Fallibility and the Phenomenal Sorites

Fallibility and the Phenomenal Sorites

Eugene MillsVirginia Commonwealth University

1. Consider a row of 50 colored patches, changing incrementally from deter-minately red at the left to determinately orange—hence not red—at the right.This familiar sort of series sets up a sorites paradox involving redness, butlet’s attack the more challenging one concerninglooking red to me~or for brev-ity, just looking red!. Given normal vision and circumstances, the left-mostpatch determinately looks red and the right-most patch determinately does not.This case suggests the following canonical sorites argument:

Categorical Premise: Patch 1 looks red.Induction Premise: If patch n looks red, then patch n11 looks red

~n 5 1,... , 49!.Absurd Conclusion: Patch 50 looks red.

I endorse the straightforward denial—as opposed to, say, a sneaky supervalua-tionist denial—of the Induction Premise. Although the predicate ‘looks red’may express different concepts~or none! on different occasions of use, I main-tain that it may also express a single concept across relevant contexts. I alsomaintain thedeterminacy thesis: a concept always either determinately appliesto a thing or determinately fails to apply. These theses require, in our case,that some patch in the series is the last patch that looks red to me. To solvethe paradox, I must diagnose the Induction Premise’s appeal and make its fal-sity plausible. That is my aim here.

2. I have called the sorites argument concerning phenomenal redness morechallenging than a non-phenomenal analogue. The reason derives from a sortof infallibility that plausibly attaches to judgements about phenomenal proper-ties that does not plausibly attach to judgements about colorper se~or bald-ness, tallness, and other non-phenomenal vague notions!. But this infallibility

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© 2002 Blackwell Publishing Inc., 350 Main Street, Malden, MA 02148, USA,and 108 Cowley Road, Oxford OX4 1JF, UK.

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poses additional challenges only if we fill in our case in a certain way. Fill itin another way, and phenomenal infallibility actually renders the phenomenalsorites an easier nut to crack than the non-phenomenal.

What is the infallibility in question? We might state it roughly by sayingthat

Necessarily, if I believe that patchn looks red, then patchn looks red.

Strictly speaking, this won’t do. For the proposition that patchn looks redentails that patchn exists, and such existence is not entailed by my believingthat patchn looks red. All that is crucial, though, is that necessarily, if I believethat I am appeared to as though there is a~large, well-illuminated! red patchbefore me, then I am appeared to in this way. Cashing out all relevant claimsin this way ruins readability; I will use ‘a patch’s looking red’ as shorthand.

It is old news that anunrestrictedthesis of phenomenal infallibility found-ers on compelling counter-examples. Still, over our restricted range—of atten-tive, reflective claims to the effect that an ordinary, well-lit patch looks red—infallibility seems strikingly plausible; similarly for claims to the effect thata patch doesnot look red. I do not insist on such infallibility in fact. If itfails, however, then phenomenal sorites warrant no special consideration. What-ever solution we endorse for non-phenomenal cases should transfer to thephenomenal—barring some other reason for a distinction, of course, but I knowof none. I grant for argument’s sake that phenomenal sorites do pose specialdifficulties, and so I grant for argument’s sake that I cannot falsely believe orjudge that one of our patches looks red to me.

3. Now, suppose we confront what I call

The Easy Case: Each patch is distinguished from its neighbors by just-noticeable differences.

If I am handed two adjacent patches from the series, I can reliably, but justbarely, distinguish them by color, ordering them according to which is closerto the red end of the series.

Just-noticeable differences generate sorites paradoxes in many cases whereit seems that~roughly put! insignificant differences can’t make a significantdifference: one hair can’t make the difference between someone’s being baldand not, one centimeter can’t make the difference between someone’s beingtall or not, and so on. Suppose Jim judges Joe non-bald, plucks one of hishairs, and pronounces him now bald. Jim’s performance would be laughable.Philosophers contend over the source of the silliness but not over the fact of it.

In phenomenal cases, though, the infallibility that we are granting makesparallel assertions less laughable. Suppose I say confidently and sincerely thatpatch 27 looks red to me and patch 28 does not, while admitting that only a

Fallibility and the Phenomenal Sorites385

minuscule—but discriminable—difference separates them. If you grant meinfallibility about looking red and about not looking red, then you must grantthe truth of my judgements. Announcing a sharp line for the application of aconcept may be indefensible in non-phenomenal sorites cases involving just-noticeable differences; phenomenal infallibility renders it, and the determi-nacy thesis, eminently defensible for the Easy Case.

Of course, I might not draw a sharp line. Suppose you point to each patchin turn and ask me, ‘Does this patch look red to you?’ Unavoidably, there willbe a last patch for which I say ‘Yes’ or give some equally unequivocal affirma-tive answer. But I may not say ‘No’ with respect to thenext patch. I mightsay, ‘I think so’, or ‘I can’t tell’, or ‘Sort of ’. The infallibility of my judge-ments to the effect that a patch looks red~or does not look red! tells usnothing about what obtains when I make no such judgement. Phenomenal infal-libility may provide no easy solution to the sorites paradox in this situation,but neither does it pose any special challenge. The solution I will shortly defenddisposes of the easy case easily.

To see why phenomenal sorites cases seem to raise special hurdles, we mustlook at

The Hard Case: Any two adjacent patches in the series are indiscrimi-nable~to me, with respect to phenomenal color!.

First-person infallibility about phenomenal color seems to require that if Ijudge two patches to look the same to me with respect to color, they do. Theindiscriminability of adjoining patches seems to require that~if I make the rel-evant judgements at all! I will judge any two adjacent patches to look the sameto me with respect to color. So the idea that I might be ignorant about whethera given patch looks red to me seems implausible for reasons that go beyondwhatever implausibility might attach to claims of soritical ignorance generally.

My diagnosis of the paradox will turn on restricting the scope of first-person infallibility concerning phenomenal color, but this restriction will notretract the allowance of infallibility I have already made. The restriction is inde-pendently motivated, and it leaves intact the pre-theoretical appeal of phenom-enal infallibility, so it is not dismissable asad hoc.

After disarming this argument concerning phenomenal color, I will disposeof an apparently different paradox involving a “propositional” notion of phe-nomenal appearance, and in so doing I will show how my treatment extendsto a sorites paradox concerning phenomenal shape. I will conclude with a briefconsideration of the connection between my solution to the phenomenal soritesand some familiar genera of solutions.

4. The appeal of the Induction Premise rests in part on the followingdiscrim-inability requirement, which seems irresistible:

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DR If patch n looks red, and patch n11 looks as though it has the samecolor as patch n, then patch n11 looks red.

Together with our supposition that adjacent patches are indiscriminable withrespect to color-appearance, DR apparently yields the Induction Premise of thecanonical sorites argument with which we started. For it seems natural to thinkthat necessarily,

IND If patch i is indiscriminable~to me, with respect to color! frompatch j, then patch i looks as though it has the same color as patch j.

We must find fault with thisargument from indiscriminability. I find it inambiguities infecting both DR and IND, concerning two patches “looking asthough they have the same color” and being “indiscriminable.” On any uni-form disambiguation of DR and IND, the argument for the Induction Premisefails.

5. One common response to the phenomenal sorites charges DR and IND withtemporal ambiguity. Suppose patch n looks red on Monday, and patch n andpatch n11 always look as though they have the same color. Still, patch n11may not look red on Tuesday, for patch n may not look red then. The twopatches might both look red on Monday and both look orange on Tuesday. Apatch’s apparent color can vary even if its relevant physical characteristics—reflectance, absorbency, etc.—do not, given the vagaries of our perceptual sys-tems and circumstances.1

This point alone may block the argument from indiscriminability whereactual phenomenal sorites sequences are concerned. Perhaps some temporalinterval, however small, always separates the experiences of perceptual atten-tion corresponding to successive elements of the soritical series. Perhaps, as amatter of nomic necessity, I can focus my attention on at most a handful ofpatches simultaneously in a way that permits confident judgements of phenom-enal color. Given our perceptual instability, DR and IND do not look plausi-ble, then, unless the experiences of perceptual attention are simultaneous.Granted that patchn looks red to me at timet1, and patchesn and n11 arechromatically indistinguishable at timet2, it obviously does not follow thatpatchn11 looks red to me at timet2. Raffman~1994! and others who appealto Gestalt switches in color perception~or the like! to block phenomenal soritesarguments focus almost exclusively on our temporal and contextual percep-tual inconstancy in offering solutions to the phenomenal sorites.

I have admitted that the instability of our perception may block the soriti-cal argument. But it may not. It is one thing to allow that a patch may havedifferent apparent colors at different times. It is quite another to insist that Icannotattend simultaneously to the apparent colors of all the patches, or at


least enough of them—as few as three—to generate paradox. To my knowl-edge, no empirical evidence supports this strong claim.

It might be argued that the fact of soritical confounding gives all the evi-dence we need. We know that we can confront a series of patches whoseextremes we can discriminate but whose adjacent members we cannot, so sometemporal intervalmustseparate our experiences of perceptual attention, evenif we cannot independently verify or measure it.

This argument relies on an unstated premise to the effect that simultaneousindiscriminability must be transitive. As we will see, this premise trades un-acceptably on an ambiguity of ‘indiscriminability’. We need not insist on theimpossibility of relevant simultaneous attention to solve the paradox.

Furthermore, even if itis nomically impossible for me to attend to the appar-ent colors of several patches simultaneously, this impossibility does not offera “deep” solution to the paradox. For we can easily imagine our perceptualinconstancy removed, yet the paradox remaining. This shows, I will argue, thatperceptual inconstancy does not lie at the heart of the paradox.

We can easily imagine perceivers less mercurial than we. For suchstableperceivers, a patch that looks red at any time will look red whenever seen,given only a trifling threshold of circumstantial constancy. They will not seethe same patch now as red, now as orange.

I will argue in more detail later that we can resurrect an intuitively compel-ling sorites argument even given the counterfactual supposition that we per-ceive stably.~Do not confound stability with acuity: distinguishing two adjacentpatches might still stump a stable perceiver who can distinguish the extremes.!For now, I want to focus on the companion claim:if we can resurrect an intu-itively compelling sorites argument given the supposition of stable percep-tion, then the actual falsity of that supposition provides no solution to theparadox.

Suppose someone “solved” Zeno’s most famous paradox by pointing outthat no tortoise moves unceasingly: Achilles could overtake his rival duringone of its rest-stops. Tortoisesdo rest, and this fact destroys the argument thatAchilles cannotcatch the tortoise. But tortoises could—conceptually, even ifnot nomically—plod perpetually, and supposing an unstopping tortoise to exist,we can produce a paradox with all the pre-theoretical perplexity of the origi-nal. Reject a Zenonian assumption about the nature of motion and you blockany such paradox. Thus the assumption about motion, rather than the one aboutunstopping tortoises, lies at the heart of the original paradox.

This case suggests a general point. Pointing out the falsity of some prem-ise in a paradoxical argument does not dissolve the paradox if a pre-theoretically compelling paradox would remain were the premise true. If nosuch paradox would remain, then showing~and illuminating! the falsity of thepremise provides a satisfactory solution.

Tortoises rest, and we perceive unstably. But as I will argue below, we caneasily construct a pre-theoretically compelling paradox while granting stable

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perception, whereas we cannot do so once we recognize the limits of phenom-enal infallibility that I will defend. Hence a genuine solution to the paradoxmust work for such stable perceivers, as appeals to perceptual fickleness donot. For now I will simply assume that we are dealing with a stable perceiver—that I am one—so we need not worry about the precise time-indexing of DRand IND. ~Henceforth I will discuss only DR, but everything I say appliesmutatis mutandisto IND!.

6. DR’s antecedent alludes to one patch’s looking as though it has the samecolor as another. What is the scope of ‘looking’? The claim that “a patch looksred to me” might be a claim of propositional attitude, saying thatit looks tome as ifthe patch is red, or—equivalently—thatthe proposition that the patchis red looks to me as though it is true. This reading is both more obscure andless challenging, in my view, than a non-propositional rendering, with whichI begin. I will return to the propositional reading later.

On the non-propositional rendering, a patch’slooking red to me is simplya matter of the object presenting me with a color-appearance of a distinctivesort.2 Something can look red on this rendering to an animal or infant wholacks the cognitive wherewithal to have any relevant propositional attitude. Thisrendering construes DR’s talk of one patch’s looking “as though it has the samecolor” as another in terms of the color-appearances of the two patches, in waysabout to be clarified.

DR alludes to one patch looking as though it has “the same color” asanother. The allusion suggests that each patch has a unique color-appearanceproperty. This suggestion is false, though not because any patch looks~say!both red and orange; we suppose that each patch looks uniformly colored. Itis false because colors nest, as “determinate” properties nest within “determin-ables” ~cf. Yablo 1992!. Anything fuchsia is red, but not vice versa. It is con-ceptually impossible for something to look red but neither fuchsia nor magentanor maroon nor.... We will never as a practical matter complete this list—wewill run out of words or time. But every patch that looks red also looks a morespecific shade.3 To recognize this is not to deny that red is a color. It is justto affirm that nothing can be or look red without also having and appearingto have some other, narrower color.4

The point iterates. Fuchsia, maroon, and the rest also correspond to rangesrather than points on the spectrum. These ranges subdivide into smaller ones,which subdivide in turn, and so on.~Ad infinitum? Almost certainly not, giventhe limits of our perceptual apparatus. But nothing in my argument will turnon the question.! Thus any red patch has many other, more determinate, mostlyunnamed colors.

“More determinate?” Maroon is determinate relative to red, but not fullydeterminate. Some terminology: color C1 isdeterminate relative tocolor C2if and only if necessarily, whatever is C1 is also C2, but not vice versa; C1 ismore determinatethan C2 if ~but not necessarily only if! C1 is determinate


relative to C2; and a color C isfully determinateif and only if there is nocolor C' such that C' is determinate relative to C.5

7. Now we can articulate DR’s ambiguity. Suppose we read DR’s apparent def-inite description~‘the same color’! as imputing to each patch a unique color-appearance property.6 DR holds on this reading—vacuously, for its antecedentis impossible. Each patch has many color-appearance properties, not just one.This rendering stalls the argument from indiscriminability, for itsmodus ponenscan succeed only if DR’s antecedent can be true.

Other interpretations of DR are available. One quantifies existentially, read-ing it as

DRE If patch n looks red, and there is a color C such that patch n andpatch n11 both look C, then patch n11 looks red.

But DRE fails, for colors nest outward from redness as well as inward. If anyunbroken spectral range corresponds to a color-property, then DRE fails quitetrivially. But even if we take colors as “natural kinds” in some sense, wherethis means~at least! that not just any unbroken spectral range corresponds toa color-property, it remains overwhelmingly plausible that some colors prop-erly subsume redness. Just as the Japanese ‘aoi’ spans blue and green, we mightdub ‘rerange’ a color spanning both red and orange.7 Patch 1 looks red whilepatch 50 does not, yet both look rerange; so much for DRE.

We could preserve DR’s intuitive point by quantifying universally, thus:

DRU If patch n looks red, and for any color C, patch n looks C if andonly if patch n11 does, then patch n11 looks red.

That is, if two patches look as if they shareall their color-appearance proper-ties, and one looks red, then so does the other. DRU is a trivial necessary truth,since it is trivially necessary that red is a color. Trivial truth is truth. But aswe shall shortly see, DRU’s truth is not enough to rescue the argument fromindiscriminability.

Necessarily, two patches share all of their color-appearance properties if andonly if they share their fully determinate one. So DRU is equivalent to

DRA If patch n looks red, and there is a fully determinate color C suchthat patch n and patch n11 both look C, then patch n11 looks red.

So far as I can see, no interpretation of DR beyond those I have consideredcombines plausibility with conduciveness to paradox. I will first offer a solu-tion to the paradox formulated in terms of DRU; later I will show how thissolution adapts, trivially, to a formulation in terms of DRA.

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8. It may seem that DRU clears the way formodus ponensand its absurdupshot:

1 Patch 1 looks red;U2 For any color C, patch n looks as if it has color C iff patch n11 does

~n 5 1, 2,... , 49!;U3 @DRU#;

so

C Patch 50 looks red.

I deny U2. At least some adjacent patches in our series do not look as ifthey share all their colors.~Hence not every pair of adjacent patches is suchthat its members share their fully determinate color-appearance property.! Thisis true even though, if handed a pair of neighboring patches and challenged totell them apart by color-appearance, I could not succeed, and I might justifi-ably believethat they share all their color-appearance properties.

9. Here I confront the objection that we have first-person infallibility aboutphenomenal color: if I think a patch looks red~to me!, it must; similarly, itseems, if I think that two patches look as if they share all their colors, theymust.

I deny the similarity of these two claims. I allow for argument’s sake thatin our imagined circumstances, I cannot falsely believe~or judge! that one ofour patches looks red. In fact, I allow that forany color C that is not fullydeterminate, I cannot err in thinking that something looks C.~If you suspectthat the restriction to determinable color-properties isad hoc, read on.!

I deny first-person infallibility for the belief that two patches look as thoughthey share all their color-appearance properties. But infallibility forthis beliefis silly anyway. Each patch has a vast array of color-appearance properties,nested and otherwise. It is fantastic to suppose that in comparing two patches,I could not fail to notice a slight difference with respect to one of these~atleast! thousands of colors. I may justifiably believe that two patches share alltheir color-appearance properties even when they don’t.

10. You might object that if two patches have different color-appearances—ifU2 is false—then the difference must be discoverable, even if not infalliblyobvious: though Icould fail to descry some difference in color-appearance prop-erties, such a difference that Icannot detecthardly seems possible. And ifI can detect a difference, then~it seems! I have rescinded my suppositionthat each patch is indiscriminable from its neighbors with respect to color-appearance. But this was the supposition that generated the paradox; I cheatby rescinding it.


I can distinguish the adjacent elements of our series by color-appearance,but this ability does not violate the supposition of indiscriminability, naturallyunderstood. The natural understanding of that supposition is that adjacentpatches arepairwise indistinguishable. Imagine each patch labeled on the backwith its number in the sequence. Shuffle two patches out of my sight and handthem to me. I try to put them in their original order, with the lower-numberedpatch to the left of the higher-numbered. Suppose that I cannot do this reli-ably: if we were to repeat this “discrimination test” indefinitely using the sametwo patches, my success rate would converge on chance.~Remember, we aregranting stable perception.! We may capture my inability by saying that thetwo patches arepairwise indistinguishable~to me, with respect to color!. I grantthat each patch in our series is pairwise indistinguishable from its immediateneighbors. This is the indiscriminability we suppose for adjacent patches.8

Pairwise indistinguishability does notgenerallyentail that two things “lookthe same.” Consider a common children’s puzzle: two line drawings are distin-guished by~say! exactly 7 noticeable differences, which I am challenged tofind. At first I fail the challenge~and a relevant discrimination test!. After muchscrutiny I finally spot a difference. It is implausible that the subjective appear-ance of the two pictures must have changed relevantly.~The dog wears a col-lar in drawing 1 but not in drawing 2. Did drawing 1 first look as though thedog was collarless and then change its phenomenal appearance to include thecollar? Did drawing 2 look at first as though the dog was collared?! The pic-tures always looked different to me, though I mistakenly judged that they didnot. I allow that the two picturescould have looked the same initially; I denythat theymusthave.

This analogy is not intended to suggest that if I simply peer at a pair ofadjacent colored patches long enough, I will eventually recognize their chro-matic dissimilarity. It shows merely, but importantly, that pairwise indistinguish-ability does not entail sameness of phenomenal appearance. In the case of thetwo drawings, even if I never succeed in distinguishing the two drawings—even if they are pairwise indistinguishable—still it is perfectly intelligible tosuppose that they look different to me.

Even if I cannot pairwise distinguish two patches, I can learn that they lookdifferent to me. Suppose I cannot pairwise distinguish patch 1 from patch 2,nor patch 2 from patch 3, but Ican pairwise distinguish patch 1 from patch 3.Then I can distinguish patch 1 from patch 2 after all, and 2 from 3, by indi-rect use of the discrimination test. I test the patches two at a time until I finda pair that I can pairwise distinguish. I know, then, that these are the outer-most patches in the three-patch series and that they flank the remaining one.Thus I can distinguish the patches in our series, though they are pairwiseindistinguishable.9

You might complain that I help myself to a weak notion of indiscriminabil-ity. Suppose I cannot distinguish adjacent patchesat all, even by indirect appli-cation of the discrimination test. In that case—if~say! patches 1 through 3 do

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not look differently colored to me—I cannot order them. But if I cannot orderthem, they are redundant for purposes of paradox. For their order within theseries is irrelevant, and we may simply remove two of them without changingthe situation’s problematic features at all. Ifeverypatch is “strongly” indiscrim-inable from its neighbors, in that even indirect application of the discrimina-tion test cannot distinguish it from them, it follows that patch 1 is stronglyindiscriminable from patch 5010 and all the patches in between. In that casewe have nothing remotely paradoxical. We simply have a series of 50 patcheswith identical color-appearance properties: I cannot distinguish the first patchin the series from the last. Paradox threatens only when we supposenon-transitivepairwise indistinguishability. But when we have such non-transitivity,we lose indistinguishabilitytout court. You can’t have it both ways.

11. This last point scotches the suggestion that we can revive the paradox byusing DRA, without confronting the hierarchy of color-appearances. The argu-ment would be as follows:

1 Patch 1 looks red;A2 Patch n11 has the same fully determinate color-appearance as patch n

~n 5 1, 2,... , 49!.A3 @DRA#;

so

C Patch 50 looks red.

Again the second premise fails. For if adjacent patches always share a fullydeterminate color-appearance, then the first and the last share it, too, so nosorites sequence exists. For sharing a fully determinate color-appearance is amatter of strict, transitive identity of color-appearance property. Infallible judge-ment about such sharing cannot be squared with the non-transitivity of pair-wise indistinguishability that generates the paradox in the first place.

What makesthe argument a paradox is that the infallibility that plausiblyattaches to ordinary judgements of color-appearance is naturally~but mis-takenly! extended to extraordinary judgements about fully determinate color-appearances. Such infallibilityneednot fail: conceptual considerations donot preclude it. But had we infallibility concerning fully determinate color-appearances, the transitivity of pairwise indistinguishability would never fail.11

It does fail,12 and so infallibility fails too.It might seem that the fallibility I assert for fully determinate color-

appearances must translate to ordinary color-appearances likelooking redandthus violate my acceptance of phenomenal infallibility for such appearances.It does translate but it does not violate. True, I insist that adjacent patches mightbe pairwise indistinguishable while one looks red and the other doesn’t. This


does not, however, conflict with my allowance that if I judge a patch to lookred, it does; this sort of phenomenal infallibility is all that plausibility and Iallow. It would conflict if it were also true that~a! whenever a patch looksred and I consider whether it does, I judge that it does, and~b! whenever twopatches are pairwise indistinguishable to me and I judge that one looks red, Ijudge that the other does as well. But~a! and ~b! are simply false,~a! moresaliently than~b! for present purposes. Their falsity leaves unthreatened myallowances of stable perception and phenomenal infallibility for looking red.13

12. On the assumption that I perceive stably, a patch somewhere along theseries does not share a fully determinate color-appearance property with itsneighbor. In fact, if the series contains no redundant patches,no two patchesshare such a property. But all that matters is that for some pair, A2~and soU2! will fail; hence DRA ~and so DRU! will give no reason to think that thesecond member of the pair looks red to me. But since DRA~or, equivalently,DRU! is the only defensible reading of DR, the argument from indiscrimin-ability collapses.

13. Infallibility concerning fully determinate color-appearances fails—given sta-ble perception. But stable perception fails given infallibility, and it seems wecan imagine infallibility as easily as stable perception. So we are entitled toconclude only that we perceiveeither unstablyor fallibly ~with respect to fullydeterminate color-appearance properties.! But we have independent evidencefor our perceptual instability. So why is such instability too weak on its ownto solve the paradox? I must revisit my dismissal of appeals to perceptualinconstancy.

Recall my earlier point about Achilles and the Tortoise: pointing out thefalsity of some premise in a paradox does not get to its heart if a compellingparadox would remain were the premise true. If no such paradox would remain,then showing~and perhaps explaining or illuminating! the falsity of the prem-ise provides a satisfactory solution.

It is true that we do not perceive stably. But pointing this out leaves thesource of conceptual puzzlement untouched. For we can easily construct a pre-theoretically compelling paradox while granting stable perception: the mere sup-position of stable perception alone does not undercut versions of the argumentfrom indiscriminability appealing to DRU or DRA. Without the assumptionof unrestricted phenomenal chromatic infallibility, on the other hand, pre-theoretical paradox vanishes. Once we see that we can be mistaken about howthings seem with respect to color, the motivation for accepting premise U2 orA2 evaporates, and with it the paradox. So the failure of infallibility that liesat the heart of my solution, rather than the failure of stable perception, is thedeeper one.

Still, you say, this fact does not show that we in fact lack infallibility inaddition to perceptual stability. The logical force of my argument is just that

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we cannot haveboth stable perceptionand infallibility while also findingourselves confronted with phenomenal soritical sequences. Perhaps we are infal-lible, unstable perceivers, and it is the instability that explains our actual per-plexity about phenomenal soritical sequences—granting that it leaves unsolvedthe intellectual puzzle that remains when we imagine away our perceptualinstability.

I have two responses. The first is concessive: even if this is right, the inter-estingphilosophicalpuzzle associated with the phenomenal sorites is solvedby appeal to phenomenal fallibility, and this solution has independent interest.

My second response is stronger. The facts support no insistence on infalli-bility ~beyond the limited sort I allow! and seem in fact to support its denial.We are surely unstable perceivers, but the empirical evidence remains out onwhether our perceptual instability is severe enough to account for soritical per-plexity. Suppose I focus on just patches 1–3 and claim sincerely to attend simul-taneously to the color-appearances of all three patches.~If we couldn’t focuson more than 2 patches at a time, then perhaps stable perception would beenough to explain actual soritical perplexity. But I can attest from my owncase—as you can probably attest from yours—that we can.! At a given instant,I claim, patches 1 and 2 look the same to me, as do patches 2 and 3, but patch1 and 3 look different. If you insist on phenomenal infallibility, you will insistthat I am mistaken in thinking that my attending to patches 1 and 2 was reallysimultaneous with my attending to patches 2 and 3. But this means that youmust accept at leasttemporalphenomenal fallibility: I may think~what I wouldexpress by saying! “Patches 1 and 2, and 2 and 3, look the same to me, whilepatches 1 and 3 look different—and all of this rightnow” and be mistaken.Furthermore, you must locate the mistake in the “now.” You must say I canmistakenly think that I am undergoing a phenomenally complex but tem-porally uniform visual experience when I am really undergoing a temporalsequence of distinct, simpler experiences.

Accept this temporal fallibility, however, and you undermine the claim ofphenomenal infallibility on which you want to insist. You want to preservethe idea that I cannot be mistaken when I judge that patch 1 and patch 2 lookthe same to me. But this can only mean, of course, that I cannot be mistakenwhen I judge that “they look the same to menow”; otherwise the extreme insta-bility of perception on which you insist would render the judgement fallible.But if I can be mistaken in thinking that I judge the color-appearances ofpatches 1, 2, and 3 simultaneously, why can I not be mistaken in thinking thatI judge the color-appearances of patches 1 and 2 simultaneously?

There could, I suppose, be a nomic necessity that might distinguish thecases: perhaps, as a matter of psychological law, humans can simultaneouslyattend to the color-appearances of two patches but not of more than two. Butno evidence in our possession supports any such law. Given that it sometimesseems to me as though I attend to the color-appearances of three patches simul-taneously, grounding the verdict that I have unstable perceptioninstead of


~rather than in addition to! phenomenal fallibility on such a law isad hocandempirically unsubstantiated.

I conclude that phenomenal fallibility about the simultaneous sameness offully determinate color-appearance properties not only yields a deeper solu-tion to the phenomenal sorites than does perceptual instability; it also seemslikely to be among our actual failings.

14. So much for the sorites paradox involving phenomenal color. Two ave-nues of extension await. One concerns the extension of my solution to otherphenomenal notions, the other to a propositional rather than purely phenom-enal notion of “looking.” I will consider these two extensions together by tak-ing up Williamson’s discussion of a sorites paradox involving~propositional!“looking square.” I will argue in this and the next three sections that there isno clear propositional sense of ‘looking’ that gives rise to a serious paradoxin the first place. Subsequent sections address the real paradox involving phe-nomenal squareness. The assumption of stable perception persists throughout.

Williamson considers the suggestion that “if itlooks as though the prem-ises of... a logically valid inference are true, then itlooksas though its conclu-sion is also true”~p. 173!. This suggestion seems to yield paradox in connectionwith a sorites sequence of quadrilaterals. For if it looks as though figure xi issquare and it looks as though figures xi and xi11 have the same shape, thengiven deductive closure for “looking,” it must also look as though figure xi11

looks square. But iteration brings incoherence, if our sequence starts with afigure that looks as though it is square and ends with one that looks as thoughit is oblong.

Williamson does not endorse deductive closure for looking, but he thinksit plausible enough to grant for the sake of argument. The real crux of theparadox, he suggests, is that the argument “equivocates over the context ofthe looking” ~p. 174!. It may look in one perceptual context, but not in another,as though figure xi is square. Once we expose the relativization to contextimplicit in the argument’s premises, he says, we will see that for at least onepair of adjacent figures, there is no constant context for which both premisescome out true—even though each premise comes out true for some context.

Thus Williamson appeals to perceptual instability for a solution to theparadox. I have already argued that no such appeal is satisfactory where phe-nomenal “looking” is concerned. But perhaps things are different where prop-ositional “looking” is at issue. So we must get clear on what propositional“looking” is.

Williamson never explains what it is for a premise to “look as though it istrue.” ‘Looks’ has a colloquial use as a mere synonym for ‘seems’, but on thatreading there is nothing directly perceptual about its employment; we can speakof it “looking” as though the continuum hypothesis is true. Something couldlook true, on this reading, even to a blind person. It is hard to see whythisnotion of looking true has any specific relevance tophenomenalsorites cases.

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Furthermore, deductive closure for this notion of looking fails quite trivi-ally and obviously. Granting it yields only banal absurdity, not bewitching par-adox. Suppose I see tracks in the woods and~a! it looks to me as though thetracks are deer tracks. The tracks lead me directly to a pig, and~b! it looks tome as though the pig left the tracks.~The tracks end at the pig’s feet.! Thepig has atypically long and slender hooves, but it is clearly a pig and not adeer. Now, if “looking true” as we are now interpreting it were closed underdeduction, then from~a! and ~b! it would follow that ~c! it looks to me asthough the pig is a deer.14 But this is absurd.

For both these reasons—its non-phenomenal character and its obvious fail-ure to yield deductive closure—this colloquial interpretation of a proposi-tion’s “looking true” generates no phenomenal paradox. It cannot be whatWilliamson has in mind.

15. Whatdoeshe have in mind? Our only clue comes from his allowance thatit might look as though a currently unseen object were square~p. 174!:

One might allow that it looks as though an unseen object had a property whenpresent visual perception provides a basis of some kind for the judgement that theobject had the property; to the hunter’s experienced eye, examining the tracks, itmay look as though the unseen deer was wounded.

This suggests the following formula for looking true:

LT1: It now looks as though x is F if and only if present visual percep-tion provides a basis of some kind for the judgement that x is F.

“A basis of some kind” might be as slight as a reason, perhaps a weak or over-ridden one. In that case, once again, no paradox threatens. For one could allowthat present visual perception provides a weak reason of some kind for thejudgement that a given figure is square even while maintaining that one alsohas much more powerful, overriding evidence—perhaps also derived frompresent visual perception—that it is not.

Consider the example of the previous section. Visual perception gives mea reason for thinking that I see deer tracks—theylook like deer tracks—andalso for thinking that a pig, and only a pig, left them. We might allow thatvisual perception gives mea reason for thinking that the pig is a deer, but ofcourse this reason is overridden by other, much stronger ones for thinking thatit is not.15

If we allow LT1 to capture the notion of “looking true,” no paradox threat-ens. There is nothing paradoxical in allowing that visual perception givesareason for thinking that it looks as though a figure is square, when it is plainlyoblong. What generates paradox must be an apparently sound argument con-


cluding that we arejustified in thinking it looks as though the figure is square,when clearly we are not. No such argument springs from LT1.

16. For paradox to arise, the “basis” provided by visual perception must be atleast as strong as justification.16 Suppose we grant this but construe the basisas nomore than this. Suppose, that is, that we construe a proposition’s “look-ing true” in accordance with

LT2: It now looks as though x is F if and only if present visual percep-tion provides justification for the judgement that x is F.

Letting LT2 guide our construal of a proposition’s “looking true” once againrobs our paradox of its phenomenal nature, I will now argue, and mislocatesits solution.

LT2’s rendering of “looking true” demands more than the colloquial render-ing on which something can look true to the blind—but just barely more. Visualperception can provide justification for a judgement remote from that percep-tion. Consider Williamson’s case of the hunter’s~ justified! judgement that adeer is wounded, or a physicist’s judgement—justified on the basis of her visualperception—that a muon has decayed into an electron and neutrinos.17

Recall: a sorites paradox can get off the ground only if we use a notion of“looking true” that is plausibly closed under deduction. Is the notion capturedby LT2 plausibly so closed?

The deductive closure of justificationsimpliciter is disputed. Suppose youthink that justificationsimpliciter is not plausibly closed, while “looking true”is. In this case, you might argue, the distinctively phenomenal nature of “look-ing true” is what generates paradox. However, LT2’s phenomenal constrainton justification is too weak. If I doubt that justification is closed under deduc-tion, why should my doubts evaporate just because the justification in a givencase has a visual basis? Suppose I take the Lottery paradox to show that justi-fication is not deductively closed. I am justified~we suppose! in believing ofeach lottery ticket 1, 2,... , n, that it is a loser, and that tickets 1, 2,... , n are allthe tickets, but I am not justified~I think! in believing that all the tickets arelosers. Why should I change my mind merely on being convinced that my twojustified beliefs have a basis in visual perception? Barring some specific argu-ment for such a view—which Williamson does not and I cannot provide—there is once again no reason to think that there is anything distinctivelyphenomenalabout the “paradox” we face. Nor anything paradoxical, for thatmatter. If justification is not plausibly closed under deduction, then absent somereason why a visual basis makes a difference, then we have no reason to thinkthat “looking true” is closed under deduction. And without such closure, welack even aprima facieparadox.

Suppose we grant, then, the plausibility of deductive closure for justifica-tion simpliciter. Then we must grant deductive closure for “looking true” sim-

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ply because it is a species of justification; its phenomenal character is irrelevant.In this case, the phenomenal character of the sorites cases we are consideringturns out to be a red~or square! herring. If this were right, a sorites paradoxmight remain, but there would be nothing distinctively phenomenal about it:there would be no important difference between a paradox involving a thing’slooking red and its being~say! a tadpole, which is not a phenomenal matter.So no one who thinks that distinctively phenomenal sorites paradoxes pose dis-tinctive challenges can endorse both LT2’s construal of “looking true” and alsothe deductive closure of justification.

Williamson might respond that the crucial role played by the phenomenalnature of “looking true” lies not in generating paradox but in solving it. Thedeductive closure of justificationsimpliciter has no bearing on the distinc-tively phenomenal nature of perceptual sorites cases. So let’s grant for the sakeof argument that itis closed, that we may focus~Williamson might say! onwhat is distinctively phenomenal: the context-relativity of looking square. Ifcontext-relativity infects phenomenal notions in ways that it does not infectthe non-phenomenal, this fact may yield a distinctively phenomenal solutionto phenomenal sorites paradoxes.

I have already argued that the context-relativity of perception cannot solvea phenomenal sorites paradox, since we can imagine away that context-relativitywithout imagining away the paradox. My point here is different. The context-relativity to which Williamson appeals does not merely fail to solve theparadox. It makes the formulation of aprima facieparadox impossible, on Wil-liamson’s own terms.

Recall that the paradox is supposed to arise from a case in which~it seems!it looks as though the premises of a valid argument are true. I will argue nextthat the context-relativity of perception, coupled with LT2’s construal of phe-nomenal “looking,” blocks the construction of aprima facie paradox, for itmakes the premises of the sorites argument come out obviouslyfalse on anyrelevant disambiguation. This fact doesn’t jibe with Williamson’s idea that weare misled because each premise istrue on somerelevant disambiguation~whileno disambiguation renders them all true!. Once again, LT2’s construal of “look-ing” is insufficiently phenomenal.

It is undoubtedly context-relative whether it looks true that a given figureis square—where this now means, remember, that visual perception providesjustification for a judgement about the figure’s squareness. One’s visual percep-tion might provide a basis for such a judgement in one context and not inanother. Consider a figure that “looks oblong” in thenon-propositional sensein a given context. One’s visual perception in this context may neverthelessunderwrite a justified belief that the figure is actually square.~It is an old andelementary point that our judgements about the shapes of external objects typ-ically derive from perceptual experiences in which the look of the object doesnot match its true shape.! No sensible person confronted with a sorites sequenceof rectangles would judge on the basis of her visual perception that adjacent


figures have exactly the same shape, even if she were unable to distinguishthem by eye. Nor would she judge on the basis of her visual perception that agiven figure from the series was square~or, except perhaps in obvious cases,non-square!. For she would see where such judgements would lead. Anyonewho did so judge would not qualify as justified in so judging. Hence it sim-ply would not look as though any of the figures is square—remember we areinterpreting “looking” in accordance with LT2—nor that any two of them haveexactly the same shape. So the problem with this rendering of “looking true”is not that the premises of the sorites argument are interestingly ambiguous,as Williamson claims; it is rather that they are patently false on any relevantdisambiguation—and in a way that leaves the original air of paradox undis-pelled. Interpreting propositional “looking true” along the lines of LT2 pre-cludes the formulation of a compelling paradox; hence no treatment of it alongthese lines can provide a solution to such a paradox.

17. LT2 does not tie the “looking true” of a proposition about a figure totheway that the figure looksso as to generate a compelling paradox. Perhaps wecan create such a tie by construing the looking-true of a proposition in accor-dance with~not LT2 but!

LT3: It looks as though x is F if and only if the judgement that x is F isjustified by x’s looking F,

where ‘x’s looking F’ is understood with our earliernon-propositional sense.18

On LT3’s construal, it is certainly context-relative whether it looks as thougha figure is square. For some particular figure xi , it may look as though xi issquare when it is viewed next to xi21 but look as though it is not square whenit is viewed next to xi11. This will typically be because xi ~non-propositionally!looks squarein the first context andlooks non-squarein the second. That is,the context-relativity of the propositional notion of “looking square” derivesfrom that of the non-propositional notion.

However, the notion of propositional looking-true captured by LT3 isnotcontext-relative in a way that permits the construction of an intuitively compel-ling sorites paradox. We have already seen why in connection with LT2: if Irealize that a sorites sequence confronts me, I cannot be justified in judgingmerely on the basis of some xi’s looking square that it is in fact square. Norcan I be justified—in many cases—in judging merely on the basis of xi’s look-ing oblong that it is in fact oblong. So LT3’s construal of propositional “look-ing true” once again makes the premises of the sorites argument patently falseon any relevant disambiguation—again, in a way that leaves the original airof paradox undispelled.

Perhaps there is some other construal of propositional looking-true that willgenerate—and then, perhaps, solve—a compelling sorites paradox. But I canthink of none and Williamson never suggests one. Although he take pains to

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distinguish the propositional from the non-propositional reading, whatever intu-itive pull attaches to his apparently propositional rendering of ‘looking true’derives from reading it implicitly with the non-propositional sense. William-son frequently talks of a figure “looking square” when he is officially sup-posed to be talking about it “looking as though the figure is square.” I haveno gripe with shorthand—but I suspect that failure to treat it consistentlyasshorthand lies behind the impression that an interesting paradox arises from apropositional reading of “looking square.”

18. There is, then, no initially compelling paradox arising from a proposi-tional notion of “looking square.” The real paradox involving squareness isan apparent analogue of our argument from indiscriminability for phenomenalredness. We suppose that figure 1~non-propositionally! looks determinatelysquare, that figure 50 looks determinately oblong, and that any two adjacentfigures are pairwise indistinguishable with respect to their apparent shapes. Butthe following analogue of DR seems initially compelling:

DRS If figure n looks square, and patch n11 looks as though it has thesame shape as patch n, then patch n11 looks square.

The solution to the paradox lies in disambiguating DRS as we disambigu-ated DR rather than in temporal disambiguation involving the context-relativityof looking square. For once again, we can easily imagine ourselves stable per-ceivers. We can imagine ourselves far less prone to perceptual illusion, so thata figure that looks square at any time looks square at every time, and a figurethat looks oblong at any time looks oblong at every time~given minimal thresh-old conditions of illumination, viewing angle, and so on!. A pre-theoreticallycompelling paradox remains even if we imagine away the context-relativityof “looking,” whereas no such paradox arises once we~non-temporally! disam-biguate DRS. The facts about closure rather than about context-relativity lieat the paradox’s heart.

19. The paradox involving phenomenal squareness is not, however, an exactanalogue of that involving phenomenal redness. Before we see how my solu-tion disposes of the paradox concerning shape, we need to see exactly whatthat paradox is.

We imagine that figure 1 determinately~and non-propositionally! lookssquare, just as we imagined that patch 1 determinately looked red. I allowedfor the sake of paradox, because it is plausible, that in standard conditions Icannot be mistaken in thinking that something looks red to me; without thisassumption, no paradox threatens. So I ought by analogy to allow for the sakeof argument that in ordinary conditions I cannot be mistaken in thinking thatsomething looks square to me. But this suggestion about phenomenal square-


ness is absurd in a way that the parallel suggestion about phenomenal rednessis not, at least if something’s “looking square” is to be interpreted as meaning“looking perfectly square, with limitless precision.” We know perfectly wellthat we cannot tell infallibly by eye that an angle is, or looks to be,exactly90 degrees, or that two lines are, or look to be, ofexactlyequal length, wherethe ‘exactly’ connotes limitless precision. Infallibility about looking exactlysquare resembles infallibility about fully determinate color-appearance. Welack it.

The paradox of phenomenal squareness seems never to get out of the gate.For there is no good reason, evenprima facie, to grant that figure 2 looks tome as if it has the same exact shape as figure 1, even if I find figures 1 and 2pairwise indistinguishable.

20. One might try to recover a paradox in this case by imagining away ourobvious infallibility about exact shape-appearance. Imagine that whenever Ibelieve a figure to look square~to me!, it does, and that whenever I believe itto look oblong, it does, and that whenever I believe two figures to look exactlyalike with respect to shape, they do. Continue to suppose that I perceive sta-bly. Given these suppositions, can we resurrect the paradox?

No. For each successive figure I confront, I judge whether it is~exactly!square, exactly oblong, and exactly similar in shape to its predecessor.19 Eachjudgement is, we imagine, infallible. It follows that if I judge that figure 1looks square and that figure 50 looks oblong, there are some adjacent figuresthat I judge to differ with respect to exact shape-appearance. To suppose other-wise generates not profound paradox but trivial contradiction. As with fullydeterminate color-appearance, we can have either infallibility about exact shape-appearance or transitivity of pairwise indistinguishability. We cannot have both.We are in fact fallible~and even unreliable! about exact shape-appearance, aswell as unstable. Recognizing this disarms the paradox.

21. We might try to rearm the paradox by finding a notion of shape that is toexact shape as ordinary color~red, blue, etc.! is to fully determinate color. Weneedn’t look far. Perfectrectangularity is a shape relative to which perfectsquareness is determinate and which is itself determinate relative tothe shapeof quadrilaterals all of whose angles are between 88 and 92 degrees. Shapes,like colors, form hierarchies of greater and lesser determinateness.

DRS is ambiguous, then, in just the way that DR is, and disambiguationdissolves paradox. For we can allow that we have infallibility about at leastsome of these determinables and still give a convincing answer to the paradox.

This case has the same structure as that involving color, so I treat it sum-marily. Any two adjacent figures sharesomeshape-appearance property—say,rectangularity. But no two shareeveryshape-appearance property, unless oneof them is redundant, since no two share their fully determinate shape-appearance. From the pairwise indistinguishability of two figures, it does not

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follow that they share all their shape-appearance properties, and any judge-ment we might make that they do is clearly fallible. If a sorites argument con-cerning squareness is a true analogue of the color-arguments invoking DRE,DRU, and DRA, it must fail, and for reasons exactly parallel to the reasonswhy the color-arguments fail.

Appealing to the hierarchy of shape-properties is overkill. For the restrictedinfallibility that plausibly attaches to judgements about~ordinary, non-fully-determinate! phenomenal color seems more doubtful for judgements about~ordinary, non-exact! phenomenal shape. But I need not force this issue. WhatI have shown is thateven if we grant such infallibility, the hierarchy of phe-nomenal colors and shapes, coupled with infallibility about the fully determi-nate bases of these hierarchies, permits a satisfying solution to phenomenalsorites paradoxes.

22. ~Coda.! As I have presented the argument from indiscriminability, it is acategorical premise~U2 or A2! that fails, rather than an induction premise~DRU or DRA!. ~For brevity, I will focus in this section on phenomenal color.Everything I say appliesmutatis mutandisto phenomenal shape.! But thiscategorical failure translates into a failure of the Induction Premise in our orig-inal, canonical sorites argument. DR seems pre-reflectively to support theInduction Premise. In exposing DR’s equivocation, I undercut the motivationit gives for the Induction Premise, and no other plausible motivation supportsit, so far as I can tell.

How does my solution fit with standard views of vagueness? We may dis-tinguish three broad views. The first, which I call ‘non-classical’, rejects clas-sical logic and locates vagueness “in the world.” A non-classical view allows~for example! both that the use of ‘red’ in this very sentence is perfectly univ-ocal and also that it can be neither true nor false~or, on some views, bothtrue and false! whether a given patch looks red. The nonclassical view sub-sumes both “paraconsistent” approaches to vagueness and also those invoking“metaphysical vagueness.”

Opposing the non-classical view is what we might call ‘simple classicism’about redness. Simple classicism is not simplistic: it does not require that ‘red’is univocal, for example. It does say that some uses of ‘red’ unambiguouslypredicate a certain property of a thing, and it applies the determinacy thesis:this property always either determinately applies to a thing or determinatelyfails to apply. Simple classicism subsumes the family of views usually knownas ‘epistemicist’, though simple classicists needn’t hold epistemicism as oftenconstrued.20

Between these views there allegedly lies a third view, “linguistic vague-ness.”21 On this view, of which supervaluationism is the predominate species,vagueness lies neither “in the world” nor in our ignorance but rather in seman-tic indecision—in our failure to specify precisely the borders of the region towhich ‘red’ applies.


My solution to the phenomenal sorites does not forbid the adoption of anyof these standard views. Supervaluationists, for example, could endorse every-thing I have said thus far.22 My solution is consistent even with non-classicalviews, if anything is.23

Simple classicism, however, is the generic solution most congenial to myown. For given my solution, any invocation of~say! supervaluations or meta-physical vagueness is idle; we don’t need such things to solve the phenomenalsorites. One could still insist on them, but my solution dissolves any theoret-ical pressure to do so. Absent such pressure, the insistence seems perverse.

My solution offers all that a simple classicist could want. It does not offerall that anepistemicistmight want. Epistemicism adds elusiveness of knowl-edge to determinacy of fact, and nothing I have said entails that onecannotknow which is the last red-looking patch. But the fallibility of judgements thattwo patches share all their color-appearances yields a diagnosis of soritical igno-rance if such there be.

To see this, imagine that I actually go down the line of patches, startingwith patch 1, saying of each in turn whether I believe it looks red. There willinescapably be a last patch such that I am prepared to say, sincerely andunequivocally, that I believe it looks red—say, patch 28.~This claim begs noquestions in favor of simple classicism; it is simply an undeniable claim aboutactual behavior.! Given the assumed infallibility of such beliefs, patch 28 mustlook red. It may not be the last red-looking patch, though. I may be unsurewhether patch 29 looks red. Infallibility in thinking that something looks redsays nothing about what the facts are when I am unsure whether somethinglooks red. Perhaps patch 29 looks red to me, perhaps not. I cannot concludethat it looks red simply on the grounds that it is pairwise indistinguishable fromits red-looking predecessor. Again, pairwise distinguishability is not distinguish-ability tout court.

If I later examine these two patches pairwise, I may be equally sure—orunsure—about whether they look red. The combination of stable perception andinfallibility for non-fully-determinate color-appearances~‘S1I’, for short! doesnot require stablejudgementwith respect to such appearances. Let’s say that ifsomething looks colored but not red, it looksanti-red. I allow that anti-red is acolor, and since it is not fully determinate I grant infallibility for judgementsof phenomenal anti-redness. Now, S1I rules out judging a patch to look red~to me! at one time and judging it to look anti-red at another, for these judge-ments would entail that it looks red at one time but not at another, violatingstable perception.24 But S1I does not rule out judging on Monday that apatch looks red and being unsure on Tuesday whether it looks red. S1I en-sures that the patchdoeslook red to me on Tuesday, if I judge on Monday thatit looks red. But that a patch looks red to me does not ensure that I will realizeit does.

Suppose, then, that I compare patches 28 and 29 pairwise. If I judge themboth red-looking, I remove my uncertainty about patch 29, in which case wesimply move farther down the series until uncertainty returns. So suppose

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instead that I am unsure whether they look red. Then, let’s suppose, I learnthat I earlier judged patch 28 to look red. If I know that S1I holds, I inferthat patch 28 looks red to me now; my uncertainty is halved, though not bymy current perception. What is important is that this inference forces no judge-ment about patch 29. I still allow that it might or might not look red, acknowl-edging my fallibility concerning fully determinate color-appearances.

It may seem surprising that simple classicism yields a compelling treat-ment of this case. For simple classicism requires that if confrontation with asorites sequence involves a lack of relevant knowledge, this lack must be under-stood in terms of ignorance of determinate fact. Such a view initially seemsweakest where phenomenal sorites sequences are concerned, since claims ofsoritical ignorance seem most tenuous in the phenomenal realm of first-personauthority. Disentangling defensible from incredible claims of infallibility re-moves the apparent weakness and the surprise, by showing straightforwardlyhow there could be a last red-looking patch in a series of pairwise indistinguish-able patches. My treatment of the phenomenal sorites paradox stands on itsown, but it also reduces the initial, apparently irreducible implausibility thatis the chief bar to simple classicism’s acceptance.25

Notes

1 See Hardin 1988a for a fascinating introduction to the complexities of color-perception.2 Cf. Williamson’s ~1994, p. 179! distinction between “the look of a thing” having a property

and its looking as though the thing has that property.3 I may name or attend to only one color-property of a visual appearance, but this does not

mean that it has only one. A child may know that something looks red to her without knowingthat it looks burgundy to her, though it does. Even if I have relevant words and concepts, I maynot apply them. Suppose I see two patches, one magenta and one maroon. I may say only thatthey both look red, perhaps because I notice only this. But they do not “look the same” in anyintuitive sense, given normal vision and circumstances.

4 Colors overlap as well as nest. Some things are both fuchsia and magenta, but some magentathings are not fuchsia and vice versa. Perhaps~a! some red things are fuchsia, but~b! some fuch-sia things are purple, not red. So perhaps fuchsia does not nest within red; but non-purple fuchsiadoes, and this will do for my point. Ignore overlapping colors.

5 My fully determinate colors are Nelson Goodman’s~1977, p. 141! “single phenomenalshades.”

6 That is: “If patch n looks red, and patch n has a unique color-appearance property, and patchn11 has a unique color-appearance property, and the color-appearance property of patch n is iden-tical with that of patch n11, then patch n11 looks red.”

7 Specificity in color-terms varies enormously, though systematically, by language and cul-ture. An extreme case are the Jalé of the New Guinea Highlands, who have only two atomic colorterms, translated by Berlin and Kay~1969, p. 23–24! as ‘black’ and ‘white’. The Jalé wouldcategorize yellow and white as “the same color,” namelyhóló ~white!. But their color vision isas good as ours~or at least nearly so; see Hardin 1988a, p. 167!, and they can surely distinguishthings that look yellow from those that look white on the basis of their apparent color.

8 Although the most natural objection, to be considered shortly, is that pairwise indistinguish-ability is not sufficient to capture the intuitive notion of indiscriminability, one might think that itis not even necessary. Suppose I can reliably order all the patches in the series, pairwise and other-wise, while sincerely professing no discernable difference in color-appearance between any two


adjacent patches. This is certainly a conceivable state of affairs, as suggested by the phenomenonof blindsight: I might take myself to be guessing, but causal processes that do not rise to the levelof awareness might reliably guide my “guesses.”~See Goldstein 2000.! Here, you might say, thepatches really are indiscernible on the basis of phenomenal coloreven thoughadjacent patches arepairwise distinguishable. This conclusion, however, is anon sequitur. First, my reliable orderingcould result from information unrelated to the patches’ color-appearances. But even assuming wecan rule this out, the case allows the interpretation that there are differences in color-appearanceof which I am unaware. Finally, and most importantly, the case that concerns us is one in whichonly phenomenal color and our judgements about it are guiding our judgements about sequentialorder. Otherwise, we are once again failing to consider aphenomenalsorites paradox.

9 This sort of argument for the discriminability of pairwise indistinguishable elements maybe found in Burns~1986! and Koons~1994!. Other parts of my argument find analogues in Burns’s,too, but many important ones don’t. For one example, Burns does not address the issues of phe-nomenal infallibility that give the phenomenal sorites its urgency. For another, her argument iscast in meta-linguistic terms concerning~e.g.! the applicability of the predicate ‘looks red’, whereasI address a non-linguistic property of looking red.~She allows, rightly, that stipulation may guidethe correct applicability of the predicate, and this allowance plays a role in her solution to theparadox. No such stipulation governs the applicability of looking red, however.!

10 Well, not quite. Strictly, what follows is that all the patches except perhaps one of the termi-nal ones are mutually strongly indiscriminable. Patch 1 or patch 50~though not both! may bedistinguishable~but not pairwise distinguishable! from all the rest. An indirect application of thediscrimination test involving a terminal patch, a non-terminal patch, and a patch outside the origi-nal series could show this.

11 I let slide some complications. Infallibility, even coupled with stable perception, does notentail the transitivity of pairwise indistinguishability. Infallibility requires thatif I judge two patchesto share a fully determinate color-appearance, then they do; it does not require that I ever so judge.Doxastic reticence brings infallibility on the cheap while allowing non-transitivity. Suppose thatat time t1 I judge patch n to look red.~Thoroughgoingdoxastic reticence would preclude eventhis and bring infallibility for free.! At time t2 I am presented with patches n and n11 and can-not distinguish them pairwise. Stable perception insists that patch n still looks red to me; it saysnothing about judgement. Infallibility requires thatif I judge patch n11 to look red, I am right;harnessed to stable perception, it requires that I will not judge patch n to look non-red. Neitherprinciple, alone or in tandem, requires that Iwill once again judge patch n to look red or judgethat the two patches share a fully determinate color-appearance.

If we add to infallibility and perceptual stability a modicum of doxastic abandon, so thatat each successive stage I do judge whether adjacent patches share a fully determinate color-appearance, we get an outright contradiction between infallibility and the non-transitivity ofpairwise-indistinguishability in our case. If we withhold doxastic abandon, we vaporize the para-dox. For if I simply refuse to make relevant judgements, the supposed infallibility theywouldhave, were I to make them, does no work.

12 Hardin notes that philosophers who accept the non-transitivity of indiscriminability betweenphenomenal colors have used it “as a stick to beat sense-datum theorists as well as to cast doubton the possibility of giving a rational reconstruction of the semantics of everyday color terms.”Unlike Hardin, I allow non-transitivity, but the distinctions I draw in this paper render it worth-less as a weapon against either sense-data or the semantic rationality of everyday color terms;see Hardin~1988b, p. 213! for those arguments.

13 If this is unobvious, see note 12 and section 22—the coda—below.14 I assume charitable interpretation: ‘It looks as though the tracks are deer tracks’ means, for

example, that it looks as though the tracks were left by exactly one deer and by nothing that isnot a deer.

15 For another appeal to this notion of a proposition’s “looking true,” see Daniels~1999, p. 207!on the famous Müller-Lyer line illusion.

16 Or perhaps warrant. If you think that warrant does not entail justification, you may read allmy uses of ‘justification’ as shorthand for ‘justification or warrant’; similarly for cognates.

406 NOÛS

17 Contentious epistemic issues surround the notion of perception justifying a judgement~orbelief!. “Minimal foundationalists” with reliabilist leanings typically allow that a belief causedby a perceptual process, or by a process of some restricted perceptual type, is justifiedceterisparibus. Others will spell out the way in which perception yields justification differently. Nonebut skeptics, however, will deny that perception plays a crucial role in the justification of manybeliefs. My claims are neutral with respect to the precise nature of this role.

18 I do not claim that LT3 in fact captures whatever sense we might intuitively attach tothe notion of a proposition’s “looking true.” The possibility of deviant justifications might under-mine such a claim. What we need is presumably that the judgement that x is F is justified~orwarranted—see note 16! in the right wayby x’s looking F. I have no idea how to spell this outinformatively, but it doesn’t matter. My arguments in the text clearly would apply to a spelled-out claim, since they allow—assume, in fact—that the justification is of the right sort.

19 This grants me doxastic abandon~see note 11!. Withhold it, and you have no paradox.20 Epistemicists typically analyze or explain vagueness in terms of ignorance of the fully deter-

minate facts.~They disagree about the centrality and strength of the ignorance in question.! Butsimple classicists may coherently deny that ignorance is constitutive or explanatory of vagueness.It is worth noting, too, that nihilists, who embrace sorites arguments as soundreductiosof theapplicability of common-sense notions, fall into the camp of simple classicism.

21 “Allegedly” because linguistic vagueness as usually stated seems just a variant of eithernon-classicism or of simple classicism. It might be construed as saying that there is no determi-nate fact about which proposition~s! a given sentence expresses. But saying that vagueness is notin the world but rather in language makes sense only if language is not in the world, a sugges-tion I cannot fathom. If the fan of linguistic vagueness says instead that we don’t know the deter-minate fact~s! about which determinately-true-or-false propositions are being expressed, it’s hardto see what recommends this position over a more straightforward version of simple classicism.

22 They would say that I have barely scratched the surface of DR’s ambiguity, for ‘red’ itselfis multiply and unresolvably ambiguous—not just because of context-relativity that infects it butbecause the borders of its application are “semantically undecided.”

23 But it isn’t.24 By definition, if something looks anti-red, it does not look red. This triviality should not

be confused with the dubious propositionalist claim that if something looks as if it is not red,then it does not look as if it is red.

25 I wrote the first draft of this paper during the 1998 Bled~Slovenia! Conference on Vague-ness, and I owe all the participants for the inspiring atmosphere. A later excerpt received usefuldiscussion at the 1999 meeting of the Central Division of the American Philosophical Associa-tion; Greg Ray’s comments prompted crucial clarifications. Timothy Williamson goaded me~incorrespondence! into addressing the propositional construal of ‘looking red’. James Cargile, Lau-rence Goldstein, Trenton Merricks, and Gayla Mills gave helpful comments. Thanks to all.

Reference

Berlin, Brent and Paul Kay 1969:Basic Color Terms. Berkeley: University of California Press.Burns, Linda 1986: “Vagueness and Coherence,”Synthese68, 487–513.Daniels, Charles 1999: “A Theism-Free Cartesian Analysis of Knowledge,”Noûs33, 201–213.Goldstein, Laurence 2000: “How to Boil a Live Frog,”Analysis60, 170–178.Goodman, Nelson 1977:The Structure of Appearance, 3rd ed. Dordrecht: D. Reidel.Hardin, C. L. 1988a:Color for Philosophers. Indianapolis: Hackett._1988b: “Phenomenal Colors and Sorites,”Noûs22, 213–234.Koons, R. C. 1994: “A New Solution to the Sorites Problem,”Mind 103, 439–449.Raffman, Diana 1994: “Vagueness Without Paradox,”Philosophical Review103, 41–74.Williamson, Timothy 1994:Vagueness. London: Routledge.Yablo, Stephen 1992: “Mental Causation,”Philosophical Review101, 245–280.


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Fallibility and the Phenomenal Sorites