Unger’s Argument for Skepticism Revisited

Igor Douven

Institute of Philosophy, University of Leuven

Diederik Olders

Department of Philosophy, Erasmus University Rotterdam

Abstract

In his [1974/2000], Unger presents an argument for skepticism that significantly

differs from the more traditional arguments for skepticism. The argument is

based on two premises, to wit, that knowledge would entitle the knower to abso-

lute certainty, and that an attitude of absolute certainty is always inadmissible

from an epistemic viewpoint. The present paper scrutinizes the arguments Unger

provides in support of these premises and shows that none of them is tenable. It

thus concludes that Unger’s argument for skepticism fails to threaten the possi-

bility of knowledge.

Unger [1974/2000] presents an argument for skepticism—which he understands as

the thesis that no one ever knows anything—that significantly differs from the more

traditional arguments for skepticism. In particular it does not proceed by sketching

some scenario that is, or at least is alleged to be, wholly distinct, but nonetheless

evidentially indistinguishable, from the world as we believe it to be, nor by providing

some other putative reason for believing that we are not in the position to obtain

justification with respect to any proposition.1 Instead, the argument seeks to show

that knowledge licenses absolute certainty, an attitude which—the argument further

claims—is always inadmissible from an epistemic viewpoint. More exactly, the argu-

ment runs as follows:2

(1) For all persons S and propositions ϕ, if S knows that ϕ, then it is all right for

S to be absolutely certain of ϕ (42).

(2) For no person S is there a proposition ϕ such that it is all right for S to be

absolutely certain of ϕ (43).

(3) Therefore, for no person S is there a proposition ϕ such that S knows that ϕ.

While Unger does not say much about the phrase “it is all right,” it is clear enough

that by it he means to indicate something like permission on the basis of some theory

of rationality or justification.

1See Williams [1999] for a survey of the standard skeptical arguments. Technically speaking these

arguments differ from Unger’s in that, in contrast to the latter, they all are or involve underdetermination

arguments; for more on this see Douven [2008a] and references given there.2All unadorned page references are to Unger [1974/2000].

1

The argument is patently valid. So there had better be something wrong with

either of the premises lest we are committed to a conclusion that at least as a matter

of psychological fact most (if not all) of us are incapable of accepting. Although some

time has lapsed since it first appeared, we believe that Unger’s paper still merits

attention because, firstly, in the meantime the paper has attained the status of a

“classic” in the field of epistemology,3 and secondly and more importantly, there are

major flaws in the arguments Unger offers in support of (1) and (2) that have gone

unnoticed in the literature. In the following, we scrutinize these arguments and show

why they are wanting.

1. Unger’s Argument for the First Premise. While Unger devotes the entire second

section of his paper to a defense of (1), he only directly argues for it in the first

paragraph of that section. In the longer, second paragraph he tries to provide indirect

support for (1) by arguing for (1′):

(1′) For all persons S and propositions ϕ, if S knows that ϕ, then S is absolutely

certain of ϕ.

(In the third paragraph, he emphasizes that he is concerned with the common, ev-

eryday notion of knowledge, and in the fourth and final one he presents a kind of

summary—neither is relevant to our present purposes.) The upshot, we claim, is

unconvincing.

We first consider the purported direct support for (1) that is supposed to come

from an example in which, Unger imagines, we take a given person to be certain of

something and then ask him, “How can you be certain of that?” Says Unger (43):

In asking this question, we manage to imply that it might not be all right for him

to be certain and imply, further, that this is because he might not really know the

thing. If the man could show that he does know, then we should withdraw the

question and, perhaps, even apologize for implying what we did by raising it.

We manage to imply as much, because, Unger thinks, “we all accept the idea that, at

least generally, if one does know then it is all right for one to be certain of it—but if

one doesn’t then it isn’t” (ibid.). And—Unger concludes this part of the argument—

“[t]his suggests that there is some analytic connection between knowing, on the one

hand, and on the other, its being all right to be certain” (ibid.).

There is considerable vagueness in this argument (“suggests,” “some analytic con-

nection”). However, let us not speculate about, for instance, how exactly the one idea

might suggest the other, but instead focus our attention on the argument’s main sup-

position, the supposition about what exactly is implied by asking someone how she

can be certain of something—namely, that it might not be all right for her to be certain

of the thing because she might not know the thing. To see why this supposition is

doubtful, first note that in order to explain the kind of behavior Unger points to in the

passage just cited, it is enough to make the rather minimal assumption that what is

implied by asking that question is that we doubt the person’s grounds of justification

for what we believe she is certain of, perhaps because we believe justification for it is

3Witness, among others, the fact that it has been anthologized several times, for instance, in Goodman

and Snyder (eds.) [1993], Williams (ed.) [1993], and Sosa and Kim (eds.) [2000].

2

hard or impossible to obtain in general, or because we doubt that this particular per-

son is or ever was in the right position to obtain justification for it. For if the person

is able to show that she knows, and hence does have justification, that should indeed

make us withdraw our question—and perhaps apologize for having had, or having

expressed, doubts concerning her epistemic position. True, that this is implied by

raising the question does not preclude that more is implied by it. But if we can ex-

plain the phenomenon Unger points to by the minimal assumption we proposed, then

it would be bad methodological practice to make stronger assumptions (unless Unger

could muster linguistic data that do require such stronger assumptions).

Let us turn, then, to his indirect argument for (1), via (1′). According to Unger,

any support for (1′) also supports (1) because “The very particular idea that knowing

entails its being all right to be certain is suggested . . . by the fact that knowing entails,

at least, that one is certain” (43). And he thinks the truth of (1′) is evident from the

(alleged) fact that people sense an inconsistency in sentences such as “He really knew

that it was raining, but he wasn’t absolutely certain that it was” and “He knew it, but

he didn’t know it for certain” (ibid.), for that seems most easily explained by supposing

that knowledge is incompatible with uncertainty. But there are things to contest here,

mostly in relation to the putative argumentative link between (1) and (1′), but also in

relation to the support that is alleged to exist for (1′).

Starting with the latter, it is worth citing what DeRose [1991:597] says in relation

to Moore’s paradox: “I don’t have a special feeling for inconsistencies; I can sense

some kind of clash, but cannot distinguish my sensing of an inconsistency from my

sensing of whatever it is that’s wrong with the Moorean sentence.” We believe that

this applies also to such sentences as “She knows it, but she does not know it for

certain.” Although anyone would admit that such sentences sound odd, it is far from

clear that they sound inconsistent. And if it is only their oddness that we are to

explain, then maybe that can be done without supposing an incompatibility between

knowledge and uncertainty. For instance, no one doubts that knowledge entails being

at least close to certain. Of course, that is consistent with assuming that the “amount”

of uncertainty knowledge permits is so minute that it is not worth mentioning even if

it exists. That might explain why we never hear sentences of the type Unger adduces

in support of (1′). As is argued in Douven [2006, Sect. 5], that by itself is already

enough to explain their odd-soundingness, for odd-soundingness may be strictly a

matter of lack of exposure.4 In short, there appear to be plausible explanations for

the phenomenon other than in terms of an incompatibility between knowledge and

uncertainty.

In fact, there is a type of linguistic evidence, entirely neglected by Unger, that

prima facie even seems to undermine (1′). As Harman [1986:71 f] points out, we of-

ten say such things as that we know we are going to meet a friend tomorrow, even

though we also know that there is a tiny chance that in the interim something will

happen that will prevent us from meeting our friend. Or to use an example from Vogel

[1990:15 f], we typically take ourselves to know where our car is parked, even though

4Here it is important to make a type/token distinction. For it might be said that there are many things

we never or hardly ever hear that when we do hear them still do not sound odd in the way, for instance,

“He knew it, but he wasn’t absolutely certain of it” does. Perhaps you have never before encountered

the sentence “Mark Smith has a crush on Peggy Johnson” and still not find the sentence odd. However,

the point is that we are quite accustomed to hearing instances of the schema “S has a crush on S′,” but

that instances of “S knew that ϕ, but S was not absolutely certain of ϕ” are rarely, if ever, encountered

in practice.

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we also know that there is a slight statistical probability that it has been stolen and

is no longer located where we parked it. Unfortunately, however, we cannot simply

conclude from such examples that people think knowledge does not require certainty.

Douven [2007] argues, drawing on recent work in pragmatics, that when we say, for

example, that we know we will meet a friend tomorrow, we are, appearances to the

contrary notwithstanding, not really claiming to know that we will meet a friend to-

morrow. Rather, we are claiming to know that we will meet a friend tomorrow, unless

something out of the ordinary happens, where for broadly Gricean reasons the qual-

ification is typically left implicit. If this is correct, then from the said linguistic data

nothing follows about people’s intuitions regarding the relationship between knowl-

edge and certainty. Needless to say, however, the burden is not on the nonskeptical

philosopher to marshal linguistic evidence against (1′); it is on Unger to marshal lin-

guistic evidence, or any other type of support, for it—and that he has not done.

As for the first point, the one concerning the putative argumentative link between

(1) and (1′), why should support for (1′) carry over to (1)? Apparently, Unger thinks

this is self-evident, for he doesn’t make any effort to explain it. However, we find

it hard to discern what the supposed relation of support between the two premises

could be based on. That (having the property of) knowing a given proposition entails

having some other property surely does not suggest that knowing that proposition

entails that it is all right, epistemically speaking, to have the other property: “S knows

that ϕ (and S is an ordinary mortal)” entails “S might forget ϕ,” yet by no reason-

able criterion could this be said to suggest that if a person knows something it is

(epistemically) all right that she might forget it. If Unger’s argument for (1) via (1′)

is meant to proceed on the basis of some different principle, he should make this

public. Meanwhile, we think it safe to assume that no principle exists that could do

the requisite linking.5

To end this section, we consider a possible escape route for Unger. It follows from

the foregoing that even granting Unger that he has succeeded in establishing (1′), he

still has not made a case for (1). And (1′) and (2) evidently do not yield the skeptical

conclusion (3).6 However, Unger could still reach that conclusion, provided he is able

to make a case for the following thesis:

(1′′) For all persons S and propositions ϕ, if S is absolutely certain of ϕ, then it is

all right for S to be absolutely certain of ϕ,

for from (1′), (1′′), and (2), the conclusion (3) does follow.

The prospects for such a case are dim, though. Arguably, no reasonable theory

of epistemic prudence or rationality could countenance a person’s being absolutely

certain of something merely on the grounds that she is absolutely certain of the thing.

But we need not even delve into the issue of epistemic rationality here to see

that (1′′) is problematic, for if premise (2) of Unger’s argument holds, then from (1′′)

5Black [1974] contains a rather different critique of (1). He claims that if Unger is right about (1′), then

he cannot be right about (1). His point is that if knowing entails certainty, then it makes no sense to say

that, on condition that one knows something, it is all right to be certain of the thing. But this is wrong,

we think. Reading—as we said we plausibly should—“it is all right” as “it is epistemically rational,” there

would for instance seem nothing untoward in saying “If S knows thatϕ, then it is all right for S to believe

that ϕ,” even though knowledge entails belief; on the contrary, on a standard conception of knowledge

the foregoing would be a conceptual truth.6Together (1′) and (2) do yield the conclusion that, for all persons S and all propositions ϕ, it is not

all right for S to know thatϕ. But while this conclusion is stunning in its own right, it is not skepticism:

a person may know that ϕ even if it is not all right for her to know that ϕ.

4

follows the claim, by contraposition, that no person is absolutely certain about any-

thing, and it would seem that this is an empirical claim which it will take scant em-

pirical investigation to refute.

Surprisingly, however, Unger would deny that the claim that no one is absolutely

certain about anything is false. According to him, “certainty” is an absolute term,

meaning that “As a matter of logical necessity, if someone is certain of something,

then there never is anything of which he is more certain” (Unger [1971:212]).7 Because

of this, Unger believes it is doubtful that anyone ever is certain of anything. Even if

people feel certain of something, he thinks it “somewhat rash for us actually to believe

that they are all so certain” (op. cit., 213). If it should indeed be the case that no one

ever is certain of anything, (1′′) would, of course, even be trivially true. But this way

of arguing is problematic.

First, neither Unger nor anyone else can reasonably deny that many people, or even

most of us, claim to be certain of at least some propositions. In order to maintain

that these people are not really certain of what they claim to be certain of, Unger

must hold that they are mistaken about the semantics of the word “certain,” or in any

event have a tendency of misapplying it. As we just saw, however, Unger attempts to

buttress (1) by adducing certain linguistic evidence crucially involving the use of the

word “certain.” And if we are mistaken about the semantics of that word, or tend to

misapply it, it is quite unclear what value evidence concerning our use of the word

has (other, perhaps, than as a further indication of our being mistaken). It would

be an infelicitous philosophical practice to point to linguistic evidence concerning

some word when it supports a thesis one wishes to maintain, and, at the same time,

appeal to an error theory, or otherwise, to help explain away other linguistic evidence

involving the same word when it seems to undermine the same thesis or some of one’s

other theses, at least without giving a principled and legitimate reason for doing so.

Second, if it is denied that anyone is ever certain of anything, then, given (1′),

which we are granting for the nonce, premise (2) becomes superfluous: (1′) and the

claim that no one is ever certain immediately yield the conclusion that no one ever

knows anything. To be sure, Unger does argue for skepticism along these lines in his

previously mentioned [1971] paper. But the argument he offers in the [1974/2000]

paper discussed here clearly is meant to be a different argument for skepticism.

2. Unger’s Argument for the Second Premise. Unger’s argument for (2) is that one’s

being certain about a given matter entails one’s being dogmatic about it in the sense

that “no new information, evidence or experience which one might ever have will

be seriously considered by one to be at all relevant to any possible change in one’s

thinking in the matter” (44); and dogmatism is an epistemic attitude to be avoided at

all costs, or so Unger thinks. More explicitly, he argues as follows:

(i) For all persons S and propositions ϕ, if S is certain of ϕ, then S is dogmatic

about ϕ (44).

(ii) For no person S is there a proposition ϕ such that it is all right for S to be

dogmatic about ϕ (47 ff).

7So, the “absolutely” which in Unger’s paper often precedes the word “certain” is not meant to indicate

a maximal degree of certainty but is rather to remind us of the (alleged) fact that certainty does not allow

of degrees.

5

(iii) Therefore, for no person S is there a propositionϕ such that it is all right for S

to be certain of ϕ.

This argument, too, is valid.8 But is it sound? We shall consider the premises in

reverse order.

It is easily imaginable how back in the 1970s, when Unger’s paper appeared, it

must have seemed something of a truism that dogmatism is wrong. And to be called

a dogmatist still may not count as a recommendation.9 But as philosophers we ought

to be interested solely in what is true, not in what sounds fashionable or counts as a

recommendation. So, is premise (ii) true?

To answer this question, and to assess properly Unger’s argument for (ii), it is

important to be clear what exactly is implied by the premise. A first thing to notice in

this connection is that being undogmatic, keeping an open mind, can hardly be con-

sidered a goal in itself (whether epistemic or otherwise). It could be a good epistemic

strategy, though, if it served our epistemic goal. Does it do so? Most authors think

that our epistemic goal is to be understood in terms of achieving true beliefs and

avoiding false ones, and endorse something like Alston’s [1985:59] proposal accord-

ing to which we ought to aim at “[amassing] a large body of beliefs with a favorable

truth–falsity ratio.”10 It is well conceivable that keeping an open mind is helpful in

attaining this aim. For instance, in those cases where we are wrongly convinced of

some falsehood, attending to contrary evidence could make us give up our false be-

lief, and thereby effect a somewhat more favorable truth–falsity ratio in our beliefs;

were we dogmatic, on the other hand, we would stick with the false belief forever,

which, we may assume, would work out less favorably for our truth–falsity ratio.11

Let us grant that keeping an open mind indeed serves our epistemic goal and thus

is a good epistemic strategy, and that dogmatism poses an obstacle to realizing our

8To see this, it may be helpful to put the argument in a more formal fashion. Let “P(ψ)” mean that it

is all right that ψ, “DS(ϕ)” that person S is dogmatic about ϕ, and “CS(ϕ)” that S is certain about ϕ.

Then the argument for the second premise can be formalized thus:

(i) For all persons S and propositions ϕ: �(

CS(ϕ)→ DS(ϕ))

.

(ii) For no person S is there a proposition ϕ such that P(

DS(ϕ))

.

(iii) For no person S is there a proposition ϕ such that P(

CS(ϕ))

.

To see that this is valid, reason semantically as follows: According to (i), in all logically possible worlds it

holds that, if a person is certain about something, she is dogmatic about it. According to (ii), there is no

deontically ideal world in which someone is dogmatic about something. Hence, there is no deontically

ideal world in which someone is certain about something, which is what (iii) expresses. This argument

assumes that the deontically ideal worlds are among the ones that are possible according to whatever

logic governs the necessity operator, but, while not entirely trivial, this assumption seems innocuous

here. (Note that, for the argument to go through, the necessity operator in the formalization of premise (i)

is compulsory. But given that Unger frequently rephrases indicative conditionals in terms of entailment—

for an instance, see the first quote in the fourth paragraph of section 1 of the present paper in which he

rephrases premise (1) in those terms—our formalization of (i) should accord with authorial intentions.)9Though see Armstrong [2006] for a recent quite friendly appraisal of an at least moderate form of

dogmatism.10See, e.g., Rescher [1973:21], Lehrer [1974:202], BonJour [1985:8], Foley [1992:183], Sartwell [1992],

and Douven [2008b]. Alston [2005:29] qualifies his earlier proposal by adding that the beliefs we should

try to amass ought to be ones that are of interest to us. The qualification seems important and plausible,

but it does not affect our argument against Unger in any essential way.11It might be that, through a lucky coincidence, a false belief sets us on a track which will eventually

lead us to adopt many truths and no or hardly any (further) falsehoods. But since we are arguing against

Unger, it won’t do any harm to grant him as much as possible on this point.

6

epistemic goal, or at any rate is of no help in realizing it, and thus is a bad epistemic

strategy.

That still does not commit us to (ii), however. For (ii) claims that it is all right

for us to be dogmatic with respect to no proposition whatsoever. And this does not

follow from the fact (presuming it is a fact) that keeping an open mind generally is a

good epistemic strategy and dogmatism generally a bad one. For example—and in the

context of Unger’s argument this question is of particular interest—even if keeping an

open mind generally is a good epistemic strategy, might being dogmatic about what

one knows not still be a good epistemic strategy, too? The two are evidently compat-

ible, just as a mathematician may do good to be generally doubtful about her first

hunches as to whether a certain proposition is provable but to trust them fully when

she is considering propositions in her own field of expertise (say, differential geome-

try). And indeed, if one knows that ϕ, then being open to the possibility that one is

wrong about ϕ might, given some misleading evidence, bring one to disbelieve ϕ, or

to adopt an agnostic attitude towardsϕ; in either case one is distancing oneself from

the epistemic goal as just circumscribed. Also, time saved by not paying attention to

possible evidence against what one knows could be spent on projects which will help

one to approach the epistemic goal in other ways (e.g., it could be spent on search-

ing for evidence for truths one does not yet believe). Hence it seems that from the

perspective of our epistemic goal, there could be nothing wrong with being dogmatic

about propositions we know; on the contrary, it seems recommendable.

One might object here that we may not, or not always, be in the position to know

what we know, and thus not be in the position to know what we should, or at least

could, be dogmatic about. This objection would be misconceived, however, because

the point is that, from the perspective of our epistemic goal, it would be good, or in

any event not bad, to be dogmatic about what we know, whether or not we know or

can know which propositions we could or should be dogmatic about. It is one thing

whether being dogmatic about what we know would be a good epistemic strategy, but

it is another whether we know, or even can know, how that strategy is to be imple-

mented. This is merely to reiterate in slightly different terms a familiar externalist

point. As externalists have long argued, it is a good epistemic strategy to use a given

rule if that rule is reliable, regardless of whether we know or can know that the rule

is reliable (see, e.g., Goldman [1986]).

These considerations help us to address Unger’s argument for premise (ii). He

claims that for any proposition one might take oneself to know, one can imagine

possible experiences that would make it intuitively reasonable to doubt at least to

some extent the proposition. For example, one might hear a voice in one’s head telling

one that one is a brain in a vat and that one is going to have such-and-such rather

bizarre experiences in the next instants—which, miraculously, one then effectively

does have (49). That would make it reasonable to doubt at least somewhat that one is

an embodied brain, Unger thinks. However, to be dogmatic vis-à-vis the proposition

that one is an embodied brain is to disregard such experiences. Thus dogmatism is

an inadmissable attitude.

Our response to this may be easy to predict. Perhaps it can be reasonable if a

person comes to doubt that she is an embodied brain following experiences of the

above kind. But supposing she truly believes that she is an embodied brain, then,

7

since reasonably doubting a proposition seems incompatible with believing it,12 from

the perspective of our epistemic goal it would still be best were she to stick to her be-

lief. Consider an analogy. It can be quite reasonable to believe a consistent liar who is

exceedingly skilled at deceiving people; “reasonable” here means something like that

it is easily understandable how a person could come to believe such a liar, or that we

can easily imagine ourselves to do the same in similar circumstances. Nevertheless,

if we are bent on realizing our epistemic goal, then presumably believing a consistent

liar is a bad thing to do. Thus, “never believe a consistent liar” seems a good epis-

temic strategy, even though some failures to follow it can be quite reasonable (in the

aforementioned sense). Equally, to be dogmatic vis-à-vis things one knows or truly

believes may be a good epistemic strategy even though we cannot reasonably be ex-

pected to follow it unexceptionably. One may thus well share Unger’s intuitions about

the imagined experiences and what would be a reasonable response to them without

necessarily having to grant that dogmatism with respect to (say) the proposition that

one is an embodied brain is an epistemically inadmissable attitude.13

We turn to premise (i) now, which prima facie seems no less problematic than

premise (ii). After all, can’t one be certain of a proposition at one point in time,

only to become uncertain of it at a later point in time, for instance because of new

evidence one obtains, or because one has had second thoughts about the reasoning

on which one had become certain of the proposition, or because doubts have arisen

about the trustworthiness of one’s informant? In addition to this one may wonder

why we couldn’t be certain of a proposition and still consider experience or infor-

mation as being relevant to its truth or falsity.14 In fact, it appears so platitudinous

to assert that being certain of something does not commit or compel one to being

certain of it forever after, that some very strong philosophical argument would be

required to convince us of the opposite. And Unger has disappointingly little to offer

in this regard. In arguing for (i), he falls back on his point that “certain” is among

the absolute adjectives, which he contrasts with relative adjectives, that is, adjectives

denoting matters of degree. According to him, “a necessary condition for the correct

application of an absolute adjective is, at least generally, that certain things denoted

by relative adjectives be entirely absent” (47). One thing that (he contends) must be

entirely absent for someone to be properly called certain of something is “any open-

ness on the part of the man to consider new experience or information as seriously

relevant to the truth . . . of the thing” (ibid.; italics omitted). But even granting what

is required for an absolute adjective to apply correctly, it would be question-begging

12The relevant notion of belief here is that of categorical belief. Given a graded notion of belief, as

supposed by Bayesian epistemology for instance (see below in the text), one could believe a proposition—

to some degree—and reasonably doubt it—to some degree—at the same time.13Another response to Unger’s argument would be to note that his point is that it would not be all right

to disregard the kind of experiences he described should they occur to one, but that nothing he says

implies or even suggests that it would not be all right to discount the possibility that such experiences

will ever occur to one. Grant him that if we should reckon with that possibility, then it would be bad

to be dogmatic, because that might make us disregard certain experiences that, pretheoretically, should

be given their due. It would then still seem that if the possibility is merely an academic one, the risk we

incur by being dogmatic is one we can rightfully dispense with. And since Unger’s examples of sequences

of experiences that are supposed to make it reasonable to doubt certain given propositions are all of a

quite bizarre, or at least fantastical, sort, we find nothing in Unger’s paper that could convince us that

the said possibility is of a more than merely academic variety.14See for criticisms of premise (i) along these lines, Dicker [1974] and Carrier [1983].

8

to assume, without further argument, that this kind of openness is, or even must be,

absent in the case of certainty. Yet this is what Unger does.

But some might want to note that premise (i) is tenable, at least against a certain,

not at all uncommon, type of opponent. For on the currently popular Bayesian epis-

temology it does hold true that certainty implies dogmatism in the intended sense.

On this epistemology, to be certain of a proposition means to assign probability 1

to it. And if a Bayesian agent does assign probability 1 to a proposition, then, given

that she updates her beliefs by means of Bayes’ rule, she will assign probability 1 to

that proposition ever after.15,16 In other terms, becoming certain about a proposition

compels the Bayesian to be certain about it forevermore. As to the question why she

couldn’t regard evidence as being relevant to a proposition she is certain of, it is im-

portant to note that according to the Bayesianϕ is evidentially relevant toψ precisely

if Pr(ψ | ϕ) ≠ Pr(ψ). So if Pr(ψ) = 1, then there can be no proposition evidentially

relevant to ψ, for it is a simple consequence of the probability calculus that, in that

case, Pr(ψ | ϕ) = 1, too, for all propositions ϕ (or, if Pr(ϕ) = 0, Pr(ψ | ϕ) is un-

defined, in which case it does not hold that Pr(ψ | ϕ) ≠ Pr(ψ) either).17 Thus if, as

a Bayesian, one is certain about a given proposition, one cannot consider any infor-

mation as being possibly relevant to the truth or falsity of that proposition, simply

because, for purely mathematical reasons, there cannot exist such information.

However, the foregoing is unavailing in making Unger’s argument for skepticism

have force at least against one type of philosopher. For Bayesianism is not an episte-

mology in the traditional sense of the word and, in particular, is not concerned with

knowledge, or the possibility thereof, but rather with coherent degrees of belief. As

a result, no skeptical argument is capable of jeopardizing this position.

We conclude that Unger has succeeded in making plausible neither premise (1)

nor premise (2). So at present there is no reason to believe that his argument for

skepticism really poses a threat to the possibility of knowledge.18

References

Alston, W. [1985] “Concepts of Epistemic Justification,” Monist 68:57–89.

Alston, W. [2005] Beyond “Justification”, Ithaca NY: Cornell University Press.

Armstrong, D. [2006] “The Scope and Limits of Human Knowledge,” Australasian

Journal of Philosophy 84:159–166.

15Someone updates by means of Bayes’ rule precisely if she sets her new probability for ϕ after she

has come to know ψ, often written as Prψ(ϕ), equal to her earlier conditional probability for ϕ given

ψ, or Pr(ϕ | ψ), for all propositions ϕ and ψ (provided Pr(ψ) ≠ 0; otherwise Pr(ϕ | ψ) is undefined).

The following way of rewriting Pr(ϕ | ψ) makes it particularly easy to see that if Pr(ϕ) equals 1, then

so does Prψ(ϕ):

Pr(ϕ | ψ) =Pr(ϕ ∧ψ)

Pr(ψ)=

Pr(ϕ)Pr(ψ |ϕ)

Pr(ψ)=

Pr(ϕ)Pr(ψ |ϕ)

Pr(ϕ)Pr(ψ |ϕ)+ Pr(¬ϕ)Pr(ψ | ¬ϕ)=

Pr(ϕ)

Pr(ϕ)+Pr(ψ|¬ϕ)Pr(ψ|ϕ) Pr(¬ϕ)

.

For if Pr(ϕ) = 1, and hence Pr(¬ϕ) = 0, the last fraction reduces to Pr(ϕ)/Pr(ϕ).16It is worth mentioning that Williamson [1998] and Douven [1999] present probabilistic update rules

that allow an agent to assign a probability less than 1 to propositions to which she earlier assigned

probability 1. But neither of these rules is part of standard Bayesian epistemology.17See note 15 for an explanation.18We are grateful to an anonymous referee for helpful comments on an earlier version of this paper.

9

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