Knowing How is Knowing How You Are (or Could Have Been) Able

1.1 Two Readings

We can illustrate the two readings with some famous cases taken to break the entailment from know-how to ability.² Stanley and Williamson say that in the following kind of example, an agent loses an ability but not the corresponding know-how:³

The Injured Pianist. Rachmaninov breaks the little finger on his right hand in a way that results in permanent damage and loss of agility. He retains perfect memory of how he used to play his Third Piano Concerto but can no longer perform various runs that are central to the piece in the way that he used to. While he knows there are ways to play the runs with just four fingers, he never learned to play the relevant passages that way.

Both of the following are true:

So, it is claimed, know-how does not entail ability.

There are also agents with know-how who have never had the corresponding ability. Stanley and Willamson, op. cit. report the following case from Jeff King:

The Armchair Ski Instructor. Alice the ski instructor is a perfect teacher: she knows exactly what actions to instruct her students to do for them to ski. However, she cannot perform those actions in that sequence herself.

Again, the following seem true:

So again, it is claimed, know-how does not entail ability.⁴

But with only slight alterations to the case, we can make the true know-how claims turn false. Consider:

The Injured Pianist’s Concert Tour. Rachmaninov’s condition is as before. With his tour due to start in a month, he needs to decide whether to change the concert program. He is struggling with the challenging runs of his concerto: while he knows that it is possible, he has failed to figure out how to play them with his four fingers. He has, however, mastered a selection of his Preludes, which he also regularly used to perform before the accident.

In the light of this variation, consider:

To my ears, this claim now sounds considerably worse. I would want to say:

We can consider one final variation on the case to drive the point home. Suppose that after many, many months of practicing with four fingers, Rachmaninov can now successfully play the runs in his concerto with four fingers. We could describe his success in this way:⁵

It would be mysterious what this meant if he unequivocally knew how to play the concerto all along. If there is no sense in which he didn’t know how to play the Concerto, then what did he learn to do? And why did he have to relearn it?

We can make similar changes to the ski instructor case. Suppose as an experiment Alice decides to take to the slopes herself. We watch her make blunder after blunder, struggling to implement her own advice to her students. Consider again:

This seems faintly ridiculous while we watch her repeatedly fall on her face: in some important sense she doesn’t know how to ski! And again, we can drive the point home by appeal to intuitions about learning; we could say:

I invite you to think of other cases with this structure; I claim the same pattern as above will emerge. This is good evidence for the following:.⁶

Two Readings. Know-how claims have two distinct readings, one which entails an ability claim and another which does not.

1.2 Indeterminacy

My second data point is that know-how claims share in the characteristic indeterminacy of ability claims.

I say a sentence is indeterminate when neither it nor its negation is clearly true in a scenario, even when we know all the relevant facts there. I leave open whether this indeterminacy is semantic, metaphysical or even epistemic. What matters is the distinctive projection behaviour of indeterminacy under negation: when ϕ is indeterminate, so is ¬ϕ.

Mandelkern, Schultheis and Boylan, op. cit. and Boylan, op. cit. have argued that indeterminacy is characteristic of certain ability claims. Returning to Dartboard, let’s think about Carol’s abilities instead. Neither of these claims are clearly true:

Claim (9) is not true because ability requires more than mere physical possibility. Claim (9) requires it be in Carol’s control to do hit the board. But it isn’t – she could easily fail upon trying. Claim (10) is not true either, because can’t entails won’t. Consider:

Both claims are defective. But in Dartboard Carol might well hit the top of the board. So, since can’t entails won’t, it cannot be determinate that she isn’t able to.

Now let’s return to know-how. Take the following case:

Unreliable Dartboard. Carol has no special talent at darts. When stood an ordinary distance away, half of the time she hits the dartboard when she tries; half of the time she misses completely.

What does Carol know how to do? Consider:

Neither seem appropriate. Both seem either to over- or underrate Carol’s dart-playing prowess.

This applies to both of the readings of know-how I isolated in the previous section. To see this, consider:

Injured Dartboard. Before she can improve at playing darts Carol loses her hands in a terrible accident.

In this case, (13) and (14) remain indeterminate – since it was indeterminate whether she knew how before the accident, she counts neither as clearly knowing how nor clearly not knowing how afterwards.

Summing up, we have as a second piece of data:

Indeterminacy. Both readings of know-how claims can share the indeterminacy of ability claims.

2.1 The Basic Tension

To bring out the basic issues raised by my data, I first consider how some simple intellectualist and anti-intellectualist views might handle them.

What is the relationship between knowing how and propositional knowledge? Intellectualists argue that know-how just is propositional knowledge: for instance, knowing how to ride a bike just is knowing some proposition about bike riding (though perhaps in a special way). Anti-intellectualists argue that know-how is not reducible to knowing that.

This is closely connected to, but not exactly the same as, the question of what kinds of things are the relata of know-how attributions. Intellectualists are required to say that know-how attributions describe relations to propositions (or sets of propositions); anti-intellectualists tend to think that know-how attributions describe relations to actions. Call these views propositionalism and non-propositionalism about know-how, respectively.⁷ Intellectualism entails propositionalism, but as Glick, op. cit. observes, anti-intellectualism does not entail non-propositionalism: there is a long tradition, for instance, of treating ability ascriptions as describing a relation between an agent and the proposition that they perform a certain action.⁸ I aim to argue for full-blown intellectualism, not just propositionalism, but I will set aside mere propositionalism until section 5.

Stanley and Willamson, op. cit. provide the canonical version of intellectualism about know-how. They say one knows how to A just in case one knows of some way that it is a way for them to A, and that knowledge must be under a practical mode of presentation:

This view does not explain Two Readings. Stanley and Williamson insist that on their understanding, there can be a way for you to do something even when you are not able to do it. This captures the true readings of know-how descriptions in The Injured Pianist and The Armchair Ski Instructor: Rachmaninov knows how to play his piano concerto because there is still a way for him to do so; Alice the ski instructor knows how to ski because there is a way for her to do so. But then it is mysterious why there should also be false readings of know-how ascriptions in these cases: after all, to say that Rachmaninov and Alice do know how, Stanley and Williamson claim that ways do not guarantee ability. And of course we still have a dilemma if we revise the relationship between ways and ability. Suppose there can be a way for you do to something only when you are able to do it. Now we correctly predict the false readings of know-how claims but not the true ones.⁹

The view also struggles with Indeterminacy. Return to Dartboard. Here there determinately is a way for Carol to hit the dartboard: there is a certain sequence of motions that will lead to her hitting the dartboard. Carol just doesn’t yet know, under the right guise, which way that is. This predicts that both know-how ascriptions (13) and (14) are perfectly determinate: (13) is false because while there is a way for Carol to hit the dartboard, Carol does not know of any given way that that is a way for her to do so; (14) is true because (13) is false.

Turn now to anti-intellectualism. Anti-intellectualism, strictly speaking, is a negative thesis: that know-how does not reduce to knowing-that. However, most anti-intellectualists are driven by the idea that know-how is a kind of capacity. Some identify know-how with a certain kind of ability: following Lewis,¹⁰ know-how could simply be the ability to do A itself, or it could be a more complex ability involving A, such as the ability to do A under normative guidance or the ability to answer questions about A.¹¹ Other anti-intellectualists identify know-how with a kind of disposition to do A.¹² To illustrate the basic difficulties, I run my arguments on simpler forms of the view, where know-how is either just the ability to do A or a disposition to do A; but these difficulties extend to other anti-intellectualisms too.

The simple ability view only partially predicts Indeterminacy.¹³ On that view, know-how just is ability, and so know-how will surely be indeterminate in cases like Unreliable Dartboard. But it does not explain why in Injured Dartboard it’s still indeterminate whether Carol knows how to hit the dartboard. After all, she determinately cannot hit the dartboard.

Anti-intellectualism struggles also with Two Readings. This is easy to see on the ability analysis. If know-how just is ability, then all know-how ascriptions must entail ability. So there cannot fail to be a reading of know-how that does not entail ability.¹⁴ This problem applies to dispositional views too. Either the relevant disposition entails the ability to do A, or it does not, and in neither case do we predict Two Readings.

2.2 Contextualism about Ability?

At this point, intellectualists and anti-intellectualists alike might question my claim that there is any reading of know-how which fails to entail an ability claim. For perhaps I simply have not looked hard enough. Ability claims are highly context-sensitive and give rise to a range of readings.¹⁵ Perhaps each know-how claim is associated with a particular reading of ability, and once we isolate that reading the entailment goes through. Not so, I argue: ordinary ability claims are not context-sensitive enough to rescue the entailment.

A first natural thought is to appeal to internal and external abilities. Internal ability is what one can do simply as a matter of one’s intrinsic make-up; external ability is what one can do in one’s present circumstances.¹⁶ Imagine a chef skilled at preparing ratatouille but lacking the right ingredients: they have the internal ability to prepare the dish but lack the external ability. Many ability modals can express either reading, depending on the context.

Return to our cases. Perhaps Rachmaninov and Alice the ski instructor simply lack external abilities but retain internal abilities to play the piano or ski.¹⁷ I find this implausible – they lack the relevant abilities in both senses.

To see this, notice that natural language itself distinguishes these senses of ability. While ‘can’ and ‘is able’ give rise to a range of readings, the locution ‘has the ability’ specifically tracks internal ability. We might say of our expert chef:

But we would never say:

Internal abilities are not inhibited by such external circumstances. Now I submit that the following is simply false in The Handless Pianist:

The same goes for Alice in The Armchair Ski Instructor:

A second kind of context-sensitivity comes from the distinction between specific and general abilities. My drunken friend is not able to drive their car in their current state. But this is not the norm: usually they’re not drunk and so are able. Call the former, the ability to drive in these exact circumstances, the specific ability to drive and the latter, the ability to drive in normal circumstances, the general ability.

Do our agents have the relevant abilities in normal circumstances?¹⁸ This does look promising, for The Injured Pianist at least: being injured is abnormal. But this proposal exploits a non-essential feature of our case – that the absent ability is a normal one. What about when having a particular ability is abnormal? In such cases, a loss of this ability makes us more normal. Take a variation on the Rachmaninov style case:

The Gymnast. Frederica is already one of the strongest, most agile gymnasts alive. But she dreams of performing a feat that nobody else has ever performed. She takes an experimental performance-enhancing drug which boosts her strength and speed even further. While she is in this physical condition, she develops a brand-new complicated, demanding version of the double back salto on the beam. Many try to imitate it but no one succeeds. Alas, the drug is soon discovered to have serious health effects, and Frederica stops taking it. She returns to her normal, pre-drug state, wherein she is not able to perform her version of the double back salto.

Like in the Rachmaninov case, even when Frederica has stopped taking the drug, we can say:

To make it especially prominent, imagine another gymnast has started taking the performance-enhancing drug, in the hope of recreating Frederica’s performance, and wants someone to teach her the routine. Claim (20) sounds like exactly what the pianist wants to know. But it is certainly not true that Frederica is able to perform the routine in normal circumstances – her post-drug physique is what is normal for her, yet she cannot do it. The Gymnast is then a counterexample to the entailment from general know-how to general ability.

Furthermore, lacking a certain ability might be neither normal nor abnormal. This is exactly the situation of Alice the ski instructor. Being able to ski is clearly not abnormal. But not being able to ski is not abnormal either – skiing is an ability acquired through hard work, not one that people necessarily have in normal circumstances. Thus, it is simply not true that in normal circumstances Alice is able to ski. Normal circumstances are compatible with various levels of skiing expertise, including none at all.

I see no grounds for further optimism here. Ability modals are indeed context-sensitive. Even so one reading of a know-how claim fails to entail any reading of an ordinary ability claim.¹⁹

2.3 Knowing How One Does A

Another common move, when faced with cases like The Injured Pianist and The Armchair Ski Instructor, is to say that know-how claims are in fact ambiguous. On one reading, the phrase ‘know how’ talks about a distinctively practical state. This, particularly according to various anti-intellectualists,²⁰ is the philosophically interesting notion. But, they claim, there is also a second, completely separate reading of ‘knowing how’ where one knows how to do A just in case they know how one does A. I’ll call this latter state pseudo-know-how.

This can save the entailment from know-how, in the distinctive practical sense, to ability. When we attribute know-how to Rachmaninov or Alice, we are in fact attributing propositional knowledge of how one plays the concerto or how one skis. This clearly does not entail ability, nor does it entail know-how: knowing how one skis doesn’t mean you know how to do so.²¹

In fact, pseudo-know-how is neither necessary nor sufficient for what Alice and Rachmaninov have.^22,23 Take necessity first. In fact, Rachmaninov was a giant of a man, and his enormous handspan made possible various techniques that are out of the question for most. The way he would play his concerto is very different from how a normal pianist would attempt it. Let’s suppose that the only way he knows how to play it is how he specifically would play it. None of this affects the truth value of (1) as said in The Injured Pianist. But it does affect the truth of (21):

This is no longer clearly true, given the addition just made to the case – Rachmaninov’s knowledge is extremely specific to him in particular.

For sufficiency, consider the following variation on the ski instructor case:

The Physically Atypical Armchair Ski Instructor. Billie the ski instructor, just like Alice, is a perfect teacher who cannot herself ski. But her unusual physique is extremely different from that of the average student, so much so that even if she did perform that sequence of actions, it would not result in her skiing; she would simply slip and fall.

The analogue of (3), our true claim about Alice the first instructor, doesn’t sound right here.

What Billie knows about skiing would never result in her skiing. Rather we would want to say:

But there should not be any difference on this strategy.

3.1 Infinitival Questions

Intellectualists take know-how to ascribe knowledge of a question.²⁴ But not just any old question – specifically, an infinitival question. Such questions combine a question word with a verb in the infinitival form. Consider:

The italicised expressions are infinitival questions.

Both have an essential modal element in their meaning. Claim (25) says something like:

Claim (26) says something like:

No true paraphrase of claims like these will be modal-free. Bhatt proposed a simple explanation that has been widely accepted:²⁵ (25) and (26) contain silent modal operators. Their real structure is something like:

3.2 Motivating and Characterising the Indicative and Subjunctive Readings

I argue that infinitivals are subject to a novel kind of context-sensitivity – they can be read indicatively or subjunctively. To see this, start with a case:

Evening Newspaper. It’s midnight. You approach me on the street and ask where to buy a newspaper. All the stores I know of are all shut. (But there may be others that I don’t know about.)

There are two possible ways for me to answer your question. I could say:

This seems truthful – I can’t advise you on where to get your newspaper. But surprisingly, the opposite answer also seems truthful:

This is not specific to knowing where. Take knowing what. We can easily imagine a situation where either of the following are apt:

Or knowing who:

So there is context-sensitivity in ascribing knowledge of infinitival questions. But where does it come from? The culprit, I think, is the silent modal. Modals are widely recognised to be context-sensitive – their meaning is partially determined by the information held fixed in the context. Following the work of Angelika Kratzer,²⁶ we can capture this feature by interpreting a modal by using a modal base f. The modal base represents the information held fixed in the form of a set of worlds; this set restricts the possibilities a modal quantifies over. My claim is that in Evening Newspaper, and other cases like it, two possible modal bases are available in the context; one I will call indicative (and write f_i) and the other I will call subjunctive (and write f_s).

What distinguishes these readings? The difference between the two is that, in general, the indicative holds all the facts fixed, whereas the subjunctive holds only a certain subset of the facts fixed.

Return to Evening Newspaper. In saying (31), I hold fixed the actual fact that the stores are closed; I say that given my actual circumstances, I don’t know where to buy a newspaper. I call this reading indicative. In saying (32), on the other hand, I quite clearly am not holding everything fixed in my utterance. The modal does not hold fixed the actual fact that the stores are closed; I could paraphrase what I said with:

But I do continue to hold a lot of other things fixed, like what stores there in fact are, which ones stock newspapers and so on. The reading in (32) holds some but not all of the actual facts fixed. For this reason, I call this reading a subjunctive reading.

The same relationship plays out in the various different cases of knowing what, where and why infinitivals. We have an indicative reading, which holds fixed the actual facts, and a subjunctive reading, which suspends some but not all of the actual facts.²⁷

But what kinds of assumptions can the subjunctive reading suspend? Certainly facts about our environment. In Evening Newspaper it is midnight and the stores are closed. But the subjunctive reading in (32) clearly does not hold this fixed; for this reason exactly it gets to be true.

Crucially for know-how, the subjunctive can also suspend assumptions about our own physical constitution. Consider:

The Hike. We are hiking and we need to find our way back to our campsite. Foolishly, we have walked too far. I alone remember the route we took to this point; but that involves jumping a chasm, and we are clearly too tired now to make it safely across. We also know that there is a shortcut back through the nearby forest, but neither of us knows exactly where that path is.

Here I can say either of the following:

Claim (38) is the familiar indicative reading. Claim (39) is the subjunctive reading, where the silent modal does not hold fixed our current physical conditions – it is (38) that does this, and that claim is false for exactly this reason.

It does appear that the subjunctive holds fixed our knowledge: if a known fact remains fixed subjunctively, so too is the fact that we know it. We see this in Evening Newspaper: the subjunctive reading clearly holds fixed my knowledge of where the relevant stores are and what they sell. We also see this in The Hike: there we hold fixed that I know where exit A is. And the subjunctive reading does not appear to add assumptions about our knowledge: in The Hike there is no true reading of:

My last claim is that the subjunctive reading is not an instance of the more general context-sensitivity of modals, of the kind we saw in section 2.2. The subjunctive reading is not accessible to modals in unembedded or indicative contexts. Return to (39) in The Hike. The covert modal must have the force of possibility; there are two ways to get out after all. But we cannot paraphrase this with a straightforward claim:

This simply sounds false – if we tried to jump the chasm, we would fall to our doom. The right paraphrase of (39) requires the modal to be in the subjunctive:

4.1 The Account of Know-How

I assume, as intellectualists typically do, that knowing how is knowing the answer to a how-infinitival question.

In general, the semantic value of a question is taken to be the set of propositions that answer it.²⁸ And when we attribute knowledge of questions, we simply attribute knowledge of an answer to the question.²⁹ A standard way to capture this, following Karttunen, op. cit., is to give ‘knows’ two meanings. One is the standard propositional meaning. The other is a question meaning, which I mark with a q-subscript. You know_q Q just in case you know a proposition that answers Q.³⁰

Infinitival questions, as we already saw, are thought to contain a silent modal. The majority of linguists also posit in infinitival questions a special silent pronoun called PRO.³¹ So the actual structure of (25) is something like:

PRO tends to corefer with the subject of the knowledge claim; so PRO here would refer to John.

I say that the silent modal in know-how ascriptions is an ability modal. That means the structure of a know-how claim is as follows:

And, given the standard assumptions above, a structure like this is true just in case for some B, S knows that S can A by B-ing.³² More officially, we have the following truth conditions:

Know-how.

⟦S knows_q how PRO CAN_f A⟧^c,w = 1 iff in w there’s some B such that S knows S ${\mathrm{CAN}}_{f_c}$ A by B-ing

Given my arguments in section 3, there will be two readings of know-how ascriptions, corresponding to the two possible modal bases. When the modal base is indicative, we get an indicative know-how claim of the form:

S knows_q how PRO ${\mathrm{CAN}}_{f_i}$ A

This kind of claim is true just in case S knows how they can ϕ, given the actual facts about the case. When the modal base is subjunctive, we get a subjunctive know-how claim:

S knows_q how PRO ${\mathrm{CAN}}_{f_s}$ A

A subjunctive know-how claim is true just in case S knows how they can ϕ, given only the facts held fixed subjunctively.

4.2 Back to Two Readings and Indeterminacy

Both my data points simply fall out of this account.

The basic explanation of Two Readings is simple: indicative know-how entails ability; subjunctive know-how does not. Let’s return to the The Injured Pianist, where there are true and false readings of the claim:

My theory assigns two possible structures to this claim, depending on whether the modal base is indicative or subjunctive:

The former is false and the latter true, I claim, because only the former entails an ability ascription.

Let’s start with (45). On my semantics, this is true just in case the following holds:

But knowledge is factive, and ${\mathrm{CAN}}_{f_{c,i}}$ is simply what ordinary ability ascriptions express: after all, those are ability ascriptions in the indicative mood. So (47) entails:

And this claim is false: Rachmaninov can’t play the concerto at all.

Now take the subjunctive reading of (46):

(46) Rachmaninov knows how he ${\mathrm{CAN}}_{f_{c,s}}$ play his Third Piano Concerto.

This entails a subjunctive ability claim:

But this does not entail an ordinary, indicative ability ascription; the subjunctive holds fewer facts fixed. What’s more, it’s plausible that Rachmaninov has the subjunctive ability to play the concerto by playing it in just the way he used to. The subjunctive reading does not hold fixed all the actual facts about one’s physical constitution, and so Rachmaninov’s injury is no barrier to (46) being true. I contend it is true, though it entails nothing about Rachmaninov’s indicative abilities.

Indeterminacy is explained because both indicative and subjunctive ability can be indeterminate; and this indeterminacy projects into knowledge claims. Recall:

Unreliable Dartboard. Carol is at an early stage in learning to play darts. Half of the time she hits the dartboard when she tries; half the time she misses it completely.

We said that it is indeterminate whether Carol is able to hit the dartboard: it neither seems right to say she can, nor that she can’t.

This indeterminacy projects into knowledge of certain questions. Consider:

No action available to Carol settles that she hits the dartboard, so unsurprisingly (50) is not true. But again, neither is its negation:

Claim (51) does not sound true because, like (50), it presupposes something that is not true: both presuppose that there is indeed some way that Alice can hit the dartboard, that there is some true answer to the question. This not being true, both fail to be true and so are indeterminate.

Given this presupposition, my theory explains why it is indeterminate whether Carol indicatively knows how to hit the dartboard. Just like (51), this presupposes there is some way that Carol is indicatively able to hit the dartboard. But there is not.

This explanation carries over to the subjunctive reading also. We said that when Carol is injured, it is still indeterminate whether she knows how to hit the dartboard. Here it is also indeterminate whether she has the subjunctive ability to hit the dartboard. The subjunctive reading of the modal here will not hold fixed Carol’s actual injury. And, as we said before, if she were uninjured, it would be indeterminate whether she was able; thus, the subjunctive reading is indeterminate. From here, the explanation is the same as that for the indicative: the know-how claim is indeterminate because all of the possible answers to the question are too.