Knowledge, Assertion, and Practical Reasoning

KNOWLEDGE, ASSERTION, AND PRACTICAL REASONING

Stewart CohenArizona State University

In his important and illuminating book, Knowledge and Lotteries, JohnHawthorne considers various solutions to an epistemological paradoxregarding lotteries. Hawthorne raises several objections to my own proposalfor resolving the paradox, viz., Contextualism. And he proposes an alter-native solution he calls ‘‘Subject Sensitive Invariantism’’. In what follows, Iwill defend Contextualism against Hawthorne’s objections and argue that itremains superior to his own proposal for resolving the paradox.1

Contextualism and the Lottery Paradox

Suppose Smith has a low-paying job with no prospect for getting ahigher-paying job. He has no investments and no other sources of income.Given his situation, it seems right to say that Smith knows that he’ll neverbe a multi-millionaire. As it turns out, Smith has a ticket in the New YorkState lottery. Should he win, he would become a multi-millionaire. But itseems wrong to say that Smith knows he will lose the lottery. Theseintuitions give rise to a paradox given the very plausible premise that entailsthat Smith knows he will never get rich only if Smith knows he will lose thelottery.

This paradox generalizes in interesting ways. So for example, if Smithrecently left his car in lot 2, it seems right to say that he now knows that hiscar is parked in lot 2. But it seems wrong to say that Smith knows his carhas not been stolen.

For virtually any ordinary proposition P (Smith will never get rich,Smith’s car is parked in lot 2) we think we know, there is some ‘‘lotteryproposition’’ L (e.g., Smith will lose the lottery, Smith’s car has not beenstolen) such that we think both that we don’t know L and that we know

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P only if we know L. This can lead us to adopt a skeptical frame of mindand hold that we do not know P after all. A successful anti-skepticalresolution of this paradox must explain how despite our skeptical intuitions,it remains true that we know what we ordinarily claim to know. But thismeans that a successful resolution of the paradox must explain away ourskeptical intuitions. Otherwise the paradox has not been resolved.

Contextualism is the thesis that ascriptions of knowledge are context-sensitive. A common thread in contextualist theories is that the salience oferror possibilities raises the standards for how strong one’s epistemicposition has to be in order for one to know. Contextualism resolves thelottery paradox by construing our apparently inconsistent intuitions asresulting from contextual shifts in these standards. So, for example, ourintuition that the sentence, ‘‘Smith knows his car is parked in lot 2’’, is trueis explained by the fact that at ordinary contexts, the statement is true. Ourapparently conflicting intuition that the sentence ‘‘Smith does not know hiscar has not been stolen’’ is false, results from our shifting to a strictercontext, when we consider the possibility that Smith’s car has been stolen.At this new context, the sentence is indeed false. But deductive closure forknowledge is preserved relative to a context. So at everyday contexts, both‘‘Smith knows his car is parked in lot 2’’ and ‘‘Smith knows is car has notbeen stolen’’ are true. At stricter contexts, neither sentence is true.

Hawthorne argues that Contextualism is unsatisfactory as a solution tothe paradox because it is unable to preserve the constitutive connectionsthat knowledge bears to both assertion and practical reasoning.

Knowledge and Assertion

Peter Unger has argued that when one asserts P, one represents oneselfas knowing P. Given the (defeasible) norm that one should not representoneself falsely, it follows that one should not assert P when one doesnot know P.2 In that same vein, Timothy Williamson has argued thatthe practice of assertion is constituted by the rule/requirement that oneassert something only if one knows it.3 Following Unger andWilliamson, Hawthorne endorses the principle that one may assert P onlyif one knows P.

Hawthorne argues that Contextualism runs afoul of this connectionbetween knowledge and assertion. Suppose John has recently parked hiscar in lot 2. Suppose further that John is in a low-standards context (cartheft is not being discussed) and someone asks him where his car is. Heasserts that it is in lot 2. If I am in a high-standards context where car theftis being discussed, then according to Contextualism, I can truly say, ‘‘Johndoes not know that his car is parked in lot 2’’. This remains true despite thefact that given John’s own low-standards context (car theft is not salient), he

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can truly say, ‘‘I know my car is parked in lot 2’’. Hawthorne suggests that‘‘given a contextualist profile’’, John has the right to assert that his car isparked in lot 2. Thus we get the odd result that at my high-standardscontext I can truly say ‘‘John may assert that his car is in lot 2 but doesn’tknow that his car is parked in lot 2’’.

Knowledge and Practical Reasoning

Hawthorne also holds that there is a constitutive connection betweenwhat one knows and what one can appeal to in practical reasoning. Inparticular Hawthorne endorses the principle that if S knows p, then S canappeal to p as a premise in practical reasoning. Hawthorne argues that thisprinciple makes trouble for Contextualism.

Suppose I am invited to give the keynote address at the APA and I’m at theairport buying my ticket. The ticket agent offers me flight insurance. I reason

I’m giving the keynote address.So I’ll be at the convention.So I don’t need insurance.

This is uncontroversially bad reasoning. Moreover, we can say truly ‘‘Thatreasoning is bad’’ at any context. But notice that if you are in a typical low-standards context, you can truly say, ‘‘Cohen knows he’s giving the keynoteaddress.’’ But then the following sentence is true at your low-standardscontext:

‘‘Cohen knows he’ll be giving the keynote address, but he should notappeal to that proposition in his practical reasoning’’.

Thus contextualism violates the practical reasoning principle.

The Alternative to Contextualism—Subject Sensitive Invariantism

Given these worries about Contextualism, Hawthorne proposes analternative view he calls ‘‘Subject-Sensitive Invariantism’’. (SSI) Suppose Isay, ‘‘John knows his car is parked in lot 2’’. Then I am the speaker/ascribermaking the ascription and John is the subject of the ascription.

Contextualism says that the truth-value of a knowledge ascription issensitive to whether error possibilities are salient to the ascriber. So if thepossibility that John’s car has been stolen is salient to me, then I speak trulywhen I say, ‘‘John does not know his car is in lot 2’’. This remains true evenif this possibility is not salient to John.

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SSI denies that there is context-sensitivity in the above sense of ascriber/speaker sensitivity. Rather, SSI says that the truth-value of a knowledgeascription is sensitive to whether error possibilities are salient to the subjectof the ascription. On this view, the truth-value of a knowledge ascription isthe same regardless of who is doing the ascribing (thus the name, ‘‘Subject-Sensitive Invariantism’’). So if the possibility of error is salient to John, then‘‘John fails to know his car is in lot 2’’, is true at every ascriber context. So ifwe say ‘‘John knows . . . ’’, because an error possibility is salient to us, wespeak falsely if an error possibility is salient to him. Moreover, if thepossibility of error is salient to us, we might say ‘‘John fails to know . . . ’’.But if it is not salient to him, again we will be speaking falsely.

Hawthorne’s invariantism takes a condition that Contextualism viewsas a kind of speaker-sensitivity for knowledge ascriptions and construes itinstead as a kind of subject-sensitivity—as an element of the subject’scircumstances that affects whether the subject knows. Of course, in itself,subject-sensitivity is a mundane phenomenon. The truth-value of a knowl-edge ascription is sensitive to many features of the subject’s circumstances—whether the proposition is true, whether the subject has evidence, etc.What’s distinctive about Hawthorne’s view is that it includes the salienceof error possibilities as an important feature of the subject’s circumstances.

According to SSI, the lottery paradox results not from shifting ascribercontext, but rather from changes in the subject’s circumstances. So S knowsthat his car is parked in lot 2, provided that the possibility the car has beenstolen is not salient to S. Once that possibility becomes salient to S, he stopsknowing his car is parked in lot 2.

SSI does not allow either the link between knowledge and assertionor the link between knowledge and practical reasoning to be broken. Forthe link between knowledge and assertion to be broken, we need a low-standards context at which S may assert P, and a high-standards ascribercontext at which ‘‘S knows P’’ is false. But SSI denies that ascriber contextcan affect the truth-value of a knowledge ascription.

For the link between knowledge and practical reasoning to be broken,we need a low-standards ascriber context at which ‘‘S knows P’’ is true, eventhough, intuitively, S reasons badly when he appeals to P in his practicalreasoning. But again, if S is in the kind of practical situation we envisioned,he will fail to know because error possibilities will be salient to him. The factthat such error possibilities are not salient to some ascriber is irrelevant.

Contextualist Replies to Hawthorne’s Objections

Suppose Hawthorne is right about the connection between knowledgeand assertion. (I’m not unsympathetic to the point.) Hawthorne shows that


Contextualism is committed to there being contexts at which the sentence‘‘S may assert P, but S does not know P’’ is true.

What can the Contextualist say in response? Recall Unger’s point thatwhen S asserts P, S represents himself as knowing P. Given this point, theassertion principle turns out to be a special case of the principle that oneshould not represent oneself falsely. But how should a contextualist view Sas representing himself when S asserts P? Surely since S is asserting P withinhis particular context, insofar as he is representing himself as knowing P, heis representing himself as knowing P by the standards that govern hisparticular (ascriber) context. This suggests that the contextualist shouldconstrue Unger’s point metalinguistically:

When S asserts P in C, S represents himself as being such that ‘‘S knowsP’’ is true at C.

But if when S asserts P in C, S is representing himself as being such that‘‘S knows P’’ is true at C, then given the underlying rationale for theassertion principle, viz., that one should not represent oneself falsely, itfollows that

S may assert P in C only if ‘‘S knows P’’ is true at C.

So the Contextualist should endorse only this metalinguistic version ofthe assertion principle. But this version of the principle entails that ‘‘S mayassert P, but S does not know P’’ is true at the high-standards context. Andas Hawthorne points out, this ‘‘sounds very odd’’. But now we can see thatthe Contextualist can explain away this counterintuitive result. It soundsodd because of a false inference about what is entailed by ‘‘S may assert P’’when uttered at the high-standards context. Since the speaker is at a high-standards context at which ‘‘S knows P’’ means that ‘‘S knows relative tohigh standards’’, it would be natural to infer from the truth of his utterance‘‘S may assert P but S does not know P’’ that S can represent himself asknowing by high standards but S does not know by high standards. Andthat would be a violation of the principle that one should not representoneself falsely.

But such an inference is mistaken. Recall the contextualist rendering ofUnger’s point, viz., when S asserts P in C, S represents himself as being suchthat ‘‘S knows P’’ is true at C. Given that S himself is in a low-standardscontext, all that follows from the truth at the high-standards context of‘‘S may assert P but S does not know P’’ is that ‘‘S may represent himself asknowing by low standards but S does not know by high standards’’. Andthat surely is unobjectionable.4

Now consider Hawthorne’s objection that Contextualism allows that‘‘S knows P, but S may not appeal to P in his practical reasoning’’ can be

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true at a low-standards context. No metalinguistic maneuver will workagainst this objection because there is no context at which it would bepermissible for S to engage in the kind of practical reasoning Hawthornedescribes.

The first thing to note, by way of reply, is that this objection applies toany view that does not require infallibility for knowledge, not just Contex-tualism. Any fallibilist view (besides SSI) will face this problem, i.e., anyview that allows that S can know P on evidence E, even though Pr (P/E)<1.For such views, we can always devise a bet where the payoff structure makesit rational for S to bet against what he knows. For example, a fallibilist viewwill allow that, having just left my car 10 minutes ago, I know my car isparked in lot 2. Suppose you offer me a bet that pays me one billion dollarsif my car is not parked in lot 2, but costs me a penny if it is parked in lot 2.Even though the probability my car has been stolen in the last 10 minutes issmall, the payoffs are such that it would be irrational for me to decline totake the bet. Despite the fact that I know my car is parked in lot 2, I cannotreason that since my car is parked in lot 2, I will be out a penny if I take thebet. I would be engaging in bad practical reasoning, even though accordingto Fallibilism, I would be reasoning from a premise I know to be true.

All the same, we have seen that SSI does not allow that S can know P,but be unable to appeal to P in his practical reasoning. This would appear togive it an advantage over competing theories.

So how should a contextualist in particular respond? On my particularversion of Contextualism, ‘knowledge’ talk can be viewed as a heuristic forsimplifying reasoning.5 If we had a considerably greater capacity for storingand computing evidential probabilities, we could do all our reasoning byrelying just on the probabilities. But given our actual capacities, we rely onthis rough and ready, imprecise notion of knowledge, and allow as a rule ofthumb, that when you know P, you can appeal to P in reasoning. So to saythat S knows P is to say that the probability of P on his evidence is closeenough to 1 for S to appeal to it in reasoning. This works fine most of thetime, except for those rare cases where the extent to which probability ofP falls short of 1, turns out to matter.

This goes some but not all of the way toward explaining the appeal ofthe practical reasoning principle. For the question remains: Why does theprinciple seem more like an axiom than a rule of thumb?

Here the Contextualist can say that the principle appears to be axiomaticbecause in general, it will be difficult to say things of the form ‘‘S knows P, but Scannot appeal to P in his reasoning’’. When we think about S in those practicalsituations where intuitively he cannot appeal to P, error possibilities will besalient to us. Thus, ‘‘S knows P’’ will be false at our context of ascription. Thiscould account for the apparent axiomatic status of the principle.6

On this way of construing matters, the contextualist will allow that.‘‘Cohen knows P but Cohen can’t appeal to P in practical reasoning’’


remains true at the low-standard context—though as we noted, it will behard to utter. Is this result unacceptable?

Rather than answer this question directly, I will note that SSI has asimilar result. Suppose I know P at t, and at the next instant t0, I will beoffered a bet with a payoff structure that makes it rational to bet against P.According to SSI, ‘‘Cohen knows P at t, but when he reasons at t0, he willnot be appeal to P’’ will be true at any ascriber context. Now Hawthornewill say that this is because according to SSI, I stop knowing P at t0. But thevery fact that I can know P and then stop knowing P, even though Icontinue believing P, P remains true, I get no new evidence against P,the sensitivity or safety of my believing P has not changed, etc., is itselfhighly counterintuitive. So I see no clear intuitive gain for Hawthorne’sview.7

Objections to SSI

Inevitably the conflict between Contextualism and SSI will come downto which view has the greater intuitive costs. And no doubt Contextualismdoes have intuitive costs, despite my best attempts to mitigate them. Butnow I want to look at a serious problem for SSI: It does not meet ourconstraint on a satisfactory resolution of the lottery paradox. Recall thatany non-skeptical response to the paradox must explain the appeal of ourskeptical intuitions. But here is a fact about those intuitions. When we are ina skeptical frame of mind, it seems to us that we have made a discovery, viz.,there are lots of things we think we know (e.g., where our cars are parked),that in fact we do not know. And not only do we have a strong intuitiveinclination to deny that we know, we have the same inclination to deny thatothers know. Moreover, we are inclined to deny that we ourselves knewpreviously.

Contextualism can explain why this is so. Our skeptical frame of mindtracks the fact that we are at a high-standards context. And when we are atsuch a context, those standards will govern not only our self-ascriptions ofknowledge, but our ascriptions to others (and to ours earlier selves) as well.So when we judge that others (along with our previous selves) fail to know,we are actually making true judgments.

But SSI is unable to explain why we make these judgements. Accordingto SSI, when we are in a skeptical frame of mind, we fail to know becauseerror possibilities are salient to us. But this has no implications for whetherothers know. That will depend on whether the chance of error is salient tothem. But we know, even when we are in a skeptical frame of mind, that inmany instances, error possibilities are not salient to others or to ourprevious selves. Yet as we have noted, when we are in a skeptical frame ofmind, we have a strong intuitive inclination to deny that others and our

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previous selves know. But SSI has no explanation for why we are soinclined, given that we know that error possibilities are not necessarilysalient to others and to our previous selves.8 But this is just to say thatSSI does not succeed in explaining our skeptical intuitions, and so has notgiven a satisfactory resolution of the paradox.9

Hawthorne is aware of this problem. To handle it, he appeals to the factthat when we reason, we make use of what psychologists call ‘‘the avail-ability heuristic’’.10 People using this heuristic assess the probability of anevent on the basis of how easy it is to recall or imagine tokens of it. Becausefrequently occurring events are generally more easy to recall or imagine, thisheuristic works well most of the time. But the availability heuristic canintroduce biases when factors unrelated to the frequency of an event facili-tate our recalling or imagining the event. Hawthorne cites studies whichshow that ‘‘ . . .when a certain scenario is made vivid, the perceived risk ofthat scenario may rise dramatically’’ (p. 164). Hawthorne then speculatesthat ‘‘when certain non-knowledge-destroying counter possibilities are madesalient, we overestimate their real danger; as a result, we may find ourselvesinclined to deny knowledge to others in cases where there is in fact no realdanger of error’’.11 So, for example, when I claim to know that I will be atthe conference and the possibility of fatal heart attacks is made salient, Itend to overestimate the probability with which heart attacks occur. Thisleads me to deny (falsely) that anyone knows he or she will not suffer a fatalheart attack and so to deny (falsely) that anyone knows that he or she willbe at the conference.

Does Hawthorne’s explanation succeed? First we should note that thisexplanation, if it succeeds, explains too much. Recall that Hawthorne holdsthat SSI does explain why we correctly deny knowledge to ourselves whenerror possibilities are salient to us. So, according to Hawthorne, the task forSSI is to explain why we incorrectly project our own lack of knowledge ontoothers (and onto our previous selves.). But if the availability heuristic leadsus to overestimate the probability of error when considering whether othersknow, then it should lead us to overestimate the probability of error whenwe consider whether we ourselves know. But if we can explain away ourintuitions that others do not know by appealing to our tendency to over-estimate the probability of error possibilities, then why not explain away ourintuition that we ourselves fail to know in the same way? Why not say that Ido know after all that I will not suffer a fatal heart attack. Moreover, wecould then say that I know that I will be at the meeting, even when thepossibility that I will suffer a fatal heart attack is salient. But then we loseany motivation for endorsing SSI.12

More importantly, it is not at all clear that the data concerning theavailability heuristic support Hawthorne’s hypothesis. What he needs toexplain is why, in general, we have skeptical intuitions when error possibil-ities are salient to us. But it is not always true that when we consider these


kinds of possibilities, we tend to overestimate the frequency with which theyoccur. For example, while people tend to overestimate causes of death thatare dramatic and sensational—car accidents, tornados, homicide—they tendto underestimate causes of death, which tend to be unspectacular events,which claim one victim at a time, and are common in nonfatal form, e.g.,smallpox vaccination, stroke, stomach cancer, and diabetes.13 People alsotend to underestimate risks to themselves. For example, people tend tomake countless automobile trips without accidents. Moreover the newsmedia shows them that when accidents do occur, they happen to others.Employing the availability heuristic, they underestimate the risk that theythemselves will be in an accident. (This leads people to decide they need notbother wearing seatbelts.)

So when error possibilities that are unspectacular, generally non-lethal,or involve ourselves, are made salient, it is not at all clear that we will tendto overestimate their frequency. So I do not see how the availability heu-ristic can explain, in general, why we have skeptical intuitions when errorpossibilities become salient to us. But then SSI fails to give a satisfactoryaccount of the lottery paradox.14

Notes

1. Space considerations prevent me from discussing all of the challenging objections

that Hawthorne raises to Contextualism. For more, see Cohen (forthcoming).

2. Unger (1975).

3. Williamson (2000).

4. Hawthorne considers a metalinguistic version of the assertion principle (equiva-

lent to mine) and argues that it is not tenable. Unfortunately, space consider-

ations prevent me from discussing his worries. He also argues that Contextualism

allows that at low-standard contexts ‘‘S knows P, but S may not assert P’’ can

turn out false. Insofar as this is a problem, contextualists can employ the same

metalinguistic strategy to account for it.

5. See Cohen (1988), and especially (1999). For other versions of Contextualism,

see DeRose (1995) and Lewis (1996).

6. As Hawthorne is aware, matters are more complicated than I have made them

out. When error possibilities are salient, there is considerable intuitive pressure

to deny knowledge ascriptions. But in some contexts this can be overridden. This

phenomenon complicates the accounts that both Contextualism and SSI must

give of the relation between knowledge and practical reasoning. Unfortunately,

space considerations prevent me from discussing this here.

7. Hawthorne considers one interpretation of how the salience of error possibilities

destroys knowledge, whereby such salience destroys knowledge by destroying

belief. But Hawthorne rejects this account, correctly I think, because in the event

that S persists in believing P even though error possibilities are salient, he may

still lose his knowledge. Hawthorne also argues that Contextualism allows that

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at high-standard contexts sentences of the form ‘‘S does not know P, but he

should appeal to P in his practical reasoning’’ come out as true. These sentences

strike me as much less clearly problematic. Insofar as they are a problem, I can

handle them in the same way.

8. As Hawthorne notes, since knowledge is factive, our own current lack of knowl-

edge prevents us from ascribing knowledge to others and to our previous selves.

But nothing prevents us from suspending judgment about whether others know.

Indeed SSI predicts that this is what we would do.

9. For more on this problem for SSI, see Cohen (forthcoming).

10. Slovic, et al. (1982).

11. Vogel (1990).

12. Indeed Vogel (1990) relies on the availability heuristic to provide precisely this

kind of general explanation for why we deny knowledge to ourselves as well as

others. I should note that Hawthorne’s views about how the practical environ-

ment, which, regrettably, I do not have space to discuss, are unaffected by this

point.

13. Slovic, et al. (1982).

14. I have benefitted greatly from discussions with John Hawthorne, Tom Blackson,

Earl Conee, John Devlin, Gregory Fitch, Richard Feldman, Jonathan Vogel,

Timothy Williamson, and audiences at New York University, University of

Rochester, Oxford University, Arizona State University, and University of

California, Santa Barbara.

References

Cohen, Stewart, ‘‘How to be a Fallibilist’’, Philosophical Perspectives, 2, 1988 (Tomberlin, ed.).

‘‘Contextualism, Skepticism, and the Structure of Reasons’’, Philosophical Perspectives,

13, 1999 (Tomberlin, ed.).

‘‘Knowledge, Speaker, and Subject’’, Philosophical Quarterly, (forthcoming).

DeRose, Keith, ‘‘Solving the Skeptical Problem’’, Philosophical Review, 1995, 104: 1.

Lewis, David, ‘‘Elusive Knowledge’’, Australasian Journal of Philosophy, 1996, 74: 4.

Slovic Paul, Baruch Fischhoff and Sarah Lichtenstein, ‘‘Facts versus fears: Understanding

perceived risk’’ in Judgment Under Uncertainty: Heuristics and Biases, Daniel Kahneman,

Paul Slovic, and Amos Tversky, eds. (Cambridge University Press, 1982).

Unger, Peter, Ignorance (Oxford, 1975).

Vogel, Jonathan, ‘‘Cartesian Skepticism and Inference to the Best Explanation’’, Journal of

Philosophy, 1990, 87: 11.

Williamson, Timothy, Knowledge, and its Limits (Oxford, 2000).


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Knowledge, Assertion, and Practical Reasoning