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Jacob Ross and Mark Schroeder
University of Southern California
May 30, 2011
Belief, Credence, and Pragmatic Encroachment
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This paper compares two alternative explanations of pragmatic encroachment on knowledge (i.e., the claim
that whether an agent knows that p can depend on pragmatic factors). After reviewing the evidence for
such pragmatic encroachment, we ask how it is best explained, assuming it obtains. Several authors have
recently argued that the best explanation is provided by a particular account of belief, which we call
pragmatic credal reductivism. On this view, what it is for an agent to believe a proposition is for her
credence in this proposition to be above a certain threshold, a threshold that varies depending on pragmatic
factors. We show that while this account of belief can provide an elegant explanation of pragmatic
encroachment on knowledge, it is not alone in doing so, for an alternative account of belief, which we call
the reasoning disposition account, can do so as well. And the latter account, we argue, is far more plausible
than pragmatic credal reductivism, since it accords far better with a number of claims about belief that are
very hard to deny.
Recently, a quandary has arisen in the literature on pragmatic encroachment. On the one hand, it has been
forcefully argued that there is pragmatic encroachment on knowledge, or in other words that whether an agent
knows that p can depend on pragmatic factors such as the costs of acting as if it were true that p when it is
not true. And it has been argued that the best way to explain pragmatic encroachment on knowledge is by
assuming that pragmatic factors affect justified belief. On the other hand, it is widely held that there is no
pragmatic encroachment on justified degrees of belief, or levels of confidence, as the latter, it is maintained,
should be strictly apportioned to the evidence.
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But this creates a problem. How can pragmatic factors
affect whether we are justified in believing a proposition (as opposed to disbelieving it or withholding
judgment concerning it) without affecting the degree of belief or level of confidence that we are justified in
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Thanks to Lara Buchak, Shieva Kleinschmidt, Julia Staffel, Brian Weatherson, Ralph Wedgwood, Jonathan Weisberg,
Matthew McGrath, an audience at Northwestern University, participants in the 2011 Formal Epistemology Workshop, and
participants in Jake Ross’s spring 2011 graduate seminar, for helpful discussion and/or comments.
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For a dissenting opinion, however, see Stanley [2005], esp. pp. 88-89.
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having in it? In other words, how can pragmatic factors affect our justification for outright belief without
affecting our justification for degrees of belief?
A number of authors, including Brian Weatherson [2005], Dorit Ganson [2008], and on a natural
reading, Jeremy Fantl and Matthew McGrath [2010], have proposed a solution to this problem.
According to their proposal, believing a proposition simply consists in having a sufficiently high level of
confidence in it, but the level of confidence one must have in a proposition to count as believing it depends
on pragmatic factors. On this view, pragmatic factors can affect whether an agent is justified in believing a
proposition, not by affecting what level of confidence she is justified in having in it, but rather by affecting
whether the agent’s having this level of justified confidence is sufficient, under the circumstances, for the
agent to count as believing the proposition. We will call this view Pragmatic Credal Reductivism (PCR)—
‘credal reductivism’ because it understands beliefs in terms of credences or levels of confidence, and
‘pragmatic’ because it implies that the level of confidence that an agent must have in a given proposition to
count as believing it depends on pragmatic factors.
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In this paper, we will argue against PCR, and we will propose an alternative explanation of the data
it was meant to explain. The paper consists of two main parts. In the first, we set out two alternative
accounts of belief: the pragmatic credal reductivist account, and an alternative account that we call the
reasoning disposition account. We show how each of these accounts can explain the possibility of pragmatic
encroachment on knowledge. We then argue, in the second part, that there is strong reason to prefer the
reasoning disposition account of belief. We do so by presenting four claims that we take to be central to
our ordinary notion of belief, and arguing that the reasoning disposition account helps to explain the truth
of each of these claims, whereas PCR conflicts with each of them.
1. Two Explanations of Pragmatic Encroachment
In the first two sections of part 1, we review some reasons for holding that there is pragmatic encroachment
on knowledge, and we show how PCR can explain such pragmatic encroachment. And in the remaining
three sections, we present an alternative account of belief, the reasoning disposition account, and we show
how it, too, can explain pragmatic encroachment on knowledge, but in a different way.
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See Fantl and McGrath [2002] for a similar argument.
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1.1 Pragmatic Encroachment and the Knowledge Action Principle
Consider the following pair of cases.
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Low: Five minutes ago, Hannah made three sandwiches and placed them in the refrigerator. She
told Sarah that she placed the peanut butter sandwich on the left, the tuna sandwich in the
middle, and the almond butter sandwich on the right. Hannah then departed just as Sarah’s
friend Almira arrived for lunch. Sarah knows that Almira has no allergies. Almira says: “I’d
love an almond butter sandwich.” And so Sarah opens the refrigerator door, points to the
sandwich on the right, and says: “The sandwich on the right is an almond butter sandwich.
You can have it.”
High: This case is just like Low, except here it is Sarah’s nephew Algernon who is visiting for lunch,
and he has a severe peanut allergy. He asks Sarah for a sandwich. Sarah knows that the
peanut butter sandwich would be fatal to Algernon, but that the almond butter sandwich
would be harmless. She also knows that he would slightly prefer the almond butter sandwich
to the tuna sandwich. When Sarah goes to the fridge, she can tell, by visual inspection, which
is the tuna sandwich, but she cannot tell, by visual inspection, which is the peanut butter
sandwich and which is the almond butter sandwich. So she gives him the tuna sandwich.
Let r be the proposition that the sandwich on the right is the almond butter sandwich. In Low, it seems
appropriate for Sarah to assert that r to Almira, since Sarah knows that r.
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This seems appropriate because
it seems Sarah knows that r on the basis of Hanah’s testimony. In High, however, the situation seems
rather different. Here we are inclined to say that it is appropriate for Sarah to give Algernon the middle
sandwich rather than the sandwich on the right, since she knows that the middle sandwich is the tuna
sandwich, but she doesn’t know that the sandwich on the right is the almond butter sandwich—it might
instead be the fatal peanut butter sandwich. And so, in Low, we are inclined to say that Sarah knows that r,
whereas in High we are inclined to say the opposite. And yet Sarah’s evidence bearing on r appears to be
the same in both cases.
Here’s a natural explanation of the difference between these two cases.
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Similar cases can be found in DeRose [1992], Cohen [1999], Stanley [2005] and Fantl and McGrath [2010].
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Throughout the paper, we will use italicized lower-case letters as schematic sentence letters, and use invisible ‘propositional
quotes’ to turn a sentence into a referring term denoting the proposition expressed by utterances of that sentence. Please note
the invisible propositional quotes wherever appropriate, as in the first appearance of ‘r’ in the main text.
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Knowledge Action Principle: For any agent S and proposition p, if S is in a choice situation in which S
could not rationally act as if p, then S does not know that p (where to act as if p is to act in the
manner that would be rationally optimal on the supposition that p is true).
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In Low, acting as if r (by affirming that r) would be perfectly rational, given Sarah’s strong evidence for r.
By contrast in High, acting as if r (by giving Algernon the sandwich on the right) would be irrational, given
the disastrous consequences of doing so if r is false. Thus, the Knowledge Action Principle is consistent
with Sarah’s knowing that r in Low, but it is inconsistent with her knowing that r in High.
Moreover, even independently of our intuitions about such cases as High and Low, the Knowledge
Action Principle has considerable plausibility. For it is very plausible that if an agent knows that p, then
she could rationally rely on p by reasoning on its basis. And it likewise seems plausible that if an agent can
rationally rely on p in her reasoning, then she can rationally act as if p, since that’s how she would choose to
act were she to reason rationally while relying on p. And so it is very plausible that if an agent knows that p,
then she can rationally act as if p.
We will assume, for the sake of argument, that the Knowledge Action Principle is true, and turn our
attention to the question of how its truth can best be explained.
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One way to explain the Knowledge
Action Principle, as we will see in the next section, is on the basis of PCR.
1.2 How Pragmatic Credal Reductivism can Explain Pragmatic Encroachment
Here’s one possible explanation of the Knowledge Action Principle. In order to know that p, an agent must
be justified in believing that p. But to believe that p is simply to have a sufficiently high credence in p to
count as believing that p under the circumstances. Hence, in order to know that p, one must be justified in
having a sufficiently high credence in p to count as believing that p under the circumstances. Accordingly,
in order to explain the Knowledge Action Principle, all we need is an account of belief on which the
minimum level of credence an agent must have to count as believing that p under given circumstances is at
least as high as the minimum level of credence the agent would need in order for it to be rational for her to
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Similar principles are endorsed in Williamson [1999], Fantl and McGrath [2002] and [2010], Hawthorne [2004], and
Hawthorne and Stanley [2008].
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Note that DeRose [1992] and Cohen [1999], among others, take such cases to instead be explained by the thesis that
knowledge-ascriptions are context-dependent. For an extensive discussion of the relative merits of these two kinds of
explanation, see Stanley [2005].
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act as if p under those circumstances. For, given such an account of belief, it will follow from the above
argument that in order to know that p, one must be justified in having sufficient credence in p to make it
rational for one to act as if p. Hence it will follow that one will know that p only if it is rational for one to
act as if p.
Weatherson [2005], Ganson [2008], and on a natural reading, Fantl and McGrath [2010] each
propose an account of belief that allows for such an explanation of the Knowledge Action Principle.
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And
the accounts they propose all share a common form. To a first approximation, they all maintain that what
it is to believe that p is to have a sufficiently high credence in p to rationalize acting as if p when choosing
among relevant actions under relevant circumstances—where the relevant circumstances and actions
include, but may not be limited to, the agent’s actual circumstances and the actions available therein. Thus,
Ganson [2008] suggests that what is required for “outright believing that p” is that one be “willing to act
as if p in all or most circumstances,” and she adds that “for those circumstances where our degree of belief
isn’t high enough [to rationalize acting as if p], we simply fail to count as believing that p in those
circumstances” (p. 451). Similarly, Fantl and McGrath [2010] propose a conception of belief according to
which “you believe that p iff you have enough credence in p for p to be your motivating reason for -ing, for
all relevant ” (p. 160).
Weatherson proposes a conception of belief that he expresses rather differently, but it amounts to a
view of the same general type. He identifies believing that p with being such that conditionalizing on p
wouldn’t affect one’s conditional preferences over relevant actions. More precisely, on Weatherson’s view,
S believes that p just in case, for any actions and in the appropriate class of actions, and any proposition q
in the appropriate class of propositions, S prefers to conditional on q if and only if S prefers to
conditional on the conjunction of p and q (p. 422). Note however that, given the rationality assumption
that Weatherson makes throughout, this is equivalent to saying that S believes that p just in case S’s
credence in p is sufficiently high to rationalize acting as if p in any circumstance in which S is choosing
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Some of Fantl and McGrath’s remarks look clearly like an endorsement of pragmatic credal reductivism. For instance, they say,
“you believe that p iff you have enough credence in p for p to be your motivating reason for -ing, for all relevant ” (p. 160).
Other remarks, as in their claim that if you believe that p “then you are prepared to put p to work as a basis for what you do,
believe, etc.” (p. 143) look more like glosses on the alternative, reasoning disposition, account that we will offer in this paper,
and in conversation, Matthew McGrath has suggested sympathies with our alternative account.
