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AN OBVIOUS-BASED ACCOUNT OF EPISTEMIC POSSIBILITY
Chris Tweedt
Concessive knowledge attributions (CKAs) are statements of the form: ‘I know that
p, but possibly q’, where q obviously entails not-p. ‘Possibly’ here expresses epistemic
possibility. But what is epistemic possibility? There are different accounts, and these
different accounts deliver different verdicts about whether or not CKAs are contradictory.
Jason Stanley (2005) argues that on the standard version of epistemic possibility—a
version based on knowledge—CKAs are contradictory. Dougherty and Rysiew (2009)
propose two non-standard accounts of epistemic possibility—each of which is based on
evidence—to argue that some CKAs are not contradictory. In this paper, I will first disagree
with Stanley and side with Dougherty and Rysiew by holding that some CKAs are not
contradictory. (Section 1) I will then give some (what I consider to be serious) problems for
Dougherty and Rysiew’s non-standard accounts. (Sections 2 & 3) After listing some
desiderata an account of epistemic possibility must meet to avoid the criticisms I’ve given
of Dougherty and Rysiew’s account (section 4), I’ll give an account—an account based on
obviousness—that parallels Stanley’s account, meets the desiderata from section 4,
overcomes the problems with Dougherty and Rysiew’s accounts, and allows some CKAs to
be true. (Section 5)
1 Stanley and Dougherty and Rysiew on CKAs
Concessive knowledge attributions seem to follow from a fallibilist view about
knowledge. That is, if I’m a fallibilist about knowledge, then I should be willing to embrace
the truth of this kind of statement:
I know Harry is a zebra, but Harry might be a painted mule.
Jason Stanley denies that fallibilists need to accept the truth of CKAs. Stanley (2005) uses
the standard account of epistemic possibility—an account based on knowledge—to argue
that concessive knowledge attributions are contradictory. Here’s his account.
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(EPk) q is epistemically possible for S iff what S knows does not entail, in a manner
that is obvious to S, not-q.1
If EPk is the correct account of epistemic possibility, then, necessarily, CKAs are
contradictory.2 Here’s the argument. Suppose for a reductio that a CKA is true for S. That is,
suppose that S knows p, that q is epistemically possible for S, and that q entails, in a manner
that is obvious to S, not-p. Since S knows p and q is epistemically possible for S, according
to EPk, p does not entail, in a manner that is obvious to S, not-q. But we supposed for a
reductio that q does entail, in a manner that is obvious to S, not-p. By contraposition,3 p
does entail, in a manner that is obvious to S, not-q. Contradiction. So, CKAs are false. And
they are contradictory, since the argument applies for all possible CKAs.
Stanley follows David Lewis (1996) in holding that CKAs are contradictory. One
reason to think so is that they sound odd: “If you are a contented fallibilist, I implore you to
be honest, be naïve, hear it afresh. ‘He knows, yet he has not eliminated all possibilities of
error.’ Even if you’ve numbed your ears, doesn’t this overt, explicit fallibilism still sound
wrong?”4 However, even when I hear CKAs afresh, some of them (even if only a few) don’t
sound wrong. Here are some examples:
1. “Of course it’s possible that oil prices will fall dramatically over the next month,
but we all know that that’s not going to happen.”5
2. “We now know that there is a top quark: we have presented considerable
evidence indicating its existence. Of course, our experiments are not conclusive, and
there is a chance that our results will be overturned. We are confident, however,
that they will be borne out.”6
3. A referee suggests making a small point explicit, and then says, “I know no one
will get confused about this, but it’s possible someone will.”7
4. “I know I have hands, even though it’s possible I’m a handless brain in a vat.”8
1Stanley
(2005), 128.
at least CKAs where the subject that knows p and the subject for whom p is epistemically possible are the
same subject. Stanley argues that CKAs in which the subject is different are still contradictory if the
knowledge norm of assertion is true.
3We have to be able to do contraposition on an obvious entailment for Stanley’s argument to work.
4Lewis (1996), 550.
5Dougherty and Rysiew (2009), 130, Rysiew (2001), 497.
6
Dougherty and Rysiew (2009), 130-131.
7Dodd (2008).
2Or
3
There is disagreement about these cases,9 but they sound felicitous to many of us.
Although I agree with Doughterty and Rysiew in holding that some CKAs are true and
felicitous, I will later give problems for their accounts of epistemic possibility. If I can offer
an account of epistemic possibility that has the result that some CKAs are not
contradictory, that account is—to those whose ears are like mine, Dougherty’s, and
Rysiew’s—preferable. Dougherty and Rysiew (2009) offer two such accounts. Their
accounts of epistemic possibility—both based on evidence—show that CKAs need not be
contradictory.
(EPevA) q is epistemically possible for S iff not-q isn’t entailed by S’s evidence.
(EPevB) q is epistemically possible for S iff q has non-zero probability on S’s total
evidence.10
If EPevA is the correct account of epistemic possibility, CKAs are not necessarily
contradictory. Suppose S knows p, and suppose q is epistemically possible for S. q
obviously entails ~p. There will be a contradiction only if S’s evidence E for p entails either
p or ~q. But it is possible that E does not entail p or ~q; it is possible that p is
underdetermined by S’s evidence but still known by S. So, CKAs are not necessarily
contradictory.
Similarly, if EPevB is the correct account of epistemic possibility, CKAs are not
necessarily contradictory. Here’s a case: suppose S knows p and p has a .99 epistemic
probability on S’s total evidence. Suppose q—and so ~p—has a .01 probability on S’s total
evidence. EPevB holds and a CKA is true for S.
There are problems, though, with both of Dougherty and Rysiew’s definitions of
epistemic possibility. I will object to both EPevA and EPevB, then I’ll propose an account of
epistemic possibility that both escapes the criticisms I offer of Dougherty and Rysiew’s
accounts and shows some CKAs to be true.
2 Problems with EPevA
8Dodd
(2008).
discussion, Dodd (2009) argues that the above examples don’t show that CKAs are sometimes true (sec.
6). Dougherty and Rysiew (2010) reply (I think successfully) in secs. 3 & 4. Hawthorne (2012) also argues
that CKAs are contradictory even if sometimes felicitous in non-core uses of the relevant terms.
10Dougherty and Rysiew (2009), 127. The definition was amended to “non-zero” from “non-negligible” in
Dougherty and Rysiew (2010).
9For
4
There are only a few arguments against EPevA in the literature. I will give what I
consider to be the strongest of these, then I will give a new argument against EPevA. Here’s
EPevA again:
(EPevA) q is epistemically possible for S iff not-q isn’t entailed by S’s evidence.
Clayton Littlejohn (2011) argues that EPevA cannot support the fallibilist
desideratum that it is possible for S that S does not have hands. To do this, Littlejohn first
argues that some beliefs in our evidence set are non-inferentially justified. Suppose S’s
belief that she has hands is non-inferentially justified. Also, suppose the following plausible
principle is true.
(IJSE) If S is non-inferentially justified in believing p, p is part of S’s evidence.
So, that S has hands is an item of her evidence. Let q be <S does not have hands>. Is it
epistemically possible for S that q? Only if not-<S does not have hands> is not entailed by
her evidence: that she has hands. But of course <S has hands> entails its double negation.
So, EPevA does not support the platitude that we might not have hands.
Littlejohn’s argument can be construed as an inconsistent set of premises.
1. <S has hands> is non-inferentially justified.
2. (IJSE) If S is non-inferentially justified in believing p, p is part of S’s evidence.
3. (EPevA) p is epistemically possible for S iff ~p isn’t entailed by S’s evidence.
4. not-<S has hands> is epistemically possible for S.
Littlejohn’s critique works for any item of evidence for which S is non-inferentially
justified but for which S says its negation is epistemically possible. Any proposition that fits
this description can be inserted into the brackets in the inconsistent set of premises above.
For example, <my senses report to me that I am being appeared to redly>, <it is .9 probable
that my senses report to me that I am being appeared to redly>, etc. If CKAs are true for S
and EPevA is true, no non-inferentially justified item of evidence can entail the target
proposition. That’s bad, especially in cases where the item of evidence is identical to the
target proposition.
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Here’s another problem for EPevA. Suppose I have contradictory evidence. That is,
suppose my evidence set contains p and not-p, and I’m not sure which one I should believe.
Are both p and not-p possible? According to EPevA, neither is possible, because the
negation of each one is entailed by my evidence.
Arguably, having contradictory evidence is not impossible.11 It actually happens
quite frequently due to compartmentalization. Suppose I believe that chairs exist—every
time I go to the furniture store, for instance. That chairs exist is in my evidence set, since I
use the proposition that chairs exist as evidence for other propositions, like the proposition
that there are a lot of chairs in a particular furniture store. Suppose also that I believe there
are no chairs—every time I am around Trenton Merricks, for instance.12 That there are no
chairs is in my evidence set, since I use the proposition that there are no chairs as evidence
for the proposition that Trenton Merricks cannot sit on a chair. I live life believing, around
Merricks, that there are no chairs, but in the furniture store I believe that there are chairs.
Then I come to the realization that I have been believing contradictory propositions. I
consider: are there chairs? Suppose I think, it’s possible there are chairs, and it’s possible
there are not. If EPevA were true, I would have contradicted myself. But surely I ought to
think: it’s possible there are chairs, and it’s possible there are not.
For a more common example, suppose that Abby goes to a church where there is an
atmosphere that encourages the belief that God exists, and Abby sincerely believes that God
exists when she’s in church. She reasons from the proposition that God exists to
propositions about certain behaviors she ought to display in church. But suppose Abby’s
philosophy professor encourages disbelieving that God exists, and when she’s in class Abby
sincerely believes that God doesn’t exist. She reasons from the proposition that God
doesn’t exist to propositions about certain behaviors she ought to display in class. Later,
Abby thinks on her own: is there a God? She thinks: it’s possible there is a God, and it’s
11Trent
Dougherty has defended the view that it is possible for someone to have false evidence. Dougherty
now waffles between whether there can or cannot be false evidence. For arguments that there can be false
evidence, see Arnold (forthcoming), Rizzieri (2011), Comesana and Kantin (2010), and Fantl & McGrath
(2009). For a response, see Littlejohn (2012). Any doxastic view, I suspect, would have to hold that there can
be false evidence. If there can be false evidence, it seems unlikely that someone cannot have contradictory
evidence. Even if you don’t find it plausible that there can be contradictory evidence, a view of epistemic
possibility should at least be open to the possibility that there can be contradictory evidence.
12Merricks (2003) argues that there are no chairs.
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possible there is not. This seems like the right thing for Abby to think, but it is not if EPevA is
true.
3 Problems with EPevB
Here’s EPevB.
(EPevB) q is epistemically possible for S iff q has non-zero probability on S’s total
evidence.
I’ll raise two problems for EPevB. First, in some cases the probability of q is 0, but q
is still epistemically possible. Take the following thought experiment.
There is a Cartesian plane where -1 ≥ x ≥ 1 and -1 ≥ y ≥ 1. A point in this coordinate
range is selected at random and labeled “X”. After this is completed, again a point in
the coordinate range will be selected at random. An intelligent mathematician is
asked, “What is the probability that the randomly-selected point will be X?”
The mathematician’s answer will be, “0, because there are an infinite number of points in
the probability space.” Consider this plausible exchange: the mathematician’s interlocutor
then objects: “I’m not asking about mathematical probability; I’m asking about epistemic
probability,” to which the mathematician replies, “Yes, I know. In this case, however, there
is no difference for me between the mathematical and epistemic probability of X being
randomly selected.”13
Arguably, the mathematician could truthfully commit himself to the following:
1. I know the randomly-selected point will not be X, and the probability for me of X
being selected is 0.
2. I know the randomly-selected point will not be X, but it is possible X will be selected.
13I
have in mind David Lewis’ New Principle in his 1994. C(A/HT) = P(A/T), where C is a rational credence
function, A is some proposition (in my example, that X will be the selected point), T is the complete theory of
chance for the world, and H is the history of the world up until the time the calculation is done. If, as I have
stated, HT and T are equal for the mathematician, then the mathematician’s credence that A equals the
probability that A.
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So, that q is epistemically possible for S does not entail that q has a non-zero probability on
S’s total evidence.
The proponent of EPevB may deny that I’m certain I’m not mistaken about the setup
of experiment. But I am sure that I’ve set up the experiment correctly and that the
mathematician would say the probability of a being the randomly-selected point is 0 given
the thought experiment. The experiment is simple, and it is an a priori thought experiment.
Even if the setup were not certain to me, it would be difficult to deny that the setup is
certain to someone—the intelligent mathematician, for example.
Here’s a similar example: Suppose ‘alpha’ is the proper name of the actual world.
What’s the probability that alpha is the actual world? The probability is 0; there are an
infinite number of possible worlds.14 However, it certainly is possible that this world is the
actual one. Indeed, is the actual one.
Objection: there are infinitesimal probabilities.15 Reply: then modify the example so
that the mathematician is betting on how probable an infinite sequence of heads is. The
mathematician correctly thinks the probability is 0,16 but it’s epistemically possible that
there is an infinite sequence of heads.
The second problem for EPevB has to do with the vexed notion of epistemic
probability when it comes apart from logical probability. EPevB explicitly relies on
epistemic probability to inform us whether or not a proposition is epistemically possible
for a subject. What is epistemic probability? What axioms does it satisfy? Epistemic
probability does not satisfy the Kolmogorov axioms, according to which the probability of a
tautology is 1. It is a desirable result for any account of epistemic possibility that it is
epistemically possible for a rational subject that a tautology is false, i.e. in cases where the
subject isn’t certain that a proposition is true even when that proposition is a tautology. But
according to EPevB, if it is epistemically possible for a subject that a tautology is false, the
epistemic probability of the tautology for the subject is less than 1. If the probability of a
tautology for a subject is less than 1, then a dutch book can be made against that subject.
14See,
for example, Peter van Inwagen (1996), 224. Dougherty questions the standard view. He finds it
intuitive that anything metaphysically possible has a non-zero probability. Dougherty (mss, “An Evidentialist
Conception of Epistemic Possibility”), 7.
15[Blind] and [Blind] independently raised this objection. See David Lewis (1986), 333.
16Timothy Williamson (2007) argues that an infinite sequence of heads has probability 0.
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Any view of probability should prevent dutch books from being made against those who
have rational credences in propositions. If EPevB is correct, then dutch books can be made
against rational agents for whom it is epistemically possible that a tautology is false. This is
a bad result. It would be better to have an account of epistemic possibility that does not
rely on a view of epistemic probability that departs significantly from any informative
account of probability.17
4 Desiderata for an account of epistemic possibility
Before giving the new account, I should say what desiderata this account of
epistemic possibility must meet to avoid the problems with EPevA and EPevB. First, the
account should allow q to be epistemically possible for S even if S is non-inferentially
justified in believing p. Second, the account of epistemic possibility should allow q to be
epistemically possible for S even if S’s evidence contains both p and not-p. Third, the
account should allow for the possibility that q is epistemically possible for S independent of
the probability of q on S’s total evidence. If q has probability 0 or .5 or 1 on S’s total
evidence, an account of epistemic possibility should be flexible enough to allow q to be
epistemically possible for S. Last, it should allow for metaphysically impossible
propositions (e.g. the negations of tautologies) to be epistemically possible for S. That is, an
account of epistemic possibility should allow that the falsity of Goldbach’s Conjecture be
epistemically possible for S. Also, the account should allow for this without appealing to an
uninformative notion of probability.
5 An obvious-based account of epistemic possibility
The account I propose should meet all the above desiderata. In this section I’ll give,
explain, and motivate the account, then I’ll show that the account meets the above
desiderata.
Here’s the account:
(EPobv) q is epistemically possible for S iff not-q is not obvious to S.
17Huemer
(2007) argues against the informativeness of Dougherty and Rysiew’s account of epistemic
probability. I have added to Huemer’s objection the bit about dutch books.
9
First I’ll say something about what it is to be obvious. No epistemologists have, to
my knowledge, offered an analysis of what it is to be obvious, but the idea is clear enough
for many epistemologists to leave the concept unanalyzed in their definitions. For example,
the definition of CKAs requires that an entailment be obvious:
(CKAs) I know that p, but possibly q, where q obviously entails not-p.
Jason Stanley’s EPk also requires that an entailment be obvious:
(EPk) q is epistemically possible for S iff what S knows does not, in a manner obvious
to S, entail ~q.18
Clayton Littlejohn’s definition of epistemic possibility also requires an obvious entailment:
(EPc) S’s assertion ‘It is possible that p’ is true iff (1) no member of the contextually
determined group knows for certain something that entails ~p in a way that is
obvious, and (2) there is no relevant way that members of the group remedy this.19
Michael Huemer’s definition of epistemic possibility also contains unanalyzed obviousness.
For Huemer, if q is epistemically possible for S, then S does not have justification for ~q
adequate for dismissing q.20 And having justification for q requires obviousness:
“S has justification for believing that P, if S justifiedly believes some proposition Q,
such that if S were to consider, using S’s actual logical abilities, whether Q supports
P, it would be obvious to S that Q supports P.”21
I will follow Stanley’s, Littlejohn’s, and Huemer’s lead in not providing an analysis of
obviousness in the definition of EPobv. Instead, I will, too, rely on the preanalytical clarity
the concept is supposed to have.
However, I should mention that an important difference between obviousness and
subjective certainty (and the reason I don’t propose an account based on subjective
certainty) is that obviousness is factive and subjective certainty is not.22 For example, if an
entailment is obvious, then the entailment holds, and if it’s obvious to me that p, then p is
true. If obviousness were not factive and epistemic necessity and possibility are duals (I
18Stanley
(2005), 128.
(2011), 615.
20Huemer (2007), 129.
21Huemer (2007), 131.
22I do not propose an account based on objective certainty, since objective certainty is a property only selfevident propositions can have, but 1) propositions that are not self-evident can be epistemically necessary
and 2) the negations of self-evident propositions can be epistemically possible.
19Littlejohn
10
think they are), then given EPobv, epistemic necessity would not be factive. But epistemic
necessity is factive.23 So, obviousness is factive. Any non-factive uses of ‘obvious’ and its
cognates are found in exactly the same kinds of examples where ‘knows’ and its cognates
are used non-factively, e.g. “But I knew John Kerry was going to win the 2004 United States
presidential election!”24
EPobv allows for some CKAs to be true. In fact, CKAs very often are true if EPobv is
true. According to EPobv, CKAs are true for S in all the cases where S knows p but p is not
obvious to S. I take it as a datum that someone can know a proposition without that
proposition being obvious to her. Suppose there is such a case: S knows p, but p is not
obvious to S. This is case compatible with not-p not being obvious to S either. So, S knows p,
but it’s not obvious to S that p, and it’s not obvious to S that not-p. Is a CKA true for S? If it
is, then it is epistemically possible for S that q, and q entails, in a manner that is obvious to
S, not-p. According to EPobv, the epistemic possibility expressed by the CKA entails that
not-p is not obvious to S. But according to the above case, that not-p is not obvious to S is
compatible with S knowing p. In fact, if obviousness is closed under obvious entailment,
EPobv is equivalent to this variation on Stanley’s account of epistemic possibility:
(EPobv’) q is epistemically possible for S iff what is obvious to S does not obviously
entail ~q
Stanley used EPk to argue that if q is epistemically possible for S, then S cannot know p. I
have used the above variation to argue that if q is epistemically possible for S, then p
cannot be obvious to S.
EPobv meets all four desiderata above. First, EPobv is compatible with it being the
case that q is epistemically possible for S even if S is non-inferentially justified in believing
p. Even if I am non-inferentially justified in believing p, so long as p is not obvious to me,
not-q (like not-p) may not be obvious to me. Just as S’s knowing p is compatible with it not
being obvious to S that p and it not being obvious to S that not-p, S’s being non-inferentially
justified in believing p is compatible with it not being obvious to S that p and it not being
23See
24I
Hawthorne (2004), 28.
got this example from [blind], but similar examples are found in Hazlett (forthcoming).
11
obvious to S that not-p.25 Second, EPobv allows q to be epistemically possible for S even if
S’s evidence contains both p and not-p. That is, it is compatible with EPobv that if S has
contradictory evidence, then it is not obvious to her that p and it is not obvious to her that
not-p. According to EPobv, if is not obvious to S that p and it is not obvious to S that not-p,
then not-p—and thus q—are epistemically possible for S. Third, EPobv allows for q to be
epistemically possible for S independent of the probability of q on S’s total evidence. For
example, in the above example the probability that the randomly-selected point is X is 0,
but this is compatible with it not being obvious to the mathematician that X not be
randomly selected. Last, EPobv is compatible with metaphysically impossible propositions
(e.g. Goldbach’s conjecture is false) being epistemically possible for S. Any time the
negation of a metaphysically impossible proposition is not obvious to a subject, the
metaphysically impossible proposition is epistemically possible for that subject.26 It is,
then, compatible with EPobv that the falsity of Goldbach’s Conjecture be epistemically
possible for S. Further, EPobv allows for the falsity of Goldbach’s Conjecture to be
epistemically possible for S without appealing to an appeal to an uninformative notion of
probability.
If my proposed definition of epistemic possibility is correct, CKAs are true in those
cases in which I know a proposition that is not obvious to me. And if (pace Stanley but with
Dougherty and Rysiew) CKAs are expressions of fallibilism, then fallibilism escapes
unscathed from the charge of contradiction.
25Here’s
an objection that EPobv does not meet a desideratum similar to the first desideratum: It is obvious
that I have hands, but the skeptic’s scenario still seems to be epistemically possible. I have two ways out. First,
we could, like G. E. Moore (1959), deny that if it is obvious that we have hands, then skeptical scenarios are
epistemically possible. If skeptical scenarios are epistemically possible, then it is no longer obvious that we do
have hands. It is a fallibilist desideratum for a view that it allow that it is epistemically possible that I am a
handless BIV given that I know I have hands, but it’s harder to see why it would be a desideratum of a view
that it allow that it is epistemically possible that I am a handless BIV given that it is obvious to me that I have
hands. Second, if the first reply is unconvincing, we can distinguish prima facie obviousness from ultima facie
obviousness. The modified view would then be that q is epistemically possible just in case it’s not ultima facie
obvious to S that ~q.
26
Similarly, Michael Huemer (2007) holds that some metaphysically impossible propositions are not
obviously impossible, so they are still epistemically possible.
12
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