3 From Knowledge to Understanding
As the examples sketched in the previous chapter show, the epistemic excellence of mature science is not easily construed as knowledge. To accommodate not just science, but disciplinary epistemic success in general, we should focus on understanding. I begin to explicate understanding and sketch how it differs from knowledge. Following Kvanvig (2003), I distinguish between propositional understanding, which is captured in an individual proposition, and objectual understanding, which is captured in an account. The cognitive competence involved in understanding is generally characterized as grasping. Propositional understanding involves grasping a fact; objectual understanding consists of grasping a range of phenomena. This seems right. But it is not clear what grasping is. I suggest that to grasp a proposition or an account is at least in part to know how to wield it to further one’s epistemic ends. To make this out requires a lengthy discussion of know-how. That discussion is far from exhaustive. It is structured to highlight the aspects of know-how that figure in objectual understanding. Disciplinary understanding, I argue, is best construed as objectual. In the first instance we understand a range of phenomena via an overall account; only derivatively, drawing on the resources of that account, do we understand that or why something is the case. I argue that scientific (objectual) understanding is nonfactive. Although it is not indifferent to the facts it concerns, an account that accommodates those facts need not consist exclusively or predominantly of truths.
The Limits of Knowledge
Bill thinks that apatosauruses and brontosauruses are distinct. He has good reason to think so. But he cannot know that they are distinct unless in fact they are. We do not consider false beliefs to be knowledge, no matter how well founded they may be. Once Bill discovers that, contrary to what he believed, the apatosaurus is the same sort of dinosaur as the brontosaurus, he rescinds his claim ever to have known that they were distinct. He may say, ‘I thought I knew that they were distinct, but I was wrong’. He may even say, ‘I had it on excellent authority that they were distinct, but I and my authorities were wrong’. He will not say, ‘I knew they were distinct, but I was wrong’. The term ‘knowledge’ is factive. An epistemic agent does not know that p unless ‘p’ is true.
Inasmuch as each bit of knowledge is keyed to a particular fact, knowledge is granular. Even so, it is (close to) impossible to know one thing at a time. Insofar as knowledge requires justification, in order to know that p, an agent’s belief that p must be backed by considerations that bear on whether p is the case. It seems that these considerations must themselves be known; otherwise even if p is (externally) justified, the agent would not be justified in believing that p. She would have no reason to trust her conviction. But if she must know the justificatory chain leading to p, an agent will have to know a lot in order to know (much of) anything.1 There is then a tension between the apparent granularity of knowledge and the nongranularity of justification. One way to alleviate the tension might be to consign the justifiers to ‘background knowledge’ and ask whether, together with the empirical evidence, the ‘background knowledge’ affords sufficient grounds to underwrite a particular claim. This might work for simple inductive cases, or the sort of amassing discrete bits of evidence that one sees in detective stories. But problems arise when an account figures in the justification for a claim. If the background ethological account together with the empirical evidence justifies the conclusion that this bit of grooming behavior manifests reciprocal altruism and if that conclusion is true, it might seem that we are in a position to know it. Unfortunately, things are not so straightforward. Such a connection reveals whether an account supports a claim, but the assumption that the ‘background knowledge’ is genuine knowledge cannot be sustained. The justification for many of the claims making up a scientific account is reciprocal; they support one another. How they do so will be discussed in the next chapter. Here the point is simply that systematic accounts are not granular in the way that mainstream epistemology takes knowledge to be.
Another, potentially more promising, strategy is to take holism at its word and relax granularity. The atomic sentences that comprise an account cannot be separately justified. Even if the focus of attention is a particular claim, evidence always bears on an account as a whole. Evidence for the claim that a given process is adiabatic is evidence for an entire account of heat transfer, which is tested along with the claim. Evidence that the grooming behavior displays reciprocal altruism is evidence for an entire account of primate behavior, which is tested along with the claim. In principle, this is epistemologically unproblematic. The contention that knowledge is propositional says nothing about the length of the propositions that constitute knowledge. We might accommodate holism by treating an account as a conjunction of its component atomic propositions and saying that the evidence bears on the truth or falsity of that long conjunction. If the conjunction is true, is believed, is justified or reliably produced, and is epistemically lucky, it is known.
This may be as good a schema for scientific knowledge as we are likely to get. But it sheds little light on the epistemic standing of science, for its requirements are rarely if ever met. In particular, the truth requirement is seldom satisfied. As we have seen, many epistemically estimable accounts contain models and idealizations that do not even purport to be true. For now, however, this complication will be set aside. The current difficulty is that even the best scientific accounts confront anomalies. They entail consequences that conflict with the evidence. A conjunction is false if any of its conjuncts is; so if a scientific account and the evidence that bears on it are a conjunction, an anomaly—being a falsifying instance—tells decisively against the account that it bears on. Since a theory that confronts an anomaly is false, it does not amount to knowledge.
Perhaps we can evade this predicament. The characterization of an account as a conjunction might seem to offer hope of isolating anomalies and screening off their effects.2 All we need to do is identify and expunge the troublesome conjuncts. Consider the following conjunction:
(1) (a) Sally is in Chicago & (b) Sam is in New York.
If Sally is in fact in Detroit, (1) is false, even though Sam is in New York. If we lack adequate evidence that Sally is in Chicago, (1) is unjustified, even though we have ample evidence that Sam is in New York. If our source of information about Sally’s whereabouts is suspect, (1) is unreliable, even though our source of information about Sam’s location is impeccable. In any of these circumstances, (1) is not something we are in a position to know. Still, we can rescind (a), leaving
(b) Sam is in New York,
which is true, justified, and reliably generated. Since neither (a) nor the evidence for (a) lends any support to (b), (b)’s acceptability is not undermined by the repudiation of (a). On standard accounts of knowledge, assuming that the relation between the truth of (b) and the evidence for (b) is not vitiated by epistemic misfortune, we are in a position to know that (b). If the components of a scientific account were related to one another as loosely as (a) and (b) are related in (1), we could simply excise the anomalous sentences and be left with a justified, reliable truth—something that could be known.
The problem is that the components of an account lack the requisite independence. An account is a tightly interwoven tapestry of mutually supportive commitments. Simply excising anomalous sentences would leave a moth-eaten fabric that would not hang together. Toward the end of the nineteenth century, physicists devised a variety of increasingly drastic expedients to accommodate the perihelion of Mercury. But even at their most desperate, they did not suggest simply inserting an exception into the theory. Although ‘All planets except Mercury have regular orbits’ is evidently true, justified, reliably generated, and believed, it pulls so strongly against the ideal of systematicity that scientists never considered incorporating it into astronomy. Temporarily bracketing anomalies can be a good investigative tactic, but simply dismissing them as exceptions that need not be accommodated is not. The reason is not merely aesthetic. An anomaly might be just a pesky irritation that stems from undetected but ultimately insignificant interference, but it might also, like the perihelion of Mercury, be symptomatic of a subtle but significant misunderstanding of the phenomena. Science would lose potentially valuable information if it dismissed anomalies as exceptions that it could simply disregard. There is then no hope of excising anomalous sentences without undermining the epistemic support for the rest of the account. The account rather than the individual sentence or proposition is the unit we need to focus on.
These points are familiar and uncontroversial, but their epistemological consequences are worth noting. An account can be construed as a conjunction of the sentences that appear in it. But science does not consist of knowledge expressed by such conjunctions. For the conjunction of the sentences that constitute an epistemically estimable scientific account is almost surely false. The unavailability of sentence-by-sentence verification or justification discredits the idea that science separately delivers knowledge of each component atomic sentence. The hopelessness of selectively deleting the falsehoods in, and the false implications of, an account undermines the plausibility of claiming that scientific knowledge is what remains when an account’s falsehoods have been expunged. Knowledge requires truth. And there seems to be no feasible way to get the scientific accounts we admire to come out true. So knowledge is not the cognitive condition that good science standardly engenders.
Refocusing Epistemology’s Lens
To accommodate science, I suggest, epistemology should shift its focus from knowledge to understanding. In speaking of understanding, we should distinguish between the objects of understanding and the vehicles of understanding (see Greco, 2014). The vehicles of understanding are whatever embody the understanding—perhaps sentences, propositions, accounts, nonpropositional representations, or dispositions. An object of understanding is whatever the understanding is about. Objects of understanding may be concrete or abstract. An epistemic agent can understand linear algebra as well as particle physics. She can understand why 
is irrational as well as why the noble gases are inert. Nor, I maintain, need the objects of understanding be articulable. A commuter can understand the New York subway system and an avid fan can understand the Celtics’ defensive strategy without being able to express that understanding in words or endorse a description of the phenomena expressed in the language that she speaks.
A critical question is whether ‘understanding’, like ‘knowledge’, is factive. If it is, then the shift from knowledge to understanding may avail us little. Pretty plainly, understanding somehow answers to facts. The question is how it does so. If ‘understanding’ is factive, all or most of the propositional commitments that comprise a genuine understanding are true. And the epistemic status of nonpropositional elements is instrumental and dependent on their role in underwriting the epistemic standing of those truths. Many epistemologists consider understanding factive (see Kvanvig, 2003; Grimm, 2006). But, I will argue, a factive conception is too restrictive. It does not reflect our practices in ascribing understanding and it forces us to deny that much contemporary science embodies an understanding of the phenomena it bears on. This is too high a price to pay. A more generous, flexible conception of understanding accommodates the deliverances of science, reflects our practices, and shows a sufficient, but not slavish, sensitivity to the facts it bears on.
We cannot settle the question by inspecting ordinary usage, as we did with ‘knowledge’; for the term ‘understanding’ is used in a variety of ways, none of which seems to dominate the rest. Some are irrelevant to epistemology; others pull in different directions. ‘I understand’ can hedge an assertion or attenuate its force. ‘I understand that you are angry with me’ may be a mild overture that gives you space to politely demur. ‘Not angry, but disappointed’, you might reply. This is a moderating use. Or I might say, ‘I understand that the committee has the authority to decide’ when I am not sure that it has the authority, but have reason to think so. Here ‘I understand’ indicates a backing away from a full-fledged claim to epistemic entitlement. This is hedging. These are not the sorts of usages that concern us here. Our concern is with cases in which understanding is a sort of epistemic success. I shall use the term ‘understanding’ as a success term for having an epistemically suitable grasp of or take on a topic. Just what constitutes a suitable grasp or take remains to be seen. Here the point is that in such cases the understander has a claim to epistemic entitlement.3 The questions, then, are what is the bearer of that entitlement and what is the claim to it? I contend that a nonfactive explication of ‘understanding’ yields a concept that better suits epistemology’s purposes than a factive one does.
I recognize the existence of factive uses of the term ‘understanding’, just as I recognize the existence of hedging and moderating uses. Nor do I deny that epistemology could incorporate a factive conception of understanding. My contention is that a factive conception cannot do justice to the cognitive contributions of science and that a more flexible conception can. But understanding is not restricted to science, so I begin with an historical example:
In 490 BCE the Athenian army confronted the invading Persians on the plain of Marathon. The Persians vastly outnumbered the Greeks. Nevertheless, the Athenian commander, Miltiades, decided to attack. Contrary to standard military practice, he arrayed his forces in a line with a weak center and strong flanks. The Persians readily repulsed the center of the line. When the Persians pursued the retreating Greeks, the flanks moved in and surrounded the Persian army, attacking them from all sides. They thereby won the Battle of Marathon. (paraphrased from Herodotus, 1985)
The first order of business is to identify the primary object of understanding. Two obvious candidates present themselves: individual facts and more comprehensive domains. The former is propositional understanding; the latter objectual understanding (Kvanvig, 2003). One might doubt that the two are distinct. Perhaps the body of information that constitutes an objectual understanding of a topic is a single long conjunctive proposition. Then objectual understanding reduces to propositional understanding. Alternatively, perhaps the understanding of an individual matter of fact qualifies as understanding only because it is backed by a complex justificatory network. Then the agent’s grasp of the network is implicated in her understanding of p.
The basic unit of propositional understanding is the individual sentence or proposition. One possibility is that its form is:
x understands that p is so.
For example,
Jack understands that Athens defeated Persia in the Battle of Marathon.
If this is correct, the difference between knowledge and understanding seems slight. To understand that Athens won the battle, Jack would presumably require a nonfortuitously justified true belief to that effect. Since he learned it from Herodotus, and Herodotus is a good source of such information, most epistemologists would probably grant that he knows it. If this is all it takes to understand that Athens won the battle, then understanding is factive, because knowledge is.
We might be disinclined to think that Jack understands that Athens won if all he can do to support his belief is point to his source. If he did not read Herodotus’s full account of the battle or did not comprehend or register the information it provides, he has no idea why Athens won. He merely knows that Athens won. It may be preferable, then, to take understanding to be a matter of knowing why, rather than merely knowing that. In that case, the fundamental schema is:
x understands why p is so.
Many hold that to understand why is to be in a position to explain (see Strevens, 2008; Grimm, 2006). Jill understands why Athens was victorious because she can explain the victory. On this sort of account, to understand a fact is different from merely knowing that fact. But it is still evidently a form of knowledge—knowledge why p is so. According to Lipton, “Understanding is not some sort of super-knowledge, but simply more knowledge: knowledge of causes” (2004, 30). This is too narrow. Knowledge of causes might account for understanding that the moon causes the tides, or that Athens won the battle of Marathon, but it cannot account for understanding that is irrational. Nonetheless, it may be that even in mathematics understanding is knowing why. This suggests that advocates of a knowing why account would do better to explicate propositional understanding in terms of knowledge of dependencies, and let knowledge of causes be a special case (see Greco, 2014; Strevens, 2010; Grimm, 2014). This is more plausible. Understanding is not just knowledge, but a particular sort of knowledge. Since knowledge of dependencies, like all knowledge, is factive, understanding is too.
Perhaps the demand for knowledge of dependencies is too strong. Understanding might be factive even if it is not knowledge. Factivity requires only that the proposition or account that embodies an understanding be true, not that it be known. In view of the plethora of threats to knowledge, factivity may be the best we can hope for. The worry comes from Gettier cases. Where there is a misalignment between truth-makers and justifiers, an agent can have a justified true belief that does not amount to knowledge. Following Pritchard (2010), let us say that a belief is environmentally unlucky if it is formed or sustained in an epistemically hostile environment. Environmental misfortune defeats knowledge since a belief formed in such an environment could too easily have been false. The question is whether such misfortune undermines understanding.
Pritchard says ‘no’. Elaborating on an example developed by Brogaard (2005), he sketches the following scenario: Suppose Fred arrives home to find his house in flames. He asks someone who appears to be a fire marshal why the house is on fire. She reports that the fire was caused by faulty wiring. Given her expertise, we would ordinarily conclude that Fred knows on the basis of her testimony that faulty wiring caused the fire. But suppose that there are several people milling around, all dressed as fire marshals. En route to a costume party, they stopped to look at the blaze. If it is just by luck that Fred asked the actual fire marshal rather than one of the costumed partygoers, he does not know. He could too easily have chosen an unreliable informant. Nevertheless, Pritchard maintains, Fred understands why the house is on fire, since he has accurate information that coheres with his relevant background beliefs. “The agent … has all the true beliefs required for understanding why his house burned down, and also acquired this understanding in the right fashion. It is thus hard to see why the mere presence of epistemic luck should deprive the agent of understanding” (2010, 78–79). I do not find this case compelling. But if it is, or if a more compelling case could be devised, then understanding is not knowledge, for one can have propositional understanding where the anti-luck condition on knowledge is violated.
Some (Kvanvig, 2003; Grimm, 2014; Hills, 2015) argue that understanding is keyed to explanation. To propositionally understand a fact is to grasp an explanation of that fact. In mathematics the explanation is not causal; in empirical disciplines it is. If an agent can provide a suitable explanation of a fact, we are inclined to credit her with understanding that fact. The challenge comes where the agent cannot provide or comprehend an explanation. Does this completely disqualify her from understanding a given fact?
Strevens (2008, 2010) takes the basic unit of understanding to be the proposition. On his picture, Sara understands why p, only if she can explain p or grasp an explanation of p, where the explanation is a derivation from more fundamental truths that ground p. If p is a matter of empirical fact, the explanation is causal. It includes all and only causal factors that make a difference to whether p obtains. If p is a fundamental truth (such as a fundamental law of nature), then the explanation why that figures in understanding it is an explanation of what derivative or higher-order facts p is a cause of. According to Strevens, then, all understanding of the material world is causal. To understand the Athenian victory is to be able to explain or comprehend an explanation of how it arose from more basic truths. Other sorts of understanding—mathematical, ethical, aesthetic—are still grounded in explanations that reflect real, metaphysical dependency relations, but the explanations are not causal (Strevens, 2010).
There are a number of worries about this picture. Not all understanding involves explanation or grounding of any sort. A savvy commuter who understands the New York City subway system may have no explanation of the regularities she observes. Her understanding is exhibited in her facility in negotiating the subway system, in accommodating her travel to its vicissitudes. She knows, for example, that the number 2 train is generally faster than the number 3, but not when it rains. She knows where to stand on the 14th Street platform to maximize her prospects of getting a seat. She readily accommodates herself to delays and disruptions, having a feel for when it makes sense to wait things out and when it is better to switch to a different line, and so forth. Such understanding is, or is akin to, know-how. I will have more to say about that below.
Nor is it obvious that all scientific understanding is causal. Ecology and population biology, for example, study patterns of population growth and diminution. Animal populations are known to regulate their own size. But the mechanisms by which populations self-regulate are not known. Still, it seems, even if they cannot fully explain how it is done, ecological models of population size embody an understanding of the dynamics of population regulation (Sarkar, 2014).
Mathematics poses an even greater difficulty. According to Strevens, “If mathematical explanation is possible at all, there must be a dependence relation whereby some mathematical facts depend in some sense on other mathematical facts. It is in virtue of this dependence relation that some mathematical facts are fundamental and others should be understood as holding in virtue of the fundamental facts”; he goes on to say, “A proof in mathematics may or may not be explanatory. In order to be explanatory, the entailment structure of the proof must mirror the relevant mathematical dependencies” (2010, 14–15). Whatever the merits of this as a view of mathematical explanation, mathematical understanding seems not so tightly tied to metaphysical grounds. Any axiomatized branch of mathematics can be reaxiomatized. Under different axiomatizations, different patterns emerge. All contribute to mathematical understanding in that each reveals networks of mathematical relations that others obscure. It seems tendentious to insist that someone who grasped a valid proof of a theorem had no understanding of the subject because the theorem in question derived from an axiomatization that did not mirror the right dependence relations.
Questions arise even with respect to the understanding of ordinary matters of fact. Must the elements of the grounding explanation be independently understood? Strevens (2008) recognizes that the ultimate laws of nature cannot be explained in terms of anything more basic. In understanding them, we understand how they underwrite less basic claims. This is not my worry. Rather, I am concerned about the epistemic relation between explanandum and explanans. If the explanandum must be epistemically prior to the explanans, it is going to be difficult to understand the Athenian victory, since the elements of the explanation—the details about the deployment of forces and the effectiveness of the strategy—seem hardly more secure than what they are adduced to explain.4 Since ultimately, most of the information that figures in the explanation comes from Herodotus, if the explanation must be known, although Jill can explain the victory, she seems to be not much better off epistemically than Jack.
If the elements of the explanans need not be known, there is something potentially misleading about claiming that to understand why p is to be able to explain it or comprehend an explanation of it. Such a contention suggests that the explanans is known independently of, and is epistemically prior to, the explanandum. What we actually see is something more holistic, with the understanding embodying not only the fact to be explained but also the elements of the explanation and whatever supports them. Herodotus’s whole account of the battle then stands or falls together. In that case, however, it appears that the basic schema for understanding is
x understands φ
where φ is a topic, discipline, or subject matter. This is objectual. Jill, in the first instance, understands the Battle of Marathon, and thereby derivatively understands and can explain or comprehend an explanation of particular matters of fact such as the course of the battle, the strategies and tactics of the two armies, and the history of relations between Athens and Persia. The epistemological standing of ‘Athens defeated Persia in the battle of Marathon’ then implicates a more comprehensive understanding of the history of Greece or of Persia or of warfare. I do not deny that the sort of understanding why that figures in explanation is real. I simply doubt that it is either as comprehensive or as fundamental as its adherents think. I believe that the understanding of a particular matter of fact derives from the understanding of a suitably unified, integrated, tenable body of information that bears on that fact. Objectual understanding, I take it, is the core conception of understanding. It affords a basis for distinguishing between understanding a topic and knowing particular truths about it.
Objectual Understanding
At a first approximation, an understanding is an epistemic commitment to a comprehensive, systematically linked body of information that is grounded in fact, is duly responsive to reasons or evidence, and enables nontrivial inference, argument, and perhaps action regarding the topic the information pertains to. This rough approximation is far from a full explication. But we can augment it with accepted verdicts about what we take to be clear cases. Astronomy affords an understanding of the motions of celestial bodies and their effects; astrology does not. Chemistry affords an understanding of the constitution of matter; alchemy does not. Biology affords an understanding of the origin of species; ‘intelligent design’ does not. An adequate epistemology should, at least for the most part, respect such verdicts.
Although one mark of understanding on this conception is an ability to explain or comprehend an explanation, no such ability is required. Gareth is incapable of explaining the apparent retrograde motion of the outer planets. Nor can he comprehend a verbal description of the phenomenon. But he can demonstrate what happens using an orrery (Lipton, 2009). If his demonstration is effective, and if he can display enough cognitive dexterity in accommodating different scenarios to show that his demonstration is not a fluke, it is hard to deny that he understands the phenomenon. Pat understands the New York subway system in that she can use it to get around the city efficiently, being aware of such matters as which lines are fastest at different times of day, how foul weather affects different subway lines, which transfer points are likely to be uncrowded, and so forth. She may have no idea how to explain such matters, no appreciation of a transportation engineer’s explanation of these matters, and no reason to think they need explaining. Her understanding is exhibited in the adroitness of her subway-riding behavior and in the advice she gives to other riders, not in any capacity to explain. A physician understands the course of a disease, being aware of the sequence of signs and symptoms, the duration of the contagious phase, the potential complications, and the ranges of responsiveness to treatment, even if neither she nor anyone else can explain why the disease presents in the way it does.
Whether this sort of understanding is factive is the question I need to address. Understanding on my view is a (perhaps tacit) endorsement of a fairly comprehensive, interconnected constellation of cognitive commitments. The understanding encapsulated in individual propositions derives from an understanding of larger bodies of information that include those propositions. In understanding the Athenian victory in the Battle of Marathon, Jill grasps how the proposition stating the fact that Athens won fits into, contributes to, is justified by reference to, and figures in the justification of a more comprehensive understanding that embeds it.
Obviously, not just any comprehensive, mutually supportive set of cognitive commitments will do. A coherent body of manifestly unfounded contentions does not constitute an understanding of the phenomena they purportedly bear on. Even if it is coherent, astrology affords no understanding of the cosmic order. The issue that divides factivists and nonfactivists is not whether understanding must answer to the facts, but how it must do so. Following Plato (1997), let us call the required connection between a comprehensive, coherent account and the facts it bears on an understanding’s tether. Even if astrology offers a comprehensive, internally coherent account of the cosmos, it yields no understanding because it lacks a suitable tether.
To be sure, we sometimes say things like ‘Joe understands astrology’, or ‘Paul understands mythology’, or ‘Michael understands rationalism’, meaning only that the epistemic agent knows his way around the field. He knows how its contentions hang together, and is adept at reasoning within the framework that they constitute. In such cases, the epistemic agent’s commitments are tethered to the doctrine or account, not to the phenomena that doctrine or account purports to be about. One can understand an account regardless of its fidelity or infidelity to the phenomena it concerns. Such an understanding takes an account—astrology, rationalism, or whatever—to be its object rather than the phenomena the account purportedly pertains to. There is nothing epistemically special about this sort of understanding. It is of a piece with understanding a natural phenomenon or a historical episode or a transportation system. Still, it is worth noting that it is possible for an account to be the object of understanding even if, owing to its untenability, it affords no understanding of its purported subject matter.
Understanding the Athenian victory involves more than knowing the various truths that belong to a suitably tethered comprehensive, coherent account of the matter. The understander must also grasp how the various truths relate to each other and to other elements of the account. Ceteris paribus, she should also be both willing and able (and perhaps be aware that she is willing and able) to use that information—to profess it, to reason with it, to apply it, perhaps to use it as a source of working hypotheses about related matters when her ends are cognitive.5 Someone who knows geometry, for example, knows all the axioms, all the major theorems and their derivations. You can acquire this knowledge by rote. But someone who understands geometry can reason geometrically about new problems, apply geometrical insights in different areas, assess the limits of geometrical reasoning for the task at hand, and so forth. Understanding a historical event like the Athenian victory is not exactly like understanding geometry, since the applications and extensions are more tentative, the range to which insights can reasonably be applied is more restricted, the evidence for a successful application is empirical (and may be hard to come by), and so on. But in both cases understanding involves an adeptness in using the information one has, not merely an appreciation that things are so. Evidently, in addition to apprehending connections, an understander needs the ability to use the information at his disposal.
Know-How
Understanding is widely held to be a matter of grasping. The difficulty is to spell out in nonmetaphorical terms what grasping is. I suggest that an important element of grasping is knowing how to exploit the information or insight one’s understanding provides. Someone who understands a proposition knows how to wield it to further her cognitive (and perhaps practical) ends. Someone who understands a topic knows how to use the epistemic resources her take on that topic affords. To make this out I need to take a detour to consider the nature of know-how.
Ryle (1949/2009) contends that knowing how is entirely a matter of habits and dispositions. To know how to ride a bicycle, he believes, is just to be disposed to behave (or to be in the habit of behaving) in certain ways while astride a bicycle. Obviously knowing how to ride a bicycle does not consist in a disposition to engage in a single specific behavior. Knowing how to ride a bicycle is not like a propensity to dissolve in water or to shatter when struck. Ryle construes knowing how to do something as a multitrack disposition, “consisting of more or less dissimilar exercises” (1949/2009, 56). Knowing how, he believes, is a propensity to perform any of a variety of systematically linked but distinct acts in a range of diverse but not wholly unanticipated circumstances. Since circumstances vary, sensitivity to circumstances gives rise to a cluster of available responses.
A standard criticism is that Ryle’s theory is excessively behaviorist. He explicates virtually every mental predicate as a disposition to overtly behave somehow or other (Carr, 1979). But we need not accept Ryle’s entire theory of mind to accept (or adapt) his explication of know-how. Nor need we hold that all the habits and dispositions involved in knowing how to do something are habits and dispositions to overt behavior. A dispositional account can recognize that knowing how often involves dispositions not only to behave, but also to think, notice, infer, and/or feel; to ignore, marginalize, emphasize, and/or find salient. To construe knowing how dispositionally is to characterize it in terms of propensities, or readinesses, or reluctances to do various things in various circumstances. It may involve propensities to think certain things, to represent things mentally in certain ways, to feel certain emotions, and to refrain from thinking, representing, or feeling others. No commitment to behaviorism is required for a dispositional account of know-how. Indeed, the knowing how that figures in epistemic understanding is largely if not completely mental. It is a disposition to reason well about a given topic in a range of relevant circumstances.
Whether or not Ryle is correct to identify knowing how to do something with a multitrack disposition, know-how clearly involves multitrack habits and dispositions. A person does not know how to ride a bicycle unless she is disposed to peddle, steer, and maintain her balance on a bike. And in different circumstances (when the surface is slippery, in traffic, on steep hills, over rough terrain, etc.) different fine-grained behaviors are required to peddle, steer, keep one’s balance, and so forth. A person does not know how to recognize ad hominem arguments unless she is disposed to spot the fallacy in a variety of rhetorical guises.
Knowing how to φ does not require reliably φ-ing. In basketball, even the best outside shooters make fewer than half of the three-point shots they attempt.6 That they even come close to 50 percent is a tribute to their know-how. A recently paralyzed pianist still knows how to play the Moonlight Sonata even though she can no longer display her know-how. An emergency medical technician knows how to perform CPR even though she is never called upon to do so. These caveats are all compatible with a Rylean position.
But knowing how is not a mere multitrack disposition. Knowing how is an achievement. It involves a capacity to do something well, or rightly, or correctly. An adequate explication should do justice to this normative character. Some habits are bad; some are neutral; some are good. Some dispositions are benign; some are beneficial; some lead us astray. If someone who takes himself to be serious about tennis is complacent about habitually stepping on the base line while serving, he evidently does not know how to serve. If he is unconcerned about or even unaware of his habit of wiping his brow before serving, it makes no difference. That habit is irrelevant to whether he knows how to serve. If he is indifferent to his propensity to hit the ball into the net, he does not know how to serve. On the other hand, if he reliably serves into the diagonally opposite service box, rarely double faults, occasionally aces, and recognizes the value of doing so, he knows how to serve. What is missing from Ryle’s account is the normative element. But what sort of normativity is at issue here?
Abel (2012) characterizes knowing how as rule-following: actions take place within practices, and the rules of the practices supply the norms that govern the actions those practices embed. Whereas bad habits and dispositions are propensities to flout relevant rules, and neutral habits and dispositions are uninfluenced by the rules, knowing how consists in a propensity to follow the rules. If Jim knows how to play chess, his chess-playing behavior typically follows the rules of chess. If Jane knows how to play tennis, her tennis-playing behavior typically follows the rules of tennis. This seems almost trivial. But it raises a number of questions.
One is whether all knowing how is a matter of following the rules of a practice. Games like tennis and chess are plainly rule-governed. So are practices like standing in line and paying one’s taxes. Participants have a pretty good idea what the rules are and what it is to follow them. But not all knowing how is keyed to the norms of a practice. Consider knowing how to swim (by which I mean no more than to propel oneself through deep water so as not to drown). Dogs can swim. They do not follow the rules of a practice. Why should we think that our basic ability to propel ourselves through water is different from a dog’s? If a child learned to swim by mimicking the motions of her dog, would we say that she did not know how to swim? Or consider Abel’s example of tying a necktie. Suppose someone regularly engages in a variety of deviant contortions that reliably result in a perfect Windsor knot. Should we say that he does not know how to tie the necktie simply because he fails to follow the rules for necktie tying that are canonical in his society? Or should we say, ‘If it works, it works’? Some know-how appears straightforwardly consequentialist. The standard for displaying it seems to be no more than reliably producing the desired result. In such cases the end justifies the means. Beyond the rules that govern all actions within a given practice (such as ‘Don’t kill anyone while doing it’), the rationale for the behavior that constitutes a straightforwardly consequentialist action seems to be justified by the ends it seeks to promote, not by rules of the practices (if any) it belongs to. It is not obvious, then, that knowing how to perform straightforwardly consequentialist actions is properly explicated as rule-following.
Still, much know-how seems to be a matter of following the rules of a practice. And it is plausible that the know-how required for epistemic acceptance is practice based. So let us consider such cases.
What is it to follow a rule? A plausible answer is that to follow a rule is to intentionally regulate one’s behavior by reference to the rule. The novice chess player mutters to herself, ‘The bishop moves diagonally’, then moves her bishop along a diagonal. As a general account, this will not do. First, it apparently sets off an infinite regress. Since language is itself a rule-governed practice, the novice would have to invoke rules for interpreting her muttering, and rules for interpreting those rules, and so forth. We cannot do this indefinitely. Nor can we plausibly maintain that there is a self-interpreting level of discourse where the regress ends. Second, it is no accident that my example concerns what a novice chess player might do. An experienced player—someone who knows how to play chess—does no such thing. In Wittgenstein’s (1953, §219) terms, she acts blindly. Although she may deliberate about strategy and tactics, she has so internalized the rules governing ways the various pieces can move that they have become second nature to her. For her, to be a chess bishop is to be able to move only along a diagonal. Once she recognizes a chess piece as a bishop, how it can move is settled. No inference need be drawn, no rules consulted. The capacity to act blindly while being subject to norms requires explanation.
If we act blindly in exercising know-how, what role do the norms play? We evidently do not consult them or intentionally regulate our behavior by reference to them. Once we know how to do something, doing it in appropriate circumstances is second nature to us. It might seem then that knowing how is simply a matter of automatically, unthinkingly behaving in accord with the norms of a practice.
This will not do. Knowing how is sensitive to why we automatically, unthinkingly behave as we do. Consider the following case: Except in New York City, drivers in the United States are permitted to turn right at a red light unless a sign saying ‘No Turn on Red’ is posted at the intersection. In New York City, right turns on red are never permitted. Drivers from out of town tend to be unaware that New York is an exception to the general rule. Suppose Meg, a denizen of a small town in Kansas, is driving in New York. Unsurprisingly, she finds the experience harrowing. She stops at every red light, not because she is aware of or sensitive to the law, but because she considers New York drivers and pedestrians reckless and wildly unpredictable. She deems it safer to proceed only when the light is green. She acts in accord with the law, but not on account of it. The regularity in her behavior is not an instance of following the traffic law. Although it may be an instance of knowing how to drive safely, it is not an instance of knowing how to obey New York traffic laws. Acting in accord with the law is not the same as acting on account of the law (see Kant, 1981). And only acting on account of the law qualifies as knowing how.
Virtue
Again we face the tension: On the one hand, knowing how to follow the rules of a practice seems to require us to be cognizant of those rules; on the other, we act blindly. How is it possible to do both? Here it pays to turn to Aristotle. The virtuous person, Aristotle says, does the right thing, in the right way, at the right time, for the right reason; and she does so from a firm and stable character (Aristotle, 1985, 1105a30). But she does not, and need not, deliberate about what to do. She need not even be conscious or expressly aware of why she does what she does. For being virtuous, she has internalized the rules. Doing the right thing in the right way, at the right time, for the right reason has become second nature to her. Aristotle (1985, 1103b) likens virtues to crafts. Anything that can be done can be done well or badly. And to do something well—not accidentally, but as a result of a stable, acquired disposition—is to do it with a trait that is, or is at least analogous to, a virtue. A good harp player knows how to play the harp and normally displays that know-how when playing the harp; a good builder knows how to build well and normally displays that know-how when building.
I suggest that, being sensitive to norms, agents who follow rules blindly exhibit something akin to Aristotelian virtues. Although Aristotle restricts the term ‘virtue’ to characteristics that make the actions of certain agents morally or intellectually good, I shall use it in a broader sense. Virtues are what make the actions of certain agents (those who standardly do the right things in the right way at the right time for the right reasons) good of their kind. The virtues integral to a practice are various, and some are matters of degree. The propensity to follow the rules of chess at all is a real but minimal virtue in a chess player. The propensity to devise and execute complicated strategies effectively is a greater chess-playing virtue, for it makes one a better chess player.
What are rules for the novice transmute into virtues when they are internalized so that they automatically, unthinkingly guide practice. The attractive element in Ryle’s account of multitrack dispositions is that it accommodates sensitivity to circumstances. What Abel and Aristotle add is that the sensitivity in question is not just to the physical, material, or sociological circumstances, but also to the normative circumstances. Human behavior is circumscribed by norms. Being duly sensitive to circumstances involves being sensitive to the norms of the practices one takes part in. Such sensitivity is a part of knowing how to participate in those practices, for the norms govern what may be done, what must be done, and what must not be done within the practice. If this sensitivity has become second nature, we need not deliberate, and may not be able to articulate the norms that constrain and guide us. Still, our behavior is responsive to those norms.
Dispositions have a counterfactual dimension. To ascribe a disposition is to indicate something not only about what does happen, but also about what would happen had circumstances been different. The glass that never is struck and never breaks nonetheless has the disposition of brittleness if it would break if it were struck. Similarly, I suggest, for dispositions that involve norms. Someone who has internalized the rules of the road automatically and unthinkingly follows them. She does the right thing. But given that her behavior is automatic, what makes it the case that she does it for the right reason? The answer depends on what counterfactuals are true of her. Meg is not only ignorant of the law pertaining to right turns in New York, she is also completely indifferent to it. She would not turn right on red in New York no matter what the law allowed. Although Mark, like Meg, stops at every red light as he drives in the city, he would often turn right on red if the law allowed. His driving behavior is constrained by the law in a way that hers is not. His propensity to modulate driving to the local laws is evidence that he knows how to drive in New York. His disposition is, as hers is not, sensitive to the normative structure of the New York City traffic laws. Displaying that sensitivity constitutes acting for the right reason.
Internalizing the norms of a practice does not just engender a disposition to behave, but a normative disposition—a disposition to hold oneself accountable. Someone who has internalized the norms of a practice considers herself subject to criticism if she violates those norms. She may flinch, or blush, or correct herself, or glance furtively around to see if anyone noticed. She may resolve to do better next time. She may also consider herself entitled to disapprove of, criticize, or correct other participants in the practice who violate its norms, and perhaps to praise or admire those who observe the norms.
The norms that concern us are epistemic norms, norms that bear on thinking or reasoning or arguing well. A fluent speaker of a language typically follows its grammatical rules automatically. She may be unable to articulate the rules she follows. She may even harbor doubts about the correctness of the rules a knowledgeable grammarian proposes. When asked what is wrong with a particular construction, she might have nothing more helpful to say than that it sounds funny. This is surely an instance of following the rules blindly. But a fluent speaker is not a flawless speaker. Occasionally she says something odd. Some odd utterances are simply unexpected. In a discussion of reverberations, Maude says, ‘A duck’s quack does not echo’. Although her claim is surprising, there is nothing untoward about her utterance. Not considering it problematic, she is not embarrassed about having uttered it and is not inclined to correct it. Nor are other speakers of the language apt to take her to task. Other utterances are factually incorrect. These may go uncorrected because the speaker is unaware of the error. If she realizes her error, she is likely to rescind or correct her claim. But to become aware, she needs either to acquire new information or to be reminded about information she already has. Then she admits (at least to herself), ‘I was wrong to say that Peoria is in Indiana; it is in Illinois’. Her correction has a different semantic content from her original claim. Yet other utterances are grammatically flawed. Here, the error may be obvious to the speaker as soon as the words leave her mouth. Perhaps she says, ‘The data demonstrates that the ice caps are melting’. She immediately recognizes that ‘data’ is a plural noun and requires a plural verb. The correction she makes is to simply change the verb form. The substantive semantic content of the claim remains the same. If she fails to recognize her error, other speakers—even those who know nothing about what the data are or show—can correct her mistake. The recognition of a need for correction shows that the agent takes herself to be answerable to a norm. The kind of correction she makes indicates what norm she takes herself to be accountable to.
An adept reasoner does much the same thing. She constructs sound arguments, draws on relevant evidence, holds herself responsible for flaws in her reasoning. The corrections she makes or accepts, as well as the principles she adduces, are indications of the norms she takes herself to be answerable to.
What may be articulable as the rules and conventions that, from the outside, constitute an agent’s rule-following behavior, function as quasi-Aristotelian virtues in the agent’s own sense of what he is doing. Once he knows how to play chess, tie a necktie, construct an argument, or speak grammatically, he does the right things at the right times for the right reasons, and does so from a steady disposition. The regularities that characterize his behavior have become second nature. And the right reasons are internalized norms.
Abel maintains that knowing how is more fundamental than knowing that. If so, the model provided by the novice chess player is misleading. She internalized antecedently articulated rules. And she was expressly aware of the rules before she internalizes them. This sometimes happens. But, Abel maintains, often no articulated rules are available. A speaker learns her native language by being brought up in a community where it is spoken. She models her utterances on those of other speakers, and subjects her linguistic behavior to correction from them. She counts as fluent when, in the opinion of her compatriots, she speaks like a native. That is all it takes. The process can occur without explicit instruction in the rules of grammar. Indeed, it can occur in a linguistic community whose grammar has never been codified. Unlike chess, where the constitutive rules are prior to the practice, grammatical rules precipitate out of the practice. What makes a construction grammatical is that fluent speakers treat it as such. They understand it and do not think it needs correction. Rather than saying that the language learner internalizes the rules, it would be more accurate to say that the linguist externalizes the linguistic virtues of competent speakers.
This sheds light on how to resolve Wittgenstein’s worry about rule-following (Wittgenstein, 1953; Kripke, 1982). Like Abel, Ginsborg (2010) recognizes that not all norms are reducible to rules. To evade the skeptical puzzle Kripke identifies as arising from the absence of rules, she argues that some norms are primitive. When asked what comes next in a series, or what the sum of 68 and 57 is, she maintains, there is an answer that we primitively ought to give. That answer is right: other answers are wrong. This is so even though it is possible to articulate a rule that a ‘deviant’ answer would conform to. Ginsborg characterizes primitive normativity negatively. It is “normativity which does not depend on conformity to an antecedently recognized rule” (2010, 233). She evidently assumes that either normativity is grounded in rules or it is sui generis. If there are virtues that are not the internalization of antecedently recognized rules, they are, on her view, primitively normative. We ought to act on them, but there is just no saying why.
This seems wrong. Practices are public; a performer learns to conform to their norms, and is subject to criticism and correction if he fails to conform. Knowing how is, as Abel says, a product of “triangular relations of subject, other subjects or agents, and the world” (2012, 248). A four-year-old child is given the first numbers in the sequence ‘1, 2, 3’ and asked what comes next. She might answer ‘4, 5, 6’; or she might answer ‘5, 8, 13’. If she does the latter, her answer is mathematically impeccable; the numbers 5, 8, 13 are the next ones in the Fibonacci series. Still, we want to say, her answer is incorrect. If correctness turns entirely on the rules of mathematics, we have no grounds for criticizing her. But if correctness turns on attuning herself not just to the rules of mathematics but to the practice she is participating in, things are different. Given the practice in effect in her preschool classroom, she has reason to give and prefer the standard answer. Assuming that the class is not studying arcane mathematical sequences, the immediately subsequent integers are standard. Because Abel recognizes the importance of other agents, he has the resources to assess practices, and assess particular behaviors within practices from a perspective that Ginsborg, who looks only at the agent, her past intentions, and her current mindset, cannot. Abel can say, as Ginsborg cannot, that what makes an action correct is that it is required (or permitted) by a practice, and that practice promotes something that the members of a given community regard as worth achieving. He can look outward to the public good that the norms achieve, rather than exclusively inward to what the agent thinks she is trying to do.
We are brought up in practices, and often learn from examples. So, unlike the chess novice, we may never have learned the “rules” of practices we participate in. Indeed, such practices may have few articulable rules. We were simply socialized to emulate adept practitioners. This is why native speakers can fail to recognize, much less be able to state, the grammatical rules of their language. Outsiders—perhaps linguists or anthropologists—may formalize the normative regularities that they find in the practice. But practices proceed without expressly formulated rules. The fact that practitioners not only typically conform to certain regularities but teach others to conform, and correct or disparage the behavior of nonconformists, makes it manifest that norms are operative. Normatively informed behavior, then, is more extensive than explicitly rule-governed behavior.
The novice tennis player hits hundreds of balls in learning how to serve. The novice cellist saws away for untold hours in learning how to bow. Abel insists that learning by doing is typically needed to acquire know-how. Aristotle agrees. One becomes just by doing just acts. But Aristotle emphasizes that “the sources and means that develop each virtue also ruin it” (1985,1103b9). What the novice does repeatedly can be repeatedly done well or repeatedly done badly, or intermittently done well and done badly. Only if it is done well will repetition lead to the development of a virtue. Rote repetition will not do. The novice’s actions must be monitored (by himself or others), and encouraged or corrected as appropriate.
That being so, the student needs standards by which to judge. But if the actions are ones for which there is no adequate articulable rule, where do they find the standards? They appeal to exemplars—telling instances—where the action is manifestly well done. With or without the aid of a mentor, the novice emulates the behavior of those who already know how to perform the actions he seeks to master. We will discuss exactly what such emulation involves in chapter 9. For our purposes here, it is enough to recognize that it is an avenue to acquiring know-how.
The epistemic norms of knowing how are quasi-Aristotelian virtues; they are goods realized in action and may be uncharacterizable apart from the practices they belong to or the ends they promote. When this is so, it is impossible to state exactly what knowing how involves. But this does not make knowing how epistemically inaccessible, or learning how mysterious. A student can learn how to perform the action by emulating exemplary performances of it. Once his behavior accords with his exemplar, he knows how to do the action in question. Knowing how, then, is not inscrutable so long as we have the resources to identify and interpret exemplary instances.
Although knowing how is subject to epistemic norms, it is fundamentally different from knowing that. It is not an attitude toward the truth of a sentence or proposition. That Fred knows how to tie a necktie is either true or false. But his knowing how is not itself truth evaluable. Nor is knowing how a matter of belief. Molière’s M. Jourdain knew how to speak in prose, even though he did not believe that he knew how to do any such thing. Henceforth, for clarity, when I use the term ‘knowledge’ and related terms without qualification, I will be speaking of knowledge that.
I said earlier that an understanding of a topic involves know-how. We now can see that it involves knowing how to wield the commitments that bear on the topic—how to draw the inferences and perform the actions that the understanding licenses. That know-how is, in Rylean terms, a multitrack disposition—an ability and propensity to make certain inferences and eschew others, to perform certain actions and refrain from others, to engage in and endorse certain forms of higher-order evaluation and criticism and avoid and repudiate others. The network of commitments functions normatively. It constitutes the permissions and prohibitions that constrain and facilitate the epistemic agent’s relevant thoughts and actions (see Hetherington, 2011). In Sellars’s (1963, 169) terms, the network structures a space of reasons. If the agent has internalized the commitments, she may deploy them blindly. In that case they function as quasi-Aristotelian intellectual virtues.
Earlier I characterized epistemic acceptance of φ as a willingness and ability to use φ as a basis of inference or action when one’s ends are cognitive. That ability is a matter of know-how. When an epistemic agent accepts a proposition, rule, norm or account, she knows how to use it to further her relevant cognitive ends.
Factivity
Knowledge is factive in that one does not know that p unless ‘p’ is true. So if propositional understanding is knowledge of dependencies, it is factive. We would not say that Lavoisier understood that phlogiston is the volatile element in combustion, since it isn’t. But objectual understanding concerns topics rather than individual propositions. So what it means to claim that objectual understanding is factive is a bit harder to make out. Perhaps objectual understanding is factive if it is impossible to understand a topic—say, the history of Athenian warfare—unless one is committed to some identifiable, suitably comprehensive proposition that is true. That proposition might be the long conjunction of all the atomic propositions belonging to the coherent body of information that constitutes the understanding. (This parallels the interpretation of coherence theories of knowledge as requiring the truth of the conjunction of the atomic propositions in a coherent system of beliefs.) On such an account, understanding would be a sort of knowledge, namely the knowledge captured in long, subject-matter-connected conjunctions.
This proposal faces several problems, beyond its difficulty in accommodating science. First, it does not respect the requirement that the understander grasp the relations among the atomic propositions—that the understander appreciate how they bear on one another. Although the body of information understood must be coherent, if the understander need only know the conjunction, there is no requirement that she grasp the coherence. Second, it does not accommodate the insight that the student who understands geometry can do more with it than the student who knows the axioms, the main theorems, and their derivations by rote. Third, it is at odds with the recognition that not all the propositions that comprise a genuine understanding of a topic need be true. We would be inclined to say that a historian understood the Athenian victory even if he harbored a few relatively minor false beliefs about the matter.
Although Kvanvig (2003) considers understanding factive, he concedes these points. He does not believe that understanding a topic consists in believing a long conjunction. Nor does he insist that every proposition in the comprehensive body of information that constitutes an epistemic agent’s understanding be true. Rather, he maintains, an agent cannot understand a topic unless most of the propositions and all of the central propositions that constitute her coherent take on that topic are true. He allows that a few peripheral falsehoods can degrade an agent’s understanding of a topic without destroying it. That understanding is factive in this sense is the thesis I want to dispute.
Unlike knowledge, understanding admits of degrees. A freshman has some understanding of the Athenian victory, while her teaching fellow has a greater understanding and her professor of military history has an even greater understanding. Epistemology should explain what such differences in degree consist in. A factive account can easily recognize three dimensions along which understanding can vary: breadth, depth, and significance. The professor might have a broader understanding of the Athenian victory, being able to embed his coherent body of largely true beliefs into a more comprehensive account of Greek warfare. He might also have a deeper understanding. In that case, his web of belief is more tightly woven; it contains more propositions, and/or more nontrivial inferential connections among propositions. But according to a factivist epistemology, both the student and the professor understand the Athenian victory insofar as they grasp coherent bodies of predominantly true propositions, and believe the propositions that belong to those bodies. The student and the professor might weigh the facts differently. Even if each believes a given truth and incorporates it into a coherent account of the matter, the professor might consider it highly significant, while the student considers it just another truth about the battle. If the truth really is significant—if, for example, it is central to explaining how the Athenians’ novel battle formation contributed to the victory—then the professor’s better understanding consists in his appreciating the significance of the truth, not merely in his recognizing that it is a truth. Strevens (2008, 2016) is a factivist who allows for what I call felicitous falsehoods; he holds that not all (or even most) of the elements of an objectual understanding need be true. But, he insists, those that are difference makers must be true. So the professor’s broader understanding consists in his incorporating more difference makers into his account; his deeper understanding consists in there being tighter connections among the difference makers. And what is important is not the weight the professor assigns to every element of the account, but the weight he assigns to the difference makers. Factive accounts, then, can accommodate some differences in degrees of understanding.
However, there is another dimension along which we can measure greater and lesser understanding which factivists cannot take on board. It involves conceding that some accounts, even though they are not true, nonetheless display a measure of understanding. The growth of understanding often involves a trajectory from contentions that, although strictly false, are in the same general neighborhood as contentions that are closer to the truth. The sequence may terminate in truths. But even the earlier steps in the sequence should fall within the ambit of epistemology. For they are, to an extent—often to a considerable extent—cognitively valuable.
An eight-year-old’s understanding of human evolution might include as a central strand the proposition that human beings descended from apes. A more sophisticated understanding has it that human beings and the other great apes descended from a common hominid ancestor who was not, strictly speaking, an ape. The child’s opinion displays some grasp of evolution. It is clearly cognitively better than the belief that humans evolved from butterflies. But it is not strictly true. Since it is central to the child’s take on human evolution, factivists like Kvanvig must conclude that her take on human evolution does not qualify as understanding. Unless we can plausibly abstract from the child’s claim about apes to some more generic ‘ape-like creatures’, which may be difficult if she does not distinguish between apes and ape-like creatures, Strevens cannot take her to harbor an understanding either. In that case, epistemology need give no account of what makes the child’s grasp of evolution cognitively good, or cognitively better than a view of her classmate who holds that humans evolved from butterflies. This may not appear to be a major objection, since the child’s opinion is fairly naïve. Perhaps it is reasonable to conclude that she does not (really) understand. But the pattern exhibited in this case is endemic to scientific education. We typically begin with rough characterizations that properly orient us toward the phenomena, and then refine the characterizations as our understanding of the science advances. Think of the trajectory from naïve folk physics through Newtonian mechanics to relativity and quantum mechanics.
Kvanvig (2003) believes that when we construe such a take on a subject as understanding, we use the term ‘understanding’ in an honorific sense, just as we use the term ‘knowledge’ in an honorific sense when we speak of ‘the current state of scientific knowledge’, while conceding that some of what belongs to the current state of scientific knowledge is false. Such honorific usages of epistemic terms, he maintains, are extended usages that fall outside the scope of epistemology. Only in an extended sense, then, does the child have any understanding of evolution.
Perhaps it would be feasible to dismiss such uses of ‘understanding’ as merely honorific if they applied only to young children or neophyte students of a subject. I think otherwise, for I believe that epistemology should have something to say about what makes the views of the child who thinks that humans evolved from apes better than the views of a child who thinks that humans evolved from butterflies. But the main problem with the contention that understanding is factive is that the trajectory displayed as she moves from the naïve view of human evolution up to the view held by the evolutionary biologist is the same trajectory that science displays in the sequence of accounts it develops. It is intellectually arrogant to insist that it is only in an extended sense that a contemporary biologist understands morphological evolution, given that the precise role of cis-regulatory sequences (noncoding sequences of DNA) is currently unclear. That there are always unclarities at the cutting edge of inquiry does not diminish the epistemic status of the understanding that brought us to the current cutting edge.
A central tenet of Copernicus’s theory is the contention that the Earth travels around the sun in a circular orbit. Kepler improved on Copernicus by contending that the Earth’s orbit is not circular but elliptical. Newton realized that because the planets exert gravitational force on each other, the Earth’s orbit is not quite elliptical. Having abandoned the commitment to absolute space, current astronomers can no longer say that the Earth travels around the sun simpliciter, but must talk about how the Earth and the sun move relative to each other. Despite the fact that Copernicus’s central claim was strictly false, the account it belongs to constitutes a major advance in understanding over the Ptolemaic account it supplanted. Kepler’s and Newton’s accounts are further advances in understanding, and the current account is yet a further advance. The advances are clearly cognitive advances. With each step in the sequence, we understand the motion of the planets better than we did before. But no one claims that science has as yet arrived at the ultimate truth about the motion of the planets. Should we say that the use of the term ‘understanding’ that applies to such cases should be of no interest to epistemology?
One might follow Kvanvig and contend that even here the use of ‘understanding’ is honorific. We apply the term in these cases only because we think that the strides scientists have taken are on the way to the truth—the comprehensive, general account of celestial motion that gets it right. In effect, current science borrows its epistemic status from its descendants. Sellars (1963) argues that in a mature science, later theories should show why their predecessors were right to the extent that they were. So later theories are supposed to at least partially vindicate their predecessors. Where this does not happen, we are apt to conclude that the earlier scientists did not understand the phenomena that their theories purported to explain. We do not, for example, consider phlogiston theorists to have had any understanding of combustion.
Suppose we concede this point. Let us admit that in saying that the various astronomical accounts embody an understanding, we take out a lien on the future of science. Still, I would urge, the cognitive achievements embodied in such accounts should be a central concern for epistemology. Even if we do not yet have (and may never get) the truth, we have made real cognitive progress. We understand the motions of celestial bodies better than our predecessors did. Epistemology should explain what makes current understanding better. If we say that the uses in question are honorific, epistemology should explain why certain attitudes toward certain topics are worthy of honor.
Another aspect of science is even more troublesome for the factive view—namely, science’s penchant for idealization. Science streamlines, simplifies, and distorts. It devises and deploys comparatively austere models that diverge from the phenomena it seeks to explain. The ideal gas law accounts for the behavior of gases by describing the behavior of a model gas composed of dimensionless, spherical molecules that are not subject to friction and exhibit no intermolecular attraction. The Hardy—Weinberg formula describes the distribution of genes in an infinite population whose members mate randomly. There are no such things. Indeed, as far as we can now tell, there could be no such things. But the ideal gas law figures in the understanding provided by thermodynamics and the Hardy—Weinberg formula figures in the understanding provided by population genetics. Scientists purport to understand the phenomena in terms of these laws. The contention that such laws degrade but do not destroy understanding is simply not credible.
Idealization is not taken by scientists to be an unfortunate expedient, but rather to be a powerful tool. Although they expect today’s idealizations to be replaced, they harbor no expectation that in the fullness of time idealizations will be eliminated from scientific theories. So the ‘promissory noteishness’ that we saw in talk about the progress in our understanding of celestial motion has no role here. Elimination of idealizations is not a desideratum. Nor is consigning them to the periphery of a theory. It is simply not the case that the bodies of information that constitute scientific understanding are, or that their ultimate successors can be expected to be, composed of truths, with any residual falsehoods occurring only at the periphery. The ideal gas law lies at the core of thermodynamics, and some such model is likely to lie at the core of any successor to current theories.
I concede that many of the propositions that fall within the scope of ‘the current state of scientific knowledge’ are not strictly knowledge because they are not true. If we are being scrupulous, we should probably not speak of the current state of scientific knowledge unless we are convinced that the propositions in question are true. But the contention that ‘understanding’ is factive does not have the same strong support from ordinary language. When ‘understanding’ applies to large, often somewhat inchoate bodies of information, it takes a direct object that is not a proposition. Jill understands the Athenian victory, Joe understands the motions of the planets, Pat understands the New York subway system. We typically acknowledge that people can have a measure of understanding even if the contentions making up the bodies of information they endorse diverge somewhat from the truth. So our ordinary use of ‘understanding’ as applied to bodies of information does not supply a strong argument for a factive analysis. There is, however, a recognition that ‘understanding’ is a cognitive success term. If I am going to reject the factive analysis, I need some way to identify or characterize that cognitive success.
Notes
1. The parenthetical caveats are included to allow for the possibility that some knowledge—e.g., perceptual knowledge—is direct knowledge and not in need of justification. I do not believe that this is so, but at this point in the argument it is advisable to leave this possibility open.
2. This maneuver is modeled on the ‘corrected doxastic system’ in Lehrer’s (1974) epistemology.
3. Although it is undeniably a cognitive accomplishment, I also bracket understanding a language and related feats like understanding a concept or a passage of prose. Understanding a language is a matter of being capable of interpreting and, perhaps, speaking, reading, and/or writing it correctly. It is integral to understanding in general. But on the face of it, it is not the same as understanding a topic, so for now I set it aside.
4. ‘Hardly more secure’ rather than ‘no more secure’, because a measure of additional support is supplied by the fact that military strategists agree that such a strategy might work.
5. The restriction to cases where her ends are cognitive is crucial. Depending on the topic and her attitude toward the topic, she may be unwilling all things considered to use the information in reasoning or in action.
6. I owe this example to Kent Bach.