so f o r t h e g o o d reason t h a t t h e Wa te rg a te scandal wo u ld
result i n Nixo n 's re mo va l. Though i t is t ru e th a t Nix o n d id
leave o ffice e a rly, A d id n o t kn o w t h is i n J u ly i f h e fa ile d
to in clu d e in h is reasons th e b e lie f th a t Nix o n mig h t re sig n
rather than wa it t o b e impeached and convicted. W e refuse
to attribute knowledge t o people wh e n t h e ir reasons f o r belie vin g th a t p f a il t o e xp la in w h y p is true. Since the possib ilit y o f such f a ilu re i s a b u ilt -in feature o f th e in te n tio n a l
interpretation o f 'good reasons' i n (5), a n y reductive analysis
of knowledge i n te rms o f (3), (4), a n d (5) ca n n o t succeed.
One w a y t o seal t h is opening against counterexamples i s
to in tro d u ce a n o th e r co n ce p t o f g o o d reasons (g o o d re a sons). Un d e r this interpretation, i t w i l l be false to sa y that A
has good reasons' fo r his b e lie f that p i f p is false. The tru th functional re la tio n between p a n d ' A has good reasons' f o r
believing that p' (R'A p ) can then be expressed by:
(6)
p R ' A p
F
F
No w A's having good reasons' fo r believing that p is simp ly
for A to be possessed of a set of other beliefs S such that if A
has S, then it is tru e that p. But we can n o w abstract S itse lf
from its truh-functional connection to p, ju st as we abstracted
A's b e lie f that p f ro m h is knowledge th a t p i so S becomes a
purely psychological component of R'Ap. But then (6) expresses
an epistemic concept, ju st as (2) does; and thus there can be no
THE IRREDUCIBILITY O F K NO WLE DG E
1
7
1
reductive analysis o f knowledge i n te rms o f t ru e b e lie f f o r
which o n e h a s g o o d reasons'.
Attempts t o p ro vid e a reductive analysis o f knowledge b y
adding a fourth concept to those expressed b y (3), (4), and (5)
fare no better. Fo r example, suppose we require that A's good
reasons b e grounded i n wh a t is 'd ire ct ly evident' t o A , a n d
suppose th a t the d ire ct ly e vid e n t is constituted b y A ' s co n scious experience. We must then ask wh e th e r the concept o f
the d ire ct ly e vid e n t is it se lf a n in te n tio n a l concept. I f i t is,
then a gap i s created f o r th e same s o rt o f counterexample
that defeated the analysis couched in terms o f (3), (4), and (5)
alone. A s an instance, consider that A 's reasons f o r believing
that a d u ck i s s wimmin g i n t h e la k e a re grounded i n h is
seeming to see one there. But if wh a t A seems to see is re a lly
a p ie ce o f debris, a n d n o t a d u ck, th e n e ve n i f th e re i s a
duck swimmin g o u t th e re someplace, A does n o t k n o w it .
We can, o f course, b a r the wa y to counterexamples lik e th is
by ma kin g wh a t is d ire ct ly evident p ro vid e a t least a t ru t h functional guarantee f o r th e tru th o f wh a t is believed. Bu t i f
we do this, then we are forced to construe the concept o f the
d ire ctly evident as a n epistemic concept, lik e good re a so n s
2 any analysis wh ich adds such a concept to those expressed
so
by
; (3), (4), and (5) wo u ld n o t constitute a reductive analysis.
III
It h a s re ce n tly been suggested th a t w e d ro p t h e re q u ire ment o f good reasons (o f either sort) in fa vo r o f either a 'n o mic' account o f knowledge, o r one wh ich is e xp licit ly causal.
The fo rme r typ e o f account is defended b y D. M. A rmstro n g '
and b y Pe te r Un g e r
by
4 A l v i n Goldman.' Fo r A t o k n o w (n o n -in fe re n tia lly) t h a t
; w h e r e a s ,
t ( h
e
ledge
l 3 a& Kegan
t
tPaul,e1968), p. 189.
()
r 4D 65 (1968), 157-170.
sophy,
t ().
y
p
64
(1967), 357-372.
e 5P
M
i )e.
t
sA
le
eR
s
p
vr
M
o iU
u
s
S
e nN
d
T
G
R
E
O
R
L
N
,G
D
172
L
.
S. CARRI ER
p, A rmst ro n g re q u ire s t h a t p b e ' e mp irica lly necessary' f o r
A's b e lie f th a t p ; whereas, Un g e r requires th a t i t be 'n o t a t
all accidental' th a t A ' s b e lie f is tru e . Goldman, o n th e o th e r
hand, demands t h a t p b e 'ca u sa lly connected i n a n a p p ro priate wa y' w i t h A ' s b e lie vin g th a t p. Despite differences i n
detail, a l l o f these accounts sh a re t h e sa me lo g ica l b a sis;
for e a ch o f t h e a n a lyse s e xh ib it s a co mmo n re la tio n sh ip
between p and A 's b e lie f that p, viz, th a t if A kn o ws th a t p,
then, had p been false, A wo u ld n o t have been come t o b e lieve that p. So it makes no difference whether we take B*Ap
in (7 ) b e lo w t o mean ' A ' s b e lie f th a t p is e mp irica lly su fficient f o r p', o r 'A 's b e lie f th a t p is n o t a t a ll accidental', o r
'A's b e lie f th a t p wa s caused i n th e appropriate w a y b y p '.
We s t i l l g e t t h e f o llo win g tru th -fu n ctio n a l re la tio n sh ip b e tween p a n d B * A p :
(
7
)
B*Ap
F
F
But sin ce t h e re i s a p u re ly p sych o lo g ica l e le me n t p re se n t
in B*Ap , viz. A ' s b e lie f th a t p, th e context created b y (7) i s
no less epistemic th a n those exhibited i n (2) a n d (6). So n o
nomic o r causal a n a lysis o f knowledge i n te rms o f (3), (4 ),
and (7) can q u a lify as a reductive analysis. Th is is n o t to sa y
that such accounts f a il to sa y something co rre ct about kn o wfor each of the analyses exhibits a common logical relationship
ledge. I t is ra th e r that wh a t th e y do sa y tu rn s out, f o r those
seeking a re d u ctive analysis, t o b e t riv ia l; f o r w e a re ju s t
offered another fo rm o f words fo r the same epistemic concept.
THE IRREDUCIBILITY O F KNO WLEDG E
1
7
3
Iv
Yet another attempt t o p ro vid e a n a n a lysis o f knowledge
is ma de b y th e Cartesian (o r b y th e s k e p t ic
knows
6
th a t p ' is h e ld t o e n ta il ' A is a b so lu te ly ce rta in th a t
), Part
p'.
i n o f wh
w aht isi co
c mmo
h n ly meant
'
Ab y 'absolute ce rta in ty' is
that t h e o n l y propositions k n o wn w i t h su ch ce rt a in t y a re
those about wh ich o n e has indubitable beliefs. T o sa y t h a t
A h a s a n indubitable b e lie f a b o u t a p ro p o sitio n i s ju s t t o
say A believes this proposition, and that it is lo g ica lly necessary that if A believes such a proposition, then this proposition
is true. The o n ly propositions kn o wn b y A, according to h ig h
standard set b y this analysis, t yp ica lly turn out to be about A's
existence o r A's o wn mental states. Let us take p* to go p ro xy
for a n y sentence u su a lly said to describe such a state (e.g., ' I
exist', ' I am in pain', o r 'I seem to see a red patch'). The fo llo wing tru th -ta b le t h e n yie ld s t h e tru th -fu n ctio n a l re la tio n sh ip
between p * and ' A has a n indubitable b e lie f that p * (B A p *):
(
9
)
p* B A p *
F
F
But we n o w see imme d ia te ly f ro m (8) th a t B A p * i s a n e p istemic concept f o r th e same reason t h a t wh a t (6 ) expressed
was. So n o reductive analysis o f knowledge results f ro m o u r
making u se o f t h e co n ce p t o f in d u b ita b le b e lie f.
Suppose th a t we decide t o proceed f u rt h e r w i t h th e Ca rtesian p ro g ra m and characterize absolute certainty, n o t o n ly
in terms o f indubitable belief, b u t also in terms o f states th a t
are sell-intimating. To sa y that A is in a se lf-in tima tin g state
is ju st t o sa y th a t A ' s b e in g in such a state g ive s a lo g ica l
(') Pet er UNGER has ret reat ed t o s uc h a v ie w i n ' A Defens e o f Sk ept icism', Philos ophic al Rev iew, 80 (1971), 198-219.
174
L
.
S. CARRI ER
guarantee that A believes that he is in it. Again, according to
the program, it turns out that A s self-intimating states w i l l be
limited to h is mental states. Let us n o w take B
viate
' A has an indubitable belief that he is in the self-intimat2
A p state
ing
*
t thoa t p *'.
a Th
b e btrurth -fu
e n- ctio n a l re la tio n sh ip between
p* and B
2
(
Ap*
9 P
w i l l
) *
t h
e n
B
F
b
' F
e
A
e No
x w (9 ) does n o t yiepld a n e p iste mic concept b u t instead
a p u re ly extensional
one. Fo r th is v e ry reason, h o wpreveals
r
*
eever,
s B
2 e
anal ysans fo r o u r concept o f knowledge. I f kn o wsappropriate
A
p
*
dledge i s limit e d t o in d u b ita b le b e lie fs a b o u t se lf-in tima tin g
c a t h e n kn o wle d g e i s n o lo n g e r b e in g vie we d a s t h e
bstates,
concept wh ich we agreed that it was. The f u ll Ca rn n
yepistemic
tesian
o
t
approach
f a ils t o a n a lyze t h e e p iste mic co n ce p t o f
:
knowledge
wit h wh ich we began, as th e difference between
e x
(2)
p and
r (9) demonstrates. Instead, th is approach has replaced
our
e es p iste mic co n ce p t w i t h a n e n t ire ly d if f e re n t concept:
as concept o f absolute ce rta in ty that creates a truth-functional
equivalence
b e twe e n t h e a c t a n d t h e o b je cts o f kn o win g .
a
c
o
V
n
c
e I ca n t h in k o f n o o t h e r p la u sib le a cco u n t o f kn o wle d g e
which
is not a variant of one or more of the accounts mentionp
ed
above.
(
t
7t
)h
Sa ( i n c
settill7 succeed, b u t I t h in k t hat this is an illus ion. M y reas on f o r s ay ing t his
nqt)h aot t here s eem t o b e o n ly t h re e s orts o f c onnec tions bet ween h a v in g
is
nu O e
oa n
fl e
m
ti i h
ef g s
ei h
ae t c
cs t o
h
u
n
THE IRREDUCIBILITY O F KNO WLEDG E
1
7
5
analysis, I conclude th a t n o such a n a lysis ca n b e g ive n f o r
knowledge. I f m y a rg u me n t has been sound, w h a t re ma in s
puzzling is that the o n ly epistemic concept cle a rly susceptible
to a correct reductive analysis is that of true belief. (We mig h t
construct ye t o th e r analogues, su ch as ' t ru ly seeming t o re member' a n d ' t ru ly seeming to perceive', b u t these locutions
are perhaps o d d enough so as n o t t o express concepts t h a t
we mig h t p ro fita b ly use.) Tru e b e lie f sp lits cle a n ly and w i t hout remainder into an extensional and an intentional component, a s witn e ss (3 ) a n d (4).
Given t h is st rikin g lo g ica l d issimila rit y between t h e co n cept o f knowledge and that o f tru e belief, i t mig h t n o w seem
odd t o in clu d e t ru e b e lie f among o u r epistemic concepts a t
all. On e q u ick wa y to exclude i t wo u ld be t o ma ke irre d u cib ilit y a fu rth e r ma rk o f a n y epistemic concept. B u t th is s l y
tactic wo u ld h a ve a l l t h e advantages o f th e ft o v e r honest
toil. I t would o n ly serve to label a d ifficu lty ra th e r than to e xplain it , a n d th e re wo u ld th e n b e n o cle a r w a y t o sa y ju st
what a n epistemic concept was. B u t re ta in in g sharp b o u n d aries fo r our epistemic concepts leaves us wit h the problem o f
explaining wh y o n ly some o f o u r epistemic concepts are irre ducible. To th is problem I mu st confess the la ck o f any solution. I pretend o n ly t o h a ve sh o wn th a t knowledge i s i rre ducible, n o t to have provided the explanation f o r its irre d u cib ility.
The p o sitive lesson t o b e learned, though, i s n o t th a t th e
failure to provide reductive analyses somehow leaves o u r concepts unclear, but rather that when we fin d reductive analyses
to be inapplicable, we should have recourse to a more humble
analytical goal. Though epistemic concepts lik e knowledge are
good reasons f o r believ ing t h a t p a n d p it s elf : ( i) lo g ic a l ent ailment , ( i i )
nomic o r c aus al c onnec tion, a n d ( i i i ) s ome e v id e n t ia l c onnec t ion t h a t i s
neither (i) n o r ( i
reasons
, and s o n o reduc t iv e analy s is c an res ult. Un d e r in t e ri ) . U nis depis
e temic
r
pretation
i n t e r( ipi i ) r t h e n o t io n o f g o o d reas ons mu s t b e int ent ional, a n d t h e
counterexamples
e t a t i o n prev ious ly mentioned again intrude.
s
(
)
a
n
d
(
i
t
h
i
i
)
176
L
.
S. CARRI ER
impervious to reductive analysis, they are still subject to illu minating analyses o f a non-reductive sort. I hope to have shown
that it is to this sort of conceptual cla rifica tio n that o u r analytical aims are best directed.
University of Mia mi
L
.
S. Ca rrie r