Philosophy and Phenomenological Research V o l . L X X X I N o . 3, N o v e m b e r 2010 © 2 0 1 0 Phi losophy and Phenomenologica l Research, L L C

Luminosity, Reliability, and the Sorites

STEWART COHEN

University of Arizona

I n his in f luen t ia l book Knowledge and it Limits, T i m o t h y W i l l i a m s o n argues that v i r tua l ly no cond i t ion is luminous . 1 A cond i t ion C is l u m i ­nous jus t i n case ( L ) holds

( L ) F o r every case a, i f i n a C obtains, then i n a one is i n a pos i t ion to k n o w that C obtains.

I w i l l argue that Wi l l iamson ' s argument is unsuccessful. Either the argument requires paradoxical sorites reasoning, or the defender o f luminos i ty can reject a crucial premise. I w i l l then examine a recon­structed argument f o r the denial o f luminous i ty and argue that i t fails as wel l .

Wi l l i amson ' s argument focuses on the cond i t ion that one feels cold . A s he tell us, " I t appears to have about as good a chance as any non-t r i v i a l cond i t ion o f being luminous" . W i l l i a m s o n argues as fo l lows:

Consider a m o r n i n g on wh ich one feels freezing cold at dawn, very slowly warms up and feels ho t by noon ... Suppose ... that th roughout the process one thorough ly considers how cold or how hot one feels. One's confidence that one feels cold gradual ly decreases ... Le t t0, t h ...,tn be a series o f times at one mill isecond intervals f r o m dawn to noon . Let at be the case at tt ... Consider a t ime tt between t0 and tn and suppose that at tt one knows that one feels cold . Thus one is at least reason­ably confident that one feels cold, f o r otherwise one w o u l d no t k n o w . Moreover this confidence must be reliably based, f o r

Knowledge and its Limits , Oxford University Press, 2000 (Al l page references are to this text.)

7 1 8 STEWART COHEN

otherwise one w o u l d sti l l not know that one feels cold. N o w at //+1 one is almost equally confident that one feels cold, by the description o f the case. So i f one does not feel cold at / / + y , then one's confidence at that one feels cold is not reliably based, f o r one's almost equal confidence on a similar basis a mill isecond later that one fel t cold is mistaken. (96-97)

F r o m this Wi l l i amson concludes

(1) I f i n a,- one knows one feels cold , then i n ai + / one feels cold.

(1) is the crucial premise i n Wil l iamson 's reductio argument f o r the f a i l ­ure o f ( L ) w i t h respect to the condi t ion that one feels cold. Combined w i t h ( L ) i t yields the conclusion that i f one feels cold at ah then one feels cold at a i + ] . So i t fo l lows f r o m one's feeling cold at dawn, that one feels cold at noon. But by the description o f the case, one feels cold at dawn but not at noon. Wi l l i amson defends (1) and concludes that ( L ) is false.

Let us examine more closely how Wi l l i amson derives (1). I n the pas­sage above, Wi l l i amson is c la iming that a re l iabi l i ty constraint on knowledge supports the f o l l o w i n g claim:

(2) I f at one knows one feels cold, and at /,•+ 7 one is almost equally confident that one feels cold, then at t i + j one feels cold.

(1) fo l lows f r o m (2) and the description o f the case. W h a t precisely is the nature o f this re l iabi l i ty constraint? I n his dis­

cussion o f the role o f re l iabi l i ty i n the argument, Wi l l i amson tell us that the in tu i t ive idea behind the reasoning f o r (1) is

(3) I f one believes ... to some degree that a condi t ion C obtains, when i n fact i t does, and at a very slightly later t ime, one believes ... on a very similar basis, to a very slightly lower degree that C obtains, when i n fact i t does not, then one's earlier belief is not reliable enough to constitute knowledge. 2 (101)

In Williamson's statement of (3) he says "believes outright" where I have said "believes". He tells us that "one believes p outright when one is willing to use p as a premise in practical reasoning" and that " ... we can think of one's degree of out­right belief in p as the degree to which one relies on p". He contrasts notion of degrees of outright belief with the notion of subjective probabilities as measured by one's betting behavior. Williamson also tells us that this notion of outright belief is the one at work in his argument for (1). Hereafter by 'believe' I wil l mean 'believe outright".

LUMINOSITY, RELIABILITY, A N D THE SORITES 719

Since one knows C obtains only i f one has a true belief reliable enough to know C obtains, (3) yields the fol lowing reliability constraint on knowledge:

(4) I f one knows that a cond i t ion C obtains and at very slightly later t ime one believes on a very similar basis to a very slightly lower degree that C obtains, then C obtains at that later t ime . 3

Does (4) support (2)? One difference between (4) and (2) is that (2) is expressed i n terms o f "degrees o f confidence" whereas (4) is f o rmu la t ed i n terms o f "degrees o f b e l i e f . Since these expressions are no ta t iona l variants, we can reformulate (2) as

(2') I f at tt one knows one feels cold , and at t i + 7 one has a very slightly lower degree o f belief that one feels cold , then at t i + j one feels cold .

Does (4) support (2 ') , given the description o f the case? Before we can answer that question, we need to sort ou t an ambigui ty i n the phrase "one believes ... to some degree" that occurs i n (3). There are t w o not ions o f believing that are relevant to the ant i - luminosi ty argument. There is the n o t i o n o f believing to a certain degree and there is the n o t i o n o f believing simpliciter. Where one believes p to degree d, d may be too low f o r one to count as believing p simpliciter. So whereas believing p simpliciter entails believing p to some degree, believing p to some degree does no t entai l believing p simpliciter.4 Thus there are two readings o f "one believes to a very slightly lower degree that C obtains" as i t occurs i n (4). O n the stronger reading, i t implies that one believes simpliciter that C obtains. O n the weaker reading there is no such impl ica t ion .

I f one's having a true belief reliable enough for knowing C obtains does not entail that one knows C obtains, then (3) yields a slightly stronger reliability constraint, viz., I f one has a true belief reliable enough for knowledge that C obtains and at very slightly later time one believes on a very similar basis to a very slightly lower degree that C obtains, then C obtains at that later time. But the difference between this principle and the weaker (4) wi l l not matter for the argument.

We noted earlier (note 2) that where Williamson talks about believing, he means what he calls "believing outright". But the distinction between believing to a certain degree and believing simpliciter still applies to this notion of believing outright. When discussing (1), Williamson says, "Even i f one's confidence at was just enough to count as belief, while one's confidence at /,-+ 7 falls just short of belief ... "(97) Here Williamson contrasts degree of confidence/belief with belief simpliciter. Since when Williamson talks about belief/confidence, he means outright belief, Williamson is here talking about degrees of outright belief and outright belief simpliciter. Thus according to Williamson, one's degree of outright belief can be too low to count as outright belief simpliciter.

720 STEWART COHEN

Thus we have a strong reading and a weak reading o f the condi­t iona l (4) 5 . Since the phrase "one believes to a slightly lesser degree" occurs i n the antecedent o f (4), the stronger in terpreta t ion o f that phrase yields the weaker condi t ional . Let (4) be interpreted as express­ing this weaker condi t ional . The stronger condi t ional , w h i c h has the weaker in terpreta t ion o f the phrase, we can express thus

(5) I f one knows that a condi t ion C obtains and i f at a very slightly later t ime one has, on a very similar basis, a very slightly lower degree o f belief that C obtains, then C obtains at that later t ime.

N o w our or ig ina l question has become two questions: Does the weaker condi t iona l (4) entail (2')? A n d i f not , does the stronger condi t ional (5) entail (2')?

Consider first (4). Given the description o f the case, (4) yields

(6) I f at tt one knows that one feels cold and i f at t i + j one believes to a very slightly lower degree that one feels cold, then at t i + j one feels cold.

Fo r the same reason that (4) is weaker than (5), (6) is weaker than (2') . Thus we cannot derive (2') f r o m (6) alone. T o derive (2') , we need the con junc t ion o f (6) and

(7) I f at ti+1 one has a very slightly lower degree o f belief that one feels cold, then at t i + j one believes to a slightly lower degree that one feels cold .

Given the strong interpretat ion o f "one believes to a slightly lower degree" i n (4), (7) w i l l be true only given the t r u t h o f

(8) I f at t i + j one has a very slightly lower degree o f belief that one feels cold , then at t i + 1 one believes that one feels cold

W h a t w o u l d j u s t i fy (8)? A t tt one knows one feels cold. Thus we have

(9) A t tif one believes one feels c o l d 6

Here and throughout the paper, I am reading the conditionals as material condi­tionals.

Presumably, Williamson assumes that knowing p entails believing p when he notes that i f one is not reasonably confident that one feels cold, then one does not know he feels cold.

LUMINOSITY, RELIABILITY, A N D THE SORITES 721

Then we can get to (8) f r o m (9) and

(10) I f at ti one believes one feels cold , and at t i + j one has a very slightly lower degree o f belief that one feels cold , then at t i + l y one believes one feels cold .

Bu t to appeal to (10) w o u l d be to exploi t the vagueness o f 'believes',

engaging i n reasoning ak in to the reasoning i n a sorites paradox. 7

One migh t t ry to avoid appealing to (10) by arguing that k n o w i n g p entails believing p to degree J, where d is significantly above the thresh­o ld f o r belief simpliciter. Then one could argue f o r (8) f r o m the stron­ger premise

(9') A t tt one believes to degree d that one feels cold .

and the weaker premise

(10') I f at // one believes to degree d that one feels cold , and at ti+1 one has a very slightly lower degree o f belief that one feels cold, then at t i + j one believes one feels cold .

(10') is no t a sorites premise. Thus we could derive (8) w i t h o u t relying on sorites reasoning. Bu t absent some argument, I do not see that one's k n o w i n g at tt that one feels cold justifies (9 ') . Insofar as we are t ry ing to derive (8), we are assuming that k n o w i n g entails believing. But i t is no t clear why , i f k n o w i n g requires believing, i t requires believing to a degree significantly above the threshold f o r believing simpliciter. I f one can jus t barely believe p, then one can just barely k n o w p.

W i l l i a m s o n himself cannot be accused o f engaging i n the sorites rea­soning out l ined above, because he endorses (1) even on the supposit ion that (10) is false:

Even i f one's confidence at was just enough to count as belief, whi le one's confidence at t i + J falls jus t short o f belief, wha t consti tuted that belief at tt was largely misplaced conf i ­dence; the belief fe l l short o f knowledge. One's confidence at tt

was rel iably based i n the way required f o r knowledge only i f one feels cold at t i + 1 . (97)

Were we to sharpen the expression 'believes', one of the instances of (1) would be false. As Williamson notes, it is characteristics of sorites paradoxes that sharpening one of the relevantly vague expressions results in a false premise.

722 STEWART COHEN

Absent some way other than the sorites reasoning o f getting f r o m (4) to (2') , (4) cannot support (2 ') . Can the stronger condi t iona l (5) sup­por t (2')? Here the entailment is t r i v i a l . Given the description o f the case, (5) entails (2 ') .

So the weaker condi t ional (4) cannot support (2') but the stronger condi t iona l (5) can support (2 ') . Is Wi l l i amson entitled to accept (5)? We can approach this question by look ing at what Wi l l i amson says more generally about the connection between rel iabi l i ty and knowledge. I n his discussion o f the role o f re l iabi l i ty i n the ant i - luminosi ty argu­ment, Wi l l i amson proposes:

(11) I f one believes p t ru ly i n case a, one must avoid false belief i n other cases sufficiently similar to a i n order to count as reliable enough to k n o w p i n a. (100)

This pr inciple is very close to what Wi l l i amson subsequently refers to

as the safety requirement on k n o w i n g . 8 Given that one's k n o w i n g p entails one's having a true belief reliable enough f o r k n o w i n g p, (11)

yields the f o l l o w i n g constraint on knowing :

(12) I f one knows p i n case a, then i n every case b sufficiently similar to a, i f one believes p, then p is true i n b9

T o keep our terminology consistent, we can rewrite (12) as

(12') I f one knows i n case a that C obtains, then i n every suff i­ciently similar case b, i f one believes i n b that C obtains, then C obtains i n b.]0

I f this is Wil l iamson 's most general statement o f the connection between rel iabi l i ty and knowledge, then i t should license any more spe­cific claims about that connection. O n the assumption that a case where one knows C obtains is sufficiently similar to a case where one

Williamson later expresses the safety condition in this way: " I f one knows, one could not easily have been wrong in a similar case."(147) This principle is weaker than (11) since it contains the further restriction that the similar case be such that one could easily be in it. Given that (11) is the stronger of the two, there is no harm in using it in Williamson's argument.

The same issue that I discussed in note 2 arises here: I f one's having a true belief reliable enough for knowing C obtains does not entail that one knows C obtains, then (12) yields a slightly stronger reliability constraint. But again, the difference in strength wil l not affect the argument.

Thanks to Nico Silins for pointing out an error in an earlier formulation.

LUMINOSITY, RELIABILITY, A N D THE SORITES 723

believes C obtains at a slightly later t ime, on a very similar basis, to a slightly lesser degree, (12') entails the weaker condi t iona l (4).

Bu t we have seen that only the stronger condi t iona l (5) entails (2 ' ) . A n d der iv ing (5) f r o m (12') w i l l face the same d i f f i cu l ty as der iving (2') f r o m (4). T o derive (5) we need the con junc t ion o f (12') and

(13) I f at a very slightly later t ime one has a very slightly lower degree o f belief that C obtains, then at that sl ightly later t ime one believes C obtains.

A n d the argument f o r (13) w o u l d involve the same k i n d o f sorites rea­soning we saw i n the argument f o r (8).

Let us take stock. W e began by asking what jus t i f i ca t ion there is f o r (2') i n the argument f o r (1). W i l l i a m s o n tells us that the in tu i t ive basis f o r (2') lies i n (3). Bu t (3) admits o f a weak and a strong in terpre ta t ion expressed i n (4) and (5) respectively. A n d whi le (5) supports (2 ' ) , we cannot get f r o m (4) to (2') w i thou t re lying on sorites reasoning. Thus Wil l iamson needs to rely on the stronger condit ional (5). But Will iamson's most general statement o f the connection between rel iabi l i ty and knowledge, the safety cond i t ion (12') , supports only (4). We cannot get f r o m (12') to (5) w i t h o u t engaging i n sorites reasoning. So there is no route f r o m the safety cond i t ion (12') to the crucial premise (2') that does no t involve sorites reasoning. W h i l e i t is the strong condi t iona l (5) that yields (2 ' ) , i t is the weak condi t iona l (4) that is supported by the safety cond i t ion . Should we conclude that the argument f o r (2 ') , and so the argument f o r (1), fa i l? 1 1

Perhaps i t is a mistake to view the argument f o r (2') as der iving f r o m the safety condi t ion . Recall that (3) is supposed to be the in tu i t ive basis behind the reasoning f o r (1), and thus f o r (2 ' ) . I n connection w i t h (3) W i l l i a m s o n says the f o l l o w i n g :

The use o f the concept is reliable here is a way o f d rawing a t tent ion to an aspect o f the case relevant to the appl icat ion o f the concept knows, ... The a im is not to establish a universal generalization but to construct a counterexample to one, the

I am indebted to Tom Blackson for raising the question of how precisely reliability considerations motivate (1). Blackson has noted that because Williamson allows that one can go f rom believing at to not believing at t i + 1 , he cannot use the safety condition in support of the argument for (1). See his "On Williamson's Argument for I , in his Anti-luminosity Argument, Philosophy and Phenomenological Research, forthcoming. M y point here is that even i f Williamson had not commit­ted himself on the question of whether one can go f rom believing at tt to not believing at the only reasoning that wi l l allow Williamson to get f rom the safety condition to (1) is sorites reasoning.

724 S T F . W A R T C . O H F . N

luminosi ty principle ( L ) . As w i t h counterexamples to proposed analyses o f concepts, we are not required to derive our j u d g ­ment as to whether the concept applies i n a part icular case f r o m general principles.(101)

I take Wil l iamson 's po in t to be that our judgment that (3) is correct represents a part icular c la im about a part icular k i n d o f case. We make that judgment as par t o f an argument f o r constructing a counterexam­ple to ( L ) . A n d we are not required to derive that judgment f r o m a more general principle l ike (12').

O f course this leaves i t open whether i n accepting (3) we are accept­ing the weaker (4) or the stronger (5). As we have seen, (5) is what Wi l l i amson needs to derive (2') . I f we grant Wi l l i amson that he does not have to derive (5) f r o m a more general principle, then the fai lure o f the safety condi t ion (12') to support (5), does not prevent (5) f r o m p rov id ing the basis f o r (2 ') .

O n this way o f viewing matters, there is more to the rel iabi l i ty con­straint on k n o w i n g than the safety condi t ion . Wi l l i amson must accept either that some other more general rel iabi l i ty constraint that yields (5), or that (5) itself expresses the most general f o r m u l a t i o n o f this part icu­lar constraint

Is (5) a plausible constraint on knowing? Once (5) is distinguished f r o m (4), this is not so clear. Moreover (5) t r iv ia l ly entails

(14) I f one knows that a condi t ion C obtains and i f at a very slightly later t ime one has, on a very similar basis, a very slightly lower degree o f belief that C obtains, and one does not believe that C obtains, then C obtains at that later t ime. 1 2

So to defend (5), Wi l l i amson must defend (14). One way to do this w o u l d be to deny that the antecedent o f (14) is possible. But this w o u l d require h i m to rely on the sorites premise (10) . 1 3 I n view o f this, he cannot deny

(15) Possibly, one knows one feels cold at t h and at t j + 1 one has, on a very similar basis, a very slightly lower degree o f belief that one feels cold, and at t i + j one does not believe one feels c o l d 1 4

Recall that I am treating (5) as a material conditional.

Of course Williamson's own view is that there wil l be a sharp but unknowable boundary between believing and not believing.

Here I assume again that one can know P even though one's degree of belief in P is just above the threshold for belief simpliciter.

LUMINOSITY, RELIABILITY, A N D THE SORITES 725

Thus, W i l l i a m s o n must defend (14) as expressing a substantive re l iabi l ­i ty constraint on knowledge. As we have seen, Wi l l i amson i n fact does defend (14). His defense proceeds f r o m the observation that one's con­fidence at tt is only slightly less than one's confidence at t i + 1 . So i f at t i + j C does not obta in , then " ... what consti tuted [one's] belief at tt

was largely misplaced confidence ... One's confidence at tt was rel iably based i n the way required f o r knowledge only i f one feels cold at t i + / ' (97).

Wi l l i amson ' s appeal to re l iabi l i ty considerations i n defense o f (14) is puzzl ing. A t / / + / one no longer believes that C obtains. So even i f C does no t obta in , one w i l l no t have a false belief. Moreover , i f C does obta in , one w i l l f a i l to detect a t r u th . T o put i t metaphorical ly, i f at t i + ] C does not obta in , one's doxastic state at t i + / is better tuned to one's cond i t ion-one does not feel co ld and one does not believe one feels cold .

Perhaps there are re l iabi l i ty constraints on degrees o f confidence that are independent o f considerations about whether one has false beliefs or fails to have true beliefs. 1 5 Wi l l i amson argues that i f at t i + / C does not obta in , then one's confidence at tt was largely misplaced. A n d i t is misplaced because " ... one's confidence at /, is only slightly less than one's confidence at /, + / . " But i t is no t obvious why one's confidence at // is misplaced. We are supposing that at tt one knows one feels cold . Thus at tj one feels cold and one believes one feels cold. I t fo l lows that i f at / / + / one no longer believes one feels cold , then at tt one just barely believes one feels cold . N o w suppose one no longer feels cold at t i + 1 . Then one jus t barely feels cold at So under these suppositions, at /, one jus t barely feels cold and one jus t barely believes one feels cold . So how is one's confidence at tt misplaced? Clearly one should not have more confidence at tt. A n d to say one should have less confidence is to say that at tt one should not believe one feels cold. But given that by s t ipula t ion, one does feel co ld at t h that is jus t to say that at one's level o f confidence should be such that luminos i ty fails. A n d that w o u l d be question-begging i n this context.

I am not c la iming that (5) is false. I find the issues concerning the status o f (5) to be obscure. But I do t h ink that (5) is questionable enough that the defender o f ( L ) can reasonably reject i t as a premise i n an argument f o r the denial o f ( L ) . This is especially true given that on the f a i r l y weak assumption that (15) is true (which is just the assump­t ion that the sorities premise is false), there is a t r i v i a l argument f r o m (5) to the denial o f ( L ) : We have noted that (5) t r iv ia l ly entails (14). But (14) and (15) t r iv ia l ly entail

Thanks to Scott Sturgeon for helping me see this.

726 S . T F W A R T C O H F . N

(16) Possibly, at t j + h one feels cold and one does not believe one feels cold.

Given that knowledge entails belief, i t fo l lows that i t is possible that one feels cold and one does not k n o w one feels cold. A n d given Wil l iamson 's s t ipulat ion that one is continuously considering whether one feels cold, i t fo l lows that there is a case where one feels cold but one is not i n a posi t ion to k n o w that one feels cold . Tha t is to say, i t fo l lows that the condi t ion that one feels cold is not luminous.

Because (5) is bo th questionable and very close to the denial o f ( L ) , I conclude that i t is not well-suited to serve as a premise i n an argu­ment against ( L ) . I f this is correct, then Wil l iamson 's argument against luminosi ty fails.

Perhaps the ant i - luminosi ty argument can be reconstructed i n more

favorable terms. The crucial premise i n Wil l iamson 's argument is

(1) I f i n üi one knows one feels cold, then i n a i + ] one feels cold.

Accord ing to Wi l l i amson , the in tui t ive basis f o r (1) is the rel iabi l i ty constraint on knowledge expressed i n (3). I have argued that an appeal to a safety principle (itself a re l iabi l i ty constraint on knowledge) w i l l not help the der ivat ion o f (1), i f that der ivat ion proceeds th rough (3). But perhaps the ant i - luminosi ty argument can be made by deriving (1) directly f r o m safety, w i thou t any appeal to (3 ) . 1 6

Later i n the book, Wi l l i amson provides a compact statement o f the safety constraint on knowledge: 1 7

(17) I f one knows, one could not easily have been wrong i n a similar case.

N o w suppose we appeal fu r ther to the empirical premise

(18) One cannot discriminate between adjacent cases i n the series

fly, a2, an, i.e., when a,- is the case, one does not k n o w that

ai+ j is not the case, (nor that a^.j is not the case).

along w i t h the premise

Versions of this argument were suggested to me by John Hawthorne, Nico Silins, and Jonathan Vogel.

In "How Must Knowledge be Modally Related to What is Known?" Philosophical Topics 26, 1999 and in A Virtue Epistemology (Oxford University Press) 2007, Ern­est Sosa defends versions of safety.

LUMINOSITY, RELIABILITY, AND THE SORITES 727

(19) Adjacent cases i n the series are similar i n the way required by (17).

These three premises are sufficient to derive (1). F r o m (18) and (19) and the description o f the case, i t fo l lows that when i n at one believes one feels cold , one could have easily believed one feels cold i n the s imi­lar case ai+ j. Then by (17), i t fo l lows that i f one knows one feels co ld i n ah then i n ai+ j one feels cold , i.e., i t fo l lows that (1) is true.

This version o f the luminos i ty argument avoids the objections I raised to the or ig ina l argument. Those objections were aimed at the der iva t ion o f (1) f r o m (3), not on the der ivat ion o f (1) directly f r o m safety. This new version o f the argument differs f r o m the or ig ina l i n two crucial respects. Whi l e (17) is a moda l pr inciple , (3) is not . A n d unl ike Wi l l iamson ' s or ig ina l argument, this new argument appeals to the empir ical premise (18). W i l l i a m s o n does say i n the in t roduc t ion to the b o o k that "The ma in idea behind the argument against luminos i ty is that our powers o f d iscr iminat ion are l i m i t e d " . A n d when he sets up the argument, he stipulates that i n the t rans i t ion between adjacent cases, one is no t aware o f any change i n one's feelings o f heat or cold . This is essentially the empir ical premise (18). But as the argument develops, this premise does not play any role i n the der ivat ion o f (1) f r o m (3). Tha t der ivat ion requires only the premise:

(20) I f i n at one believes one feels cold, then i n ai+ j one believes one feels co ld o n a very similar basis to a very slightly lower degree.

But (20) could be true even i f (18) were false. These differences t u r n out to be crucial . The or ig ina l argument runs

in to t rouble because the specification o f the case does not rule out the possibil i ty that at t i + j one does not believe one feels cold . Thus even i f at t i + j one does not feel cold , one is no t thereby mistaken. This means that as fa r as (3) is concerned, the re l iabi l i ty o f one's belief at at that one feels cold is no t (clearly) impugned. But even i f at t i + 7 one does not believe one feels cold , the empir ical premise (18) ensures that at tt one could easily have believed one feels cold . This fact combines w i t h the moda l safety pr inciple (17) to yield (1) (given the s imi lar i ty o f adjacent cases).

Is this new version o f the argument successful? Recall Wi l l iamson ' s earlier f o r m u l a t i o n o f the safety condi t ion :

(11) I f one believes p t r u ly i n case a, one must avoid false belief i n other cases sufficiently similar to a i n order to count as reliable enough to k n o w p i n a. (100)

728 STEWART COHEN

He goes on to say

The vagueness i n 'suff icient ly similar ' matches the vagueness i n 'reliable' and i n ' know ' . Since the account o f knowledge devel­oped i n Chapter 1 implies that the rel iabi l i ty cond i t ion w i l l not be a conjunct i n a non-circular analysis o f the concept knows, we need not even assume that we can specify the relevant degree and k i n d o f s imilar i ty w i thou t using the concept knows. (100)

Will iamson 's po in t is that our s imilar i ty judgments that ground our re l iabi l i ty judgments may themselves be epistemic. This means that our acceptance o f (19) may depend on judgments about when one knows. So our judgment that a i + 1 is similar to at may require the judgment that i f one could wrongly believe one feels cold i n a i + ] , then i n at one does not k n o w one feels cold. Given (18), this requires the judgment that i n one knows one feels cold only i f i n a i + ; one feels cold. A n d this is just the judgment that (1) is true. I n that case, the new argument turns out to be c i rcular . 1 8

Can the argument succeed i f we suppose, pace Wi l l i amson , that we can apply safety by mak ing s imilar i ty judgments independently o f mak­ing epistemic judgments? One migh t suppose that adjacent cases i n the series are sufficiently similar by any reasonable s imilar i ty metr ic . 1 9 This supposit ion w o u l d avoid the circular i ty problem. But i t also allows us to subject the safety principle (17) to more r igorous scrutiny. O n Wil l iamson 's view, that s imilar i ty judgments cannot be made indepen­dently o f judgments about knowledge, i t is pointless to t ry to construct counterexamples to safety. Such an example w o u l d require that one knows i n case W, even though one could easily have been wrong i n a similar case W. But i f our s imilar i ty judgments are epistemic, the pos­sibi l i ty remains that our judgment that one knows i n W, shows that W is not sufficiently similar. O f course this does not mean that the safety principle does not have explanatory value. I t only means that we can­not appeal to safety independently o f our judgments about knowledge. Bu t i f we view safety as an independently assessable cr i ter ion o f k n o w l ­edge, then this w o r r y about alleged counterexamples does not arise.

One could argue against luminosity by appealing directly to (1) as a premise. But a defender of luminosity could reject (1) for reasons similar to the reasons that would allow rejection of (5).

A further complication stems f rom Williamson's claim that the degree of similarity required for purposes of determining whether 'safety' applies, depends on the con­text.(124) Does it follow that 'knowledge' judgments are context-sensitive? I f so, then luminosity may hold relative to some contexts but not relative to others.

LUMINOSITY, RELIABILITY, AND THE SORITES 729

So consider the f o l l o w i n g case 2 0. Suppose I k n o w what Oak trees look l ike. U n k n o w n to me, there is a species o f tree (call i t T ' ) w i t h one remaining ind iv idua l that looks very much l ike an Oak tree. I am unable to discriminate between an Oak tree and a T tree. As i t turns out , I am i n a meadow w i t h an Oak tree and this last remaining T tree. I have yet to l ook i n the direct ion o f the trees, but they are so posi­t ioned that the T tree blocks m y view o f the Oak tree. Just as I l o o k i n the d i rec t ion o f the trees, a highly improbable quan tum event occurs so the atoms o f the T tree disperse widely in to the surrounding space. Because o f this, I see the Oak tree. In tu i t ive ly , since I k n o w what Oak trees l o o k l ike, I k n o w that I see an Oak tree. Bu t had the atoms o f the T tree no t dispersed, I w o u l d have seen i t and falsely believed that I see an Oak tree. Tha t is to say, m y belief that I see an Oak tree could have easily been w r o n g i n a similar case.

This case shows that one cannot appeal to safety as an indepen­dently assessable cr i ter ion o f knowledge. I conclude that the at tempt to reconstruct the ant i - luminosi ty argument by der iving (1) directly f r o m safety fa i l s . 2 1

I n "Unsafe Knowledge", Synthese 146, 2005, Juan Comesana presents a case with essentially the same structure. He also supplies an illuminating diagnosis of why safety fails in these kinds of cases.

I thank Tom Blackson, Mark Budolfson, Wayne Davis, Patrick Greenough, John Hawthorne, Scott Sturgeon, Jonathan Vogel, Michael White, and especially Nico Silins, for valuable discussion.

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