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Two Kinds of Stakes

Alex Worsnip

Forthcoming in Pacific Philosophical Quarterly; please cite published version

Abstract: I distinguish two different kinds of practical stakes associated with

propositions. The W-stakes (world) track what is at stake with respect to whether the

proposition is true or false. The A-stakes (attitude) track what is at stake with respect

to whether an agent believes or relies on the proposition. This poses a dilemma for

those who claim that whether a proposition is known can depend on the stakes

associated with it. Only the W-stakes reading of this view preserves intuitions about

knowledge-attributions, but only the A-stakes reading preserves the putative link

between knowledge and practical reasoning that has motivated it.

Recently, the intuitive notion of the practical stakes has been put to serious work in epistemology by

subject-sensitive invariantists.1 Unlike contextualists about knowledge, subject-sensitive invariantists claim

that the truth-conditions for ‘S knows that P’ are invariant across contexts of utterance. However,

unlike both contextualists and classical invariantists, they claim that the epistemic standards which a

subject has to meet in order to qualify as having knowledge (even holding the semantic value of

‘knowledge’ constant) vary according to what is practically at stake for that subject.

In this paper, I claim that the idea of the stakes as it is employed in SSI admits of two

readings. On the first reading, we hold a potential doxastic attitude of the subject constant and

measure the costs of the target proposition of her would-be belief being true versus being false. On

the second reading, we hold a potential truth-value of the proposition constant and measure the

costs of relying on the proposition versus withholding. As it turns out, only the first reading tracks

intuitive knowledge-attributions, whereas only the second reading preserves the putative link

between knowledge and practical reasoning that SSI-ists have used to motivate their view.

Furthermore, the two kinds of stakes can come apart from each other. This yields a dilemma for

SSI-ists, which all existing versions of the view are subject to: either give up the claim to vindicate

intuitions about knowledge-attribution, or give up the putative connection between knowledge and

practical reasoning. If there is any potential version of SSI that escapes this dilemma, it will be a

highly nonstandard, and so far undefended, variant.

1. Distinguishing two kinds of stakes

Subject-sensitive invariantism (SSI) is often motivated by appeal to pairs of cases where the stakes

with respect to some proposition differ radically, but the evidence for it remains the same. Jason

Stanley (2005: 3-4) presents two ‘bank cases’ (adapted from DeRose [1992]), whereby Hannah and

Sarah are passing a bank, and have a check to deposit. The lines are long, and they consider coming

back the following day, which is a Saturday. The question is whether Hannah knows that the bank

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will be open the following day, a proposition for which she has the same good but not indefeasible

evidence in both cases. In the first case (call it BANK 1), nothing much is at stake, and Hannah is

said to know that the bank will be open the following day. In the second case (call it BANK 2), it is

very important that Hannah and Sarah are able to make the deposit by the end of the weekend, and

Hannah is said not to know that the bank will be open. The subject-sensitive invariantist posits an

explanation for the difference in verdict: the high stakes in BANK 2 prevent Hannah from knowing.

According to the SSI-ist, what prevents Hannah knowing in the high-stakes case is that were

she wrong, the costs would be high. But this is not a straightforward claim to interpret as it might

seem. In BANK 2, Hannah faces the following matrix of outcomes:

Hannah’s action

Come back on Sat Wait in line today

State of

the world

The bank is open on Sat (i) success (ii) success (with mild inconvenience)

The bank is closed on Sat (iii) disaster (iv) success (with mild inconvenience)

Table 1: BANK 2, outcome of action matrix

When we are told that there is a high cost in BANK 2 to Hannah’s ‘being wrong’, we are

presumably supposed to be thinking of outcome (iii). So when SSI-ists talk of the costs of ‘being

wrong’, they mean the cost of Hannah relying on her belief that the bank is open on Saturday, and

the belief turning out to be false. Nothing seriously bad happens merely because Hannah believes that

the bank is open on Saturday, as long as she does not rely on this belief.2

So let us use the notion of ‘reliant belief’ to mark the kind of belief that is at issue here.

Someone reliantly believes some proposition p iff she is willing to rely on it in her reasoning in the

circumstances.3 And we will say that someone withholds with regard to that proposition only if she

is not willing to rely on it in her reasoning in the circumstances. We can safely discount the

possibility that the subject reliantly disbelieves the proposition – that is, reliantly believes its negation –

on the assumption that this is not among the options when (by the subject’s lights) the evidence for

the proposition outweighs the evidence for its negation.4

So now we can formulate our matrix in terms of Hannah’s attitudes rather than her actions.

Letting o be the proposition that the bank is open on Saturday, BS(p) signify that S reliantly believes

p, and WHS(p) signify that S withholds with respect to p:

Hannah’s attitude

BH(o) WHH(o)

State of

the world

o (i) success (ii) success (with mild inconvenience)

¬o (iii) disaster (iv) success (with mild inconvenience)

Table 2: BANK 2, outcome of attitude matrix

SSI-ists claim that the bad result in outcome (iii) explains the putative fact that Hannah does not

know that o in BANK 2. However, in order to talk of these bad results as being ‘costs of Hannah

being wrong’, there has to be an implicit contrast with some possible outcome in which Hannah is

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not wrong, and these bad results do not obtain. And there are two candidate outcomes to provide

this contrast: (i) and (iv). In (i), Hannah is not wrong because, while her attitude remains the same

(compared with state (iii)), the state of the world changes (from state (iii)) to match her attitude. In

(iv), Hannah is not wrong because, which the state of the world remains the same, she avoids

committing to the attitude that fails to match it.

The contrast between (iii) and (iv) reflects how much it matters, under a fixed potential state

of the world,5 what Hannah’s attitude is. The contrast between (iii) and (i) reflects how much it matters,

under a fixed potential attitude of Hannah’s, how the world turns out. Let’s call the stakes determined by

the first contrast – where the world changes but Hannah’s attitude remains constant – W-stakes, and

the stakes determined by the second contrast – where the attitude changes but the (external) world

remains constant – A-stakes. (We will see in the next section that more needs to be said to fully

characterize these notions.) Put most simply, the W-stakes are the stakes as to whether a proposition

p obtains, whereas the A-stakes are the stakes as to whether the subject reliantly believes or

withholds from p. Talking of the ‘costs of being wrong’ does not, on its own, make it clear which of

the two we are talking about.

Now, in BANK 2, the costs are significant whichever way you measure them. (iii) is a

disaster compared either with either (i) or (iv). The question that then arises is whether it is the high

W-stakes or the high A-stakes that is supplying the putative explanation of our verdict that Hannah

does not know. This is not a merely theoretical question, however, for it is possible for the two

kinds of stakes to come apart.

Consider the simplest kind of case: one where it really matters to you whether p, but nothing

much turns on whether you reliantly believe p. For example, you might be waiting to hear about

some job that you really want to get, and the result will be announced today. Suppose your evidence

that you’ll get the job is pretty good. If you fail to get the job, you will be penniless and unhappy. If

you get the job, your life will be wonderful. But the interview is over, and you have no further

capacity to affect the outcome; moreover, you’re not facing any major planning decisions which

need to be made before discovering the result. Letting j be the proposition that you’ll get the job,

you face the following matrix:

Your attitude

BH(j) WHH(j)

State of

the world

j (i) eternal happiness (ii) eternal happiness

¬j (iii) eternal pain (iv) eternal pain

Table 3: JOB, outcome of attitude matrix

The W-stakes are high: it matters a lot whether you get the job. But the A-stakes are low: it really

doesn’t matter what your attitude is.

Since the W-stakes and A-stakes come apart here, we see that a W-stakes version of SSI and

an A-stakes version can potentially yield contradictory verdicts about whether a subject knows a

proposition, given the right evidential position for the subject. If it’s W-stakes that matter, then

some good but moderate amount of evidence will not be enough to count you as knowing in JOB,

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simply because it matters so much to you whether you get the job. If it’s A-stakes that matter, then

the same amount of evidence might well be enough to count you as knowing, because you risk

nothing in reliantly believing that you will get the job. Consequently, when the SSI-ist says that

knowledge depends upon the stakes, she must choose between saying that knowledge depends upon

the W-stakes or A-stakes.

2. Generalizing the distinction

More generally, let’s designate the possible world-attitude combinations with respect to any

proposition as follows:

Subject’s attitude

BS(p) WHS(p)

State of

the world

p (i) (ii)

¬p (iii) (iv)

Table 4: Generic outcome of attitude matrix

Let CS(x/y) designate the costs for a subject S of x, as opposed to y, obtaining. So, for example,

CS(iii/i) picks out the costs that occur in outcome (iii) but not in outcome (i), including any benefits

that occur in (i) but not (iii), which can be thought of as a kind of ‘opportunity cost’ of (iii). Then,

the W-stakes stakes interpretation of ‘the costs of the subject being wrong’ is: CS(iii/i). The A-

stakes interpretation is: CS(iii/iv).

However, the costs of the subject being wrong may not exhaust the stakes. This point is

clearer in the case of A-stakes, so we will start there. The A-stakes reflect the costs of reliantly

believing a proposition versus withholding from it. So far, we have focused on the two states where

¬p obtains. The only reason for this is that we have so far been focusing on the potential costs of

the subject being wrong. But, as Mark Schroeder (2012: 277-79) has pointed out, the rationality of

relying on some proposition can be affected not only by the costs that would arise were the

proposition to be false and one to rely on it, but also by the costs that would arise were the

proposition to be true and one to fail to rely on it. These latter sorts of costs come from fixing on

state (ii), and then comparing it with state (i).

In general, if a potential cost of relying on a belief makes one less rational in relying on it,

then a potential cost of failing to rely on a belief surely makes one more rational in relying on it.

Consequently, what we want – if we are to construct a notion of A-stakes whereby, the higher the

A-stakes, the higher the epistemic standards one must meet in order to be rational in relying on a

proposition – is to subtract this second category of cost from the first.6 In other words,

A-stakes = CS(iii/iv) – CS(ii/i)

We now have the possibility of ‘negative’ A-stakes: these will be cases where certain kinds of costs

make it more rational to rely on a proposition than if there were no significant potential costs at all. It

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might be tempting to say that what matters to whether it is rational to rely on a proposition is only

whether the A-stakes are positive or negative: that no situation with positive A-stakes can count as a

‘low’ stakes context in the relevant sense. However, this would be a mistake. For the measure of the

stakes itself says nothing about the strength of your evidence for the proposition under

consideration. The A-stakes set the epistemic bar for how good one’s evidence for p has to be in order

for it to be rational to rely on the proposition at hand. One’s evidence does not affect where this bar

is: rather, it affects whether one meets the bar. And there will be many situations where the stakes are

positive, but still low enough to make it rational to rely on the proposition at hand given the strength

of one’s evidence.

It could be argued that, just as we need to complicate our characterization of A-stakes to

reflect cases (i) and (ii), we likewise need to complicate our characterization of W-stakes to reflect

cases (ii) and (iv). The proposal for a parallel complication of the W-stakes would have it that the W-

stakes are not just CS(iii/i) but rather,

W-stakes = CS(iii/i) - CS(ii/iv)

I will not get into the question of whether this complication is a good move for a W-stakes theorist,

except to note that the case for it is perhaps less cut-and-dried than it was for the parallel

complication of the A-stakes. The important point for our purposes is that even with our widened

characterizations of A-stakes and W-stakes, the two still come apart in cases like JOB. Recall the

matrix for this case:

Your attitude

BH(j) WHH(j)

State of

the world

j (i) eternal happiness (ii) eternal happiness

¬j (iii) eternal pain (iv) eternal pain

Table 3 redux: JOB, outcome of attitude matrix

The A-stakes here are low: CS(iii/iv) is zero, CS(ii/i) is zero, and so CS(iii/iv) – CS(ii/i) is also

zero. The W-stakes, however are high: CS(iii/i) is a large positive number, but CS(ii/iv), however, is

an equally large negative number, since (ii) is a much better outcome than (iv). Since subtracting a

negative number from a positive total makes that positive total higher, subtracting CS(ii/iv) from

CS(iii/i) leaves us with an even larger positive number than we started with. So, the W-stakes are

high, even on our new characterization. So the need to complicate our account of A-stakes (and

perhaps W-stakes) does not affect the fact that they can come apart.

3. Pressures toward a W-stakes account

Is it W-stakes or A-stakes that SSI-ists mean to appeal to? It is not clear. In this section, I will

present some considerations which exert pressure on SSI-ists toward a W-stakes account (and, thus,

away from an A-stakes account). In the following section, I will present some considerations which

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exert pressure on SSI-ists toward an A-stakes account (and, thus, away from a W-stakes account). In

both cases, the considerations are to be found in the work of SSI-ists, presented in favor of adopting

an SSI account of knowledge. So considering each will help us work up to the eventual dilemma that

I want to pose for SSI-ists.

Many SSI-ists, most notably Jason Stanley,7 think that intuitions about cases, such as the

bank cases, help to motivate their account. But, as I have suggested, to the extent that there is an

intuitive difference between knowledge-verdicts in the bank cases, it remains an open question

whether this difference is driven by the shift in W-stakes or the shift in A-stakes, since the bank

cases just happen to keep the W-stakes and the A-stakes together. It is useful, then, to consider cases

like JOB, where the W-stakes and A-stakes come apart.

In such cases, I suggest, it is highly counterintuitive to say (for example) that the low A-

stakes help you to know that you will get the job. After all, the very fact that it matters a lot to you

whether you get the job, it seems, would make you extremely reluctant to self-ascribe knowledge,

even if your evidential position is quite strong, and even though nothing hangs on whether you

believe that you will get the job. The mere fact that you are powerless to affect the outcome in JOB

does not seem to help you out here: powerlessness does not help to secure knowledge. Moreover, it

is very natural to describe JOB as a ‘high-stakes’ situation in the ordinary sense. So to the extent that

SSI feeds off this ordinary sense of ‘stakes’, it again seems to favor a W-stakes account.

It also seems that in a case like JOB you would be very reluctant to flat-out assert that you

will get the job, again even if your evidential position is quite strong. This is relevant because SSI-ists

sometimes try to motivate their view by claiming – with numerous other philosophers – that

knowledge is the epistemic norm of assertion.8 But in that case, if it’s A-stakes that make a

difference to knowledge, then it should be OK to assert that you know you’ll get the job. This does

not seem right. After all, why would questions of the costs of her relying on a proposition affect

whether she was warranted in asserting it? The costs of her asserting it might, but this is yet another

different view, and not one that seems helpful to the SSI-ist.9

The comparative intuitions can be brought into even sharper focus by considering a third

bank case to complement the first two, similar to one described by Schroeder (2012: 278). In this

case, BANK 3, it’s already Saturday, and Hannah suddenly realizes that she has a check that she

needs to deposit by the end of the weekend. Now, however, Hannah’s options are more constrained

than they are in the first two cases: she does not have the ‘safe’ option of waiting in line on Friday.

The only thing for it is to go to the bank and hope that it’s open. With respect to the proposition

that the bank is open that day, the W-stakes are high, since she really needs to make the deposit. But,

as in JOB, the A-stakes are low, since Hannah does not risk anything by reliantly believing that the

bank is open here. If the bank is closed, after all, it makes no difference what her attitude is: she’s in

deep trouble either way.

We can think of BANK 2 and BANK 3 as a kind of minimal pair, where we vary the A-

stakes (high in BANK 2, low in BANK 3), while keeping the W-stakes high. This helps us to see

whether, intuitively speaking, the change in A-stakes makes for a difference to whether a subject has

knowledge. I suggest that it does not: pre-theoretically, it seems no better to say that Hannah knows

in BANK 3 than in BANK 2.10 Again, what Hannah experiences in BANK 3, but not in BANK 2, is

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a kind of powerlessness: if the bank isn’t open, there’s nothing she can do about it. Hannah’s

powerlessness does not incline me to attribute knowledge to her. Likewise, it would seem bizarre

and inappropriate for Hannah to flat-out assert that the bank is open in BANK 3, as she and Sarah

drive to the bank, presumably in a state of extreme anxiousness and panic. The only case in which it

seems more OK for Hannah to make a confident assertion is BANK 1, where the W-stakes are low.

All of this suggests that an A-stakes account seriously undermines the intuitive basis for SSI,

which creates pressure for the SSI-ist to go for the W-stakes interpretation. Of course, this is not to

say that it is definitely the W-stakes that is driving our unwillingness to attribute knowledge in cases

like JOB and BANK 3: there are numerous other competing explanations, of both contextualist and

classical invariantist kinds, some of which can explain the indirect relevance of stakes to the truth-

values of knowledge attributions under certain conditions.11 Moreover, some empirical work

questions whether changing stakes really do affect intuitions about knowledge-attributions.12 Indeed,

this empirical work may dovetail nicely with some of the competing explanations, which do not

make precisely identical predictions to a W-stakes version of SSI, but rather offer a combination of

vindication of intuitions in the nearby area and debunking of particular intuitive predictions that are

unique to SSI.

However, regardless of all this, what does seem clear is that an A-stakes account gets the

intuitive predictions wrong in an important range of cases. Whilst not all SSI-ists follow Stanley in

using intuitive cases to motivate SSI,13 it is nevertheless surely still evidence against the A-stakes

theory that it issues unintuitive results, not just about cases, but about the general capacity of

powerlessness to issue in knowledge. This creates pressure for the SSI-ist to adopt a W-stakes

account. If one prefers to adopt an A-stakes account, one cannot rely on the intuitive predictions

that only the W-stakes account makes.

4. Pressures toward an A-stakes account

On the other hand, however, SSI-ists have also stressed that there is an intimate connection between

knowledge and practical reasoning. Specifically, they think that whether a proposition can be relied

upon by a subject as a premise in practical reasoning can depend on whether the subject knows it. In

fact, SSI-ists have tried to use this connection between knowledge and practical reasoning as an

argument for SSI.14 For whether a proposition can be relied on as a premise in practical reasoning

seems, fairly uncontroversially, to depend on what is at stake. And so if there is the appropriate sort

of tie between knowledge and practical reasoning, this suggests that knowledge varies with the stakes

too.

However, it is the A-stakes, not the W-stakes, that practical reasoning follows, as the

discussion in section 2 implicitly shows. For whether it is warranted to rely on a proposition in

practical reasoning (holding evidence constant) surely depends at least in part on the potential costs

and benefits that one risks by relying on it. But this is just not tracked by the W-stakes. The W-

stakes do not compare the costs of relying and withholding; they track how important the truth of

the proposition is to the subject. The question of whether a subject is rational to rely on a

proposition, however, is a question which presupposes that she has two options: relying on it and

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withholding from it. To take her doxastic attitude as given, and then to measure how important it is

to the subject whether the proposition at hand obtains, would just be to answer the wrong question

when it comes to whether she is rational to rely on the proposition.

Now, it might be objected here that this presupposes an account of what makes it rational to

rely on a proposition which the SSI-ist would not accept.15 Here I have been presuming a broadly

decision-theoretic account of what makes it rational to rely on a proposition, where this is fixed by

the potential costs and benefits of doing so,16 together with the strength of one’s evidential position

with respect to the proposition.17 Given such an account, it is obvious that it is the A-stakes, not the

W-stakes, which track what it is rational to rely on, since only the A-stakes track the costs and

benefits of reliance versus withholding.

But perhaps the SSI-ist could reject this picture of what makes it rational to rely on a

proposition, and in doing so preserve a connection between knowledge and practical reasoning

whilst sticking with a W-stakes account. Note that, since the W-stakes do not even incorporate the

costs and benefits of reliance versus withholding, the resulting account of when is rational to rely on

a proposition will have to depart from the decision-theoretical conception very radically in saying

that the costs and benefits of relying on versus withholding from a proposition make no difference

to whether it is rational to do so. But perhaps the SSI-ist is willing to bite that bullet.18

The most obvious way for the SSI-ist to do this is to embrace a ‘knowledge-first’ view of the

norm for practical reasoning and say that what makes it the case that you are rational to rely on p is

simply that you know p. She can then simply deny that whether it’s rational to rely on p has anything

to do with the costs and benefits of doing so. The problem with this, however, is that it will then no

longer be the case the knowledge-practical reasoning link commits one to SSI. The argument from

one to the other goes something like this:

(1) Knowledge-Practical Reasoning. S knows p only if S is rational to rely on p

(2) Practical Reasoning-Stakes. S is rational to rely on p only if the stakes are adequately low

So,

(3) Knowledge-Stakes. S knows p only if the stakes are adequately low.

Now, however, it is unclear what motivates the second premise, Practical Reasoning-Stakes. If

whether it is rational to rely on p has nothing to do with the costs and benefits of doing so, why

accept that what it is rational to rely on is connected with stakes? Someone with this view could just

be a classical invariantist, holding that knowledge is tied to practical reasoning, but denying that the

stakes make a difference either to what it is rational to rely on or to knowledge. It seems to me that

Practical Reasoning-Stakes gets its independent appeal from the decision-theoretic model of what

it is rational to rely on; once that is taken away, there is no reason independent of a prior

commitment to SSI to accept it. So the argument to SSI is undercut.

Remember that the reason we have made all these maneuvers on the SSI-ist’s behalf,

rejecting the decision-theoretic view of what it is rational to rely on, is to see whether it is possible to

save a W-stakes account which nevertheless preserves the link between knowledge and practical

reasoning. For that to be correct, we would have to say that the W-stakes track what it is rational to

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rely on. But there is no reason independent of a prior commitment to SSI to think that this should

be the case. By contrast, there is a lot to say about why the A-stakes might make a difference to what

it is rational to rely on – in fact, this just straightforwardly falls out of any picture of what it is

rational to rely on that even partially invokes the decision-theoretic picture. So, I suggest that if the

SSI-ist wants to preserve the link between knowledge and practical reasoning, and especially to use

that link to argue for SSI, she is pressured towards an A-stakes account.

SSI’s concordance with a knowledge-practical reasoning link is supposed to be a major

advantage for it over contextualism.19 For a contextualist, it can be right for the subject to rely in

practical reasoning on things which she does not know (at some attributer’s context). However, we

can now see that this is also true of a W-stakes version of SSI. For if knowledge is tied to W-stakes,

then since W-stakes are not tied to norms for practical reasoning, knowledge cannot be tied to

practical reasoning. So W-stakes SSI-ists must give up the knowledge-practical reasoning link, losing

their purported advantage over contextualists. Those who want to preserve a link between

knowledge and practical reasoning have to go for an A-stakes account.

5. Brief interlude: forced reliance cases

This puts us in a position to throw some light on an existing dispute within the literature on SSI.

Recall BANK 3, where it is already Saturday and Hannah just has to hope that the bank is open.

Some similar cases have been raised in the literature, as putative counterexamples to the claim that a

subject may only rely on that which she knows. The idea is that in such a case, the subject intuitively

lacks knowledge of a proposition, but is simply forced by circumstances to rely on that proposition

anyway. So, for example, Hannah is forced to rely on the proposition that the bank is open – and we

can see that she does so by seeing that she does indeed drive to the bank. The standard SSI-ist reply

to this is to argue that in such cases, the subject relies on a probabilistic premise rather than an

unqualified prediction.20 They deny that Hannah is warranted in relying on the unqualified

proposition that the bank is open, and correspondingly deny that she knows that it is open.

Fortunately, however, the proposition that it is probably open suffices to rationalize her action of

driving there.

But our framework helps us to see that even granting this last point, this reply fails to help.

For the case is still a low A-stakes case, even with respect to the unqualified proposition. Indeed, its

matrix is similar to that of JOB. Letting, once again, o be the proposition that the bank is open:

Hannah’s attitude

BH(o) WHH(o)

State of

the world

o (i) success (ii) success

¬o (iii) failure (iv) failure

Table 5: BANK 3, outcome of attitude matrix

Note that we have granted Hawthorne & Stanley’s point by conceding that in case (ii), where

Hannah withholds from o, she still manages to make the deposit, due to her ability to ‘fall back’ on

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the proposition that the bank is probably open. Still, even with respect to the unqualified

proposition o, it is a low A-stakes case: Hannah risks nothing by relying on the all-out, unqualified,

proposition that the bank is open. So it’s unclear what motivates the claim that she isn’t rational to

rely on the unqualified proposition. Indeed, it also suffices to rationalize Hannah’s action in BANK

1 that she knows that the bank is probably open, yet SSI-ists do not claim that this means we should

deny that she is warranted in relying on her unqualified belief in that context.

It isn’t enough for the SSI-ist to simply insist that Hannah knows the unqualified

proposition in BANK 1 but not in BANK 3, and that this is what makes the difference. For, since

this SSI-ist is defending a connection between knowledge and practical reasoning, she needs an A-

stakes rather than a W-stakes account – as I argued in the previous section. And the A-stakes are

low in both BANK 1 and BANK 3. So the account does not predict a difference in knowledge-

verdicts between the two.

6. The dilemma for SSI-ists

We are now in a position to state the dilemma for SSI-ists. When we examine what kinds of stakes

actually govern practical reasoning, we find that it is the A-stakes that matter. A-stakes versions of

SSI, however, yield highly counterintuitive verdicts about knowledge-attributions, and allow

powerlessness to help to secure knowledge. W-stakes accounts, on the other hand, handle the

intuitions about knowledge-attributions nicely. But the W-stakes have nothing to do with norms for

practical reasoning, and so W-stakes accounts will not link knowledge to practical reasoning. SSI-ists,

then, have a dilemma: give up the connection between knowledge and practical reasoning, or give up

an account which handles the intuitions about knowledge-attributions (and warranted assertion).

Interestingly, the dilemma also poses a problem – though a slightly different one – for Brian

Weatherson’s (2005) version of SSI on which high stakes prevent Hannah from even counting as

believing that the bank will be open in high-stakes cases. This is supposed to be the case because, in

high-stakes cases, the subject does not rely on the proposition, and so (on a certain picture of belief,

where belief is essentially tied to what one is relying on) does not count as believing it. But in cases

like JOB and BANK 3, where the A-stakes are low, there is every reason to think that Hannah does

meet this particular condition for belief: there is no obvious way in which she is not relying on the

bank being open. Consequently, if the SSI-ist is to avoid attributing knowledge in such cases, she

must do the explanatory work in terms of the justification condition for knowledge, not the belief

condition.21

7. A hybrid account?

The SSI-ist might now try to say that in some way, both kinds of stakes matter. In order for this to

be a helpful response to the dilemma, it would have to both save the intuitions that drive us towards

W-stakes and preserve the knowledge-practical reasoning link that drives us towards A-stakes. Is this

possible?

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A first way to interpret the suggestion is as a denial that the W-stakes and A-stakes are really

independent: perhaps they are just two aspects of a general notion of the stakes simpliciter.22 On this

proposal, what matters for knowledge is whether the stakes are high, and both the W-stakes and the

A-stakes contribute to whether the stakes are high.

The problem here is that the W-stakes and the A-stakes really do seem to be measuring

distinct things which do not amalgamate. To see this, let us draw a contrast. I might ask you the

following question: “what are the costs of having a child?” You might, quite naturally, say that there

are different sorts of costs involved: financial costs, emotional costs, opportunity costs in terms of

forgone pleasures, and so on. But it would be quite natural to say that all of these costs contribute

together toward the costs of having a child. The more financial cost, the more the overall cost; the

more emotional cost, the more the overall cost, and so on. Each kind of cost is still a cost of having a

child; they are costs with respect to the same thing.

The distinction that I have drawn between the different kinds of stakes not like this,

however. Rather, the two kinds of stakes measure the stakes with respect to different things.

Crudely, the W-stakes measure what is at stake with respect to whether a proposition that you might

or might not rely on is true or false, whereas the A-stakes measure what is at stake with respect to

whether or not you rely on a proposition that might be true or false. Unlike the different kinds of

costs in having a child, then, we should not expect them to amalgamate. In the child case, the

different kinds of costs are each costs with respect to the same thing: having a child. There is

nothing, however, to play the role of the single thing with respect to which the stakes simpliciter (as

some amalgam of W-stakes and A-stakes) are high or low.

That said, this does not rule out the possibility that the W-stakes and A-stakes both

independently contribute to whether a subject has knowledge of a proposition. How could this

proposal be developed? Usually SSI-ists have thought that for any proposition p, the epistemic

standards S must meet to know p systematically vary with the stakes. Specifically, they usually claim

that the higher the stakes, the higher the standards. Stanley (2005: 92), for example, writes that to

have knowledge, “the subject must have evidence that reduces the probability of the negation of this

proposition to a sufficiently low level, where what is sufficiently low is determined by the costs of

being wrong.” If we are to say that both kinds of stakes matter, then this needs to be changed. After

all, as we have seen, the two kinds of stakes can come apart, so it simply can’t be that for both kinds

of stakes, low stakes entail low standards for knowledge and high stakes entail high standards for

knowledge.

One proposal would be that both the W-stakes and A-stakes need to be high for the

standards for knowledge to be high. This proposal, however, would generate all the same intuitive

problems that the A-stakes account generated, by allowing powerlessness to make knowledge easier,

however important the truth of the proposition at hand. The more plausible proposal, I take it, is

that if either kind of stakes are high, the standards for knowledge are high. That allows us to say that

the subject does not know in JOB and BANK 3, since the W-stakes are high in those cases. So it

avoids the horn of the dilemma that the A-stakes account suffered from. What about the other horn

of the dilemma: having to abandon the knowledge-action link?

12

Here things depends on the precise nature of the knowledge-action link which we are trying

to save: in particular, on what direction the conditional runs in. John Hawthorne and Jason Stanley

(2008: 577) endorse the following claim:23

Necessity. S may rely on a proposition p in practical reasoning only if S knows p.

However, as already observed, what S may rely on in practical reasoning depends on the A-stakes,

and not on the W-stakes. So, in a case like JOB or BANK 3, where the A-stakes are low with respect

to some proposition p, S may rely on p even though the W-stakes are high. But then, by Necessity,

S must also know p. Yet our hybrid account predicts that S does not know p in this case. So

Necessity and the hybrid account are inconsistent. To preserve Necessity, an SSI-ist must opt for

a pure A-stakes account, and accept the bad intuitive results that come with it.

Jeremy Fantl and Matthew McGrath (2002: 78, 2009: 49), however, only endorse a

conditional running in the opposite direction:

Sufficiency. S may rely on a proposition p in practical reasoning if S knows p.24

Sufficiency allows the SSI-ist to avoid the bad intuitive results in cases like JOB and BANK 3, since

even though one is permitted to rely on the proposition at hand in these cases, Sufficiency does not

entail that the subject thereby knows that proposition. By the same token, it avoids contradicting the

hybrid account’s predictions about these cases. So it looks like a hybrid account may allow us to

preserve Sufficiency.

It’s tempting to say that, by the same token, an A-stakes version of SSI which only embraces

Sufficiency might be able to escape our dilemma. After all, as we have seen, Sufficiency does not

on its own commit us to the bad intuitive results that we get in JOB and BANK 3. This kind of A-

stakes theorist would have to deny that low A-stakes always make knowledge easier, but they could

still hold that high A-stakes are enough to prevent knowledge. And this modification would make

sense in light of the direction in which Sufficiency runs.

However, the natural question for this kind of A-stakes theorist is: what explains why the

subject doesn’t know in (say) BANK 3? It isn’t the stakes, since this theorist says that A-stakes are all

that matters, and the A-stakes are low. And it isn’t a lack of evidence, since the subject has the same

evidence in BANK 1, where Hannah is said to know that the bank is open. So this theorist seems

forced to posit a mysterious further necessary condition for knowledge, neither evidential nor

stakes-related, which has to be present in BANK 1 but not BANK 3. This is a very unattractive

result. The obvious thing for the SSI-ist to say about what makes the difference between BANK 1

and BANK 3 is that the W-stakes are high in BANK 3. So it seems that we are forced back into

accepting the hybrid account: the pure A-stakes account conjoined with Sufficiency is not good

enough.

8. Going forward

13

To date, SSI-ists have not distinguished the two kinds of stakes. Much of the appeal of the position

may come from a lack of clarity about which account of stakes is being adopted, which allows the

view to appear to do more than it can. The primary aim of this paper has been to introduce the

distinction between the two kinds of stakes, and to persuade SSI-ists that they need to take account

of it in formulating and arguing for their views. In addition, I have argued that the distinction throws

up a dilemma for almost every existing version of SSI: they cannot both vindicate intuitions about

knowledge and warranted assertion on one hand, and preserve the link between knowledge and

practical reasoning which they have used to motivate their position on the other. A-stakes accounts

fail to do the former, whilst W-stakes accounts fail to do the latter.

The only version of SSI which may be able to escape the dilemma is one which involves

embracing the ‘hybrid account’ – where both kinds of stakes matter – along with Sufficiency, but

not Necessity. This position, however, is so far both unarticulated in any detail, and undefended. If

the hybrid account is true, then there is not just one phenomenon at work in connecting knowledge

to practical stakes, but two; and the two phenomena are quite heterogeneous. SSI-ists would have to

make out the case for this hybrid position for it to be compelling, and this is work that is yet to be

done. Meanwhile, the vulnerability of simpler SSI positions to the dilemma I have posed may make

the whole view less attractive in the broader debate between contextualists, SSI-ists and classical

invariantists.

The distinction between W-stakes and A-stakes, as we’ve seen, creates real problems for

subject-sensitive invariantism. But it may also be of wider significance. One by-product of my

argument, for example, is that whilst norms for practical reasoning follow the A-stakes, norms for

assertion do not seem to do so; if they follow any kind of stakes, it is the W-stakes. This suggests

that norms for assertion and practical reasoning differ importantly, and moreover that knowledge

cannot be biconditionally linked to both.25 So, I hope, the distinction between W-stakes and A-

stakes may be capable to illuminating future debates not just about knowledge, but also about

assertion, practical reasoning, and any other areas in which stakes are thought to be of fundamental

importance.26

Department of Philosophy

Yale University

NOTES

1 See, esp. Fantl & McGrath (2002, 2009), Hawthorne (2004), and Stanley (2005). Two interesting newer versions

of similar ideas come from Schroeder (2012) and Weatherson (2005, 2011, 2012). Hawthorne and Schroeder are

more equivocal about their endorsements of SSI than the other authors cited here. Some of these writers prefer

the terms ‘interest-relative invariantism’ or ‘pragmatic encroachment account’ to ‘subject-sensitive invariantism’. I

use the latter purely for convenience to cover all such accounts. 2 Some dispositionalist theories of belief may collapse these possibilities. For a sampling of dispositionalist

accounts, see Stalnaker (1984), Schwitzgebel (2002), Weatherson (2005), Fantl & McGrath (2009: Ch. 5) and Ross

& Schroeder (2012).

14

3 Some SSI-ists (Fantl & McGrath 2002) prefer to talk of subjects ‘acting as if p’ rather than ‘relying on p’. I use the

latter formulation to have one account to work with, but the central thrust of my objections could be recast for a

version SSI framed in the former. 4 Thanks to Mike Ridge for pointing this out to me. Here I differ with Schroeder (2012), who measures the costs

of relying on p versus relying on not-p, rather than, as I do, the costs of relying on p versus withholding. For the

reason just given, I do not think the case of relying on not-p needs to be considered. By contrast, Schroeder treats

the case of withholding derivatively, attempting to get reasons for withholding out of situations where relying

either on p or on not-p is costly. I do not think this works: there can be situations where the costs of relying on

not-p extend to withholding from p, and so do not speak in favor of withholding whatsoever. 5 It is worth stressing that the state of the world we hold constant need not be the actual state of the world; indeed,

in the bank cases, we are standardly told that the bank is in fact open. However, we have been asked by the SSI-ist

to focus on the costs of Hannah being wrong. This focuses us on case (iii), and on the A-stakes reading we want to

then hold the state of the world constant and vary Hannah’s attitude, taking us to case (iv). But this is not to say

that cases (i) and (ii) are unimportant; in the next section, I will make clear how they can come into the picture for

the A-stakes too. 6 It is, admittedly, a little unnatural to label the resulting net figure as representing the ‘stakes’, since it allows high

potential costs of certain kinds (those that are subtracted) to ‘lower’ the stakes. (This may be part of what leads

Weatherson (2011: 592-93), who prefers a quasi-decision-theoretic model of SSI related to what I am labeling as

the ‘A-stakes’ model, to claim that it is ‘odds’, not ‘stakes’, that matter.) If all this jars with the intuitive notion of

the ‘stakes’ that SSI-ists meant to draw on, this just feeds into the dilemma that I will eventually be presenting in

section 6. 7 See Stanley 2005: v-vii, 12-13. 8 E.g. Hawthorne 2004: 23. 9 It might now be objected that assertion is just a special case of action, so norms for assertion can’t come apart

from norms for practical reasoning. (Thanks to Keith DeRose here.) But the question of what it is proper to assert

is distinct from the question of what it is proper to rely on in reasoning about what to assert, even if assertion is a

special case of action. See Brown (2012: 130-134) for further discussion of this point. 10 Schroeder (2012) appears to dispute this, so to test my suggestion, Jonathan Phillips and I ran an experimental

study where we presented subjects with pairs of bank cases and asked questions involving whether Hannah knows

that the bank is open. Our findings confirmed my suggestion: we found a statistically significant difference in

verdicts between Bank 1 and Bank 3, but no statistically significant difference in verdicts between Bank 2 and Bank

3. In other words, ordinary subjects without theoretical commitments judge Bank 3 in line with Bank 2 rather than

Bank 1; to the extent that stakes do drive their intuitions about knowledge, it is the W-stakes and not the A-stakes

that do so. 11 For a contextualist explanation, see esp. DeRose (2009: Chs. 6-7). For classical invariantist explanations, see esp.

Williamson (2005) and Nagel (2008). 12 See Feltz & Zarpertine 2010; May et al. 2010. See Weatherson 2011: 595-598 for a response to these charges. 13 See, e.g., Weatherson (2011: 595) and Fantl & McGrath (2009: Ch. 7) 14 See, e.g., Hawthorne 2004: 179; Fantl & McGrath 2009: 26-27. 15 I thank an anonymous referee for this suggestion. 16 Of course, this leaves open how these costs and benefits are to be understood. They need not be exhausted by

self-interested considerations of the deciding agent; they could include, for example, moral costs and benefits. 17 The latter factor is relevant on the decision-theoretic framework because it ought to play a role in fixing one’s

credence for p. This is required in order to arrive at an estimate of the expected value of relying on p versus

withholding from p, which requires consideration of both case where p obtains and that where not-p obtains,

weighted according to the probability of each case.

15

18 In fact, the anonymous referee suggested that she will have to reject it anyway, since it would open her up to a

simpler and more obvious problem, namely that if what it is rational to rely on depends on the costs and benefits

of doing so, then it is rational to rely on anything whenever one’s attitude does not matter, and that commits the

SSI-ist to saying that we can know anything that doesn’t matter. In fact, a similar objection has actually been made

against SSI, by Jonathan Schaffer (2006). However, there are two points which mitigate it. First, the SSI-ist could

modify the decision-theoretic picture without jettisoning it entirely, for example by claiming that there is at least

some minimum bar for the epistemic position you need to be in with respect to p to be rational in relying on p,

regardless of the expected value of doing so. (This modified picture of what it is rational to rely on would still,

however, not be tracked by W-stakes as long as it had a strong decision-theoretic component.) Second, as

discussed in section 7 below, not all SSI-ists accept that you are rational to rely on p only if you know p – many

accept only the reverse conditional. In that case, your being rational to rely on p does not imply that you know p,

so the SSI-ist can avoid the bad result. So, I do not think it is obvious that the SSI-ist must reject the decision-

theoretic picture from the start. 19 See Hawthorne 2004: 85-91. 20 See Hawthorne & Stanley 2008: 581-2. 21 Weatherson, incidentally, no longer believes that everything can be explained in terms of the belief condition; see

Weatherson 2012: § 3. 22 Thanks to an anonymous referee for this suggestion. 23 Hawthorne & Stanley also endorse the opposite direction, but I want to consider this direction for now, and treat

the other direction separately. 24 Fantl & McGrath do, however, endorse some related biconditional principles, which may themselves be more

vulnerable to the dilemma I have presented. See Fantl & McGrath 2009: 123, 175. 25 Brown (2012) argues against the various would-be motivations for keeping norms for assertion and norms for

practical reasoning together, but does not give a positive argument that they come apart. My argument on this

score can thus be seen as complementing hers by providing this positive argument. 26 For helpful comments, suggestions, and discussion, I am indebted to Patrick Butlin, Julianne Chung, Keith

DeRose, Tamar Gendler, Josh Knobe, Stephanie Leary, Robin McKenna, Jonathan Phillips, John Pittard, Mike

Ridge, Raul Saucedo, Zoltán Szabó, Jonathan Vertanen, Bruno Whittle, Crispin Wright, and an extremely helpful

anonymous referee for Pacific Philosophical Quarterly.

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