1. The nature of understanding-why

Before addressing the objection to veritism, a few words on the nature of understanding-why are in order. Philosophers generally agree on two necessary conditions for understanding-why. (C1) Understanding why p requires believing the truth that p is the case because of q.Footnote ³ (C2) Understanding why p requires grasping how p depends on q. Yet there is no consensus about what “grasping” precisely consists in. Since this paper mainly discusses the ideas of Stephen Grimm, Alison Hills, and Duncan Pritchard, I will only introduce their accounts of grasping.Footnote ⁴

First, following Woodward (Reference Woodward2003), Grimm holds that to grasp how the different aspects of a system depend upon one another is “to be able to anticipate how changes in one part of the system will lead (or fail to lead) to changes in another part” (Grimm Reference Grimm, Bernekjer and Pritchard2010a: 89; cf. Grimm Reference Grimm2006). To illustrate this idea, Grimm (Reference Grimm, Bernekjer and Pritchard2010a, 2014) offers the following example: Suppose that your knee bumps the table at your local coffee shop, leading your cup to spill, and that I am a few tables over, taking this all in. To understand why the coffee spilled, I must not only believe that the coffee spilled because of the jostling, but also grasp how the spilling of the cup depends on the jostling of the knee, that is, to have an ability to anticipate what things would have been like, if the bump were less forceful, or if the knee bump did not occur, or if it were a fist bump instead, etc. Grimm further suggests that this idea of grasping can also be put in terms of the ability to answer what-if questions. For if one is able to anticipate how changes in one part of the system will lead (or fail to lead) to changes in another part, then one is able to answer a series of the relevant “What if …?” questions, and vice versa. Thus, to grasp how p depends on q is to be able to answer a series of the relevant “What if …?” questions.

Second, on Hills’ (Reference Hills2016) view, grasping a relationship between two propositions requires “cognitive control,” which is a set of abilities. These abilities include following some explanation of why p given by someone else, giving an explanation of why p in your own words, drawing the conclusion that p (or that probably p) from the information that q, etc. (Hills Reference Hills2016: 663). Further, Hills suggests that to have cognitive control to a great enough extent is to able to answer a series of the relevant “What if …?” questions, as she writes, “After all, how do you test whether someone really understands why global warming is occurring …? You ask them a series of ‘What if …?’ questions. What if the initial conditions were different? What would be the consequences? What if there was a different outcome? How could that be explained?” (Hills Reference Hills2016: 666). Hills suggests if one cannot answer these questions, one does not understand why p very well, whatever else one can do. Thus, Hills largely agrees with Grimm that to grasp a dependency relationship is to be able to answer a series of the relevant “What if …?” questions.

Finally, Pritchard claims that grasping how q depends on q amounts to an ability to give an explanation of why p. He writes, “There is more to understanding why an event took place than simply having some conception of how cause and effect might be related. In particular, what is required is some sort of grip on how this cause generated this effect, a grip of the kind that could be offered as an explanation were someone to ask why the event occurred” (Pritchard Reference Pritchard and Fairweather2014a: 321). Pritchard does not tell us what counts as an explanation, though. He might think that a legitimate explanation must take a certain specific form such as the DN model. But if he endorses a counterfactual theory of explanation and thinks that to give an explanation of why p is to answer a series of the relevant “What if …?” questions, then his account of grasping is no different from Grimm and Hills’.

So much for the nature of understanding-why. I will now turn to the major objection to the veritist account in recent literature.

2. The objection from testimony

Pritchard (Reference Pritchard, Pritchard, Millar and Haddock2010: 81) uses a case of testimony to argue that knowing that p because of q is not sufficient for understanding why p:

Drawing on similar cases, some philosophers (e.g., Grimm Reference Grimm and Fairweather2014; Hills Reference Hills2016) further suggest that understanding-why is not a species of propositional knowledge.

To this view, Sliwa (Reference Sliwa2015) responds that Pritchard is right – merely knowing via testimony that the house burned down because of faulty wiring is not sufficient for understanding why the house burned down. But it does not follow that understanding-why cannot be reduced to knowing a set of true propositions. If Pritchard's son also knows, via the fire expert's testimony, many other true propositions about faulty wiring, fire, and the house (in addition to the proposition that the house burned down because of faulty wiring), perhaps he would understand why the house burned down. Put differently, if Pritchard's son does not understand why the house burned down, that is because he lacks sufficient (propositional) knowledge. If he has sufficient knowledge, he will understand why the house burned down.

However, some philosophers would disagree with Sliwa. On their view, even if Pritchard's son acquires via testimony exactly the same beliefs (and thereby exactly the same knowledge-that) as the fire expert has, he might fail to have any understanding of why the house burned down. This is because understanding why p requires grasping how p depends on q, but one might acquire via testimony exactly the same beliefs as the testimony giver (who understands why X happened) has, but fail to have any grasp of how p depends on q. To establish this point, Ahlstrom-Vij and Grimm (Reference Ahlstrom-Vij and Grimm2013: 341) ask us to imagine an experienced fire investigator who is trying to teach her apprentice how to identify the causes of fires:

At this point, the investigator has explained everything she knows about how to identify the causes of fires, and she has answered every question the apprentice could ask. Further, the apprentice epistemically defers to the investigator and is willing to believe whatever the investigator says. Still, the apprentice feels puzzled about certain things, and unlike the investigator, she is unable to read a new complex fire scene on her own.

The best explanation of this, according to Ahlstrom-Vij and Grimm (Reference Ahlstrom-Vij and Grimm2013: 341), is not that the apprentice fails to believe certain propositions that the investigator believes, but that the apprentice does not – while the investigator does – “grasp certain causal dependencies between the variety of factors that went into the starting of the fire.” Thus, one might acquire via testimony exactly the same beliefs as the testimony giver (who is an expert and understands why p) has, but fail to have any grasp of the relevant dependency relations that the testimony giver has.Footnote ⁵

Drawing upon this idea, Ahlstrom-Vij and Grimm (Reference Ahlstrom-Vij and Grimm2013) raise the following objection to veritism:

1. (1) Understanding why p requires not only believing that p is the case because of q but also grasping how p depends on q.

2. (2) One might acquire via testimony exactly the same beliefs as the testimony giver (who is an expert and understands why p) has, but fail to have any grasp of how p depends on q.

3. (3) Thus, one might acquire via testimony exactly the same beliefs as the testimony giver has, but fail to have any understanding-why that the testimony giver has. (from 1 & 2)

4. (4) The person who understands why p is doing finally epistemically better than the person who does not (ceteris paribus).

5. (5) Therefore, one might be doing finally epistemically better than another even though they share exactly the same beliefs. (from 3 & 4)

6. (6) Veritism implies that two people who share exactly the same beliefs must enjoy the same final epistemic goods: One is not doing finally epistemically better than the other.

7. (7) Thus, veritism is false. (from 5 & 6)

This is the objection from testimony. We have explained Premises 1–3, which are endorsed by many philosophers (e.g., Zagzebski Reference Zagzebski and Steup2001, Reference Zagzebski2008; Pritchard Reference Pritchard, Pritchard, Millar and Haddock2010; Hills Reference Hills2016) who hold that grasping is an ability that often cannot be transmitted via testimony. And many seem to take Premise 4 to be a datum that a good account of the value of understanding-why should explain. Premise 5 follows from 3 & 4. Premise 6 is trivially true.

3. Why the objection from testimony fails

In this section, I will critically examine the objection and argue that Premise 2 is false. To refute Premise 2, we must show that if one acquires via testimony exactly the same beliefs as the testimony giver (who is an expert and understands why p) has, then one must have some grasp of how p depends on q. Here is an outline of my argument:

1. (1) If one acquires via testimony exactly the same beliefs as the testimony giver (who is an expert and understands why p) has, then one knows that p is the case because of q.

2. (2) If one knows that p is the case because of q, then one must be able to rule out a few alternatives to [p is the case because of q].

3. (3) If one is able to rule out a few such alternatives, then one must be able to answer a few relevant “What if …?” questions.

4. (4) If one is able to answer a few relevant “What if …?” questions, then one must have at least a rudimentary grasp of how p depends on q.

5. (5) Therefore, if one acquires via testimony exactly the same beliefs as the testimony giver (who is an expert and understands why p) has, one must have at least a rudimentary grasp of how p depends on q.Footnote ⁶

Premise 1 can be justified as follows. Since the testimony giver understands why p, she must believe the truth that p is the case because of q. Accordingly, if one acquires via testimony exactly the same beliefs as the testimony giver has, then one acquires via testimony the belief that p is the case because of q. Now the testimony giver is a reliable source of information (as she is an expert). It follows that if one acquires via her testimony the belief that p is the case because of q, one knows that p is the case because of q.

Premises 2 & 3 are both intuitively plausible. Reconsider the fire case. If one knows that faulty wiring caused the fire, then one must be able to rule out a few alternatives such as that a certain wire being red caused the fire, that the house spontaneously erupted into flames, that the house owner's washing his hands caused the fire, and so on. If one is able to rule out a few such alternatives, then one is able to answer a few “What if …?” questions such as “If the color of the wire were different, would the house have burned down? If faulty wiring did not occur, would the house have spontaneously erupted into flames? If faulty wiring did not occur, would the house have burned down if the owner washed his hands?” (N.B., Premise 2 can be derived from the more general principle that knowing that p entails the ability to rule out at least some alternatives to p. This principle is intuitively appealing. The relevant alternatives theory of knowledge purports to capture this intuition.)

Premise 4 is true according to Grimm and Hill's account of grasping, which I take for granted for the sake of argument. On this account, grasping how p depends on q is defined in terms of the ability to answer a series of “What if …?” questions. Premise 4 is couched in terms of “rudimentary grasp,” which indicates that grasping comes in degrees. Grimm (Reference Grimm and Fairweather2014) suggests that understanding-why comes in degrees because grasping comes in degrees, and grasping comes in degrees in the following sense: the more one's grasp of how p depends on q, the more relevant dependency relations one grasps, and the more “What if…?” questions one can answer. To illustrate, consider two people, S1 and S2, who both believe that X was caused by Y and have some grasp of how X causally depends on Y. Suppose S1 sees a middle step between X and Y: Y first caused M, which then caused X. Suppose S1 grasps both how X causally depends on M and how M causally depends on Y. Then S1's grasp of how X causally depends on Y consists of (a) a grasp of how X causally depends on M and (b) a grasp of how M causally depends on Y. By contrast, S2 does not see any middle step between X and Y. Consequently, S2 grasps neither how X causally depends on M nor how M causally depends on Y. Intuitively, S2 has less grasp of how X causally depends on Y than S1, for S1 grasps more relevant dependency relations than S2, which enables S1 to answer more “What if …?” questions than S2. For example, S1 can answers questions such as “If Y changed into Y*, how M would have changed?” and “What if a certain thing prevented M from happening?” S2 is unable to answer such questions.Footnote ⁷

Given Premises 1–4, it follows that Premise 2 of the objection from testimony is false. A logical consequence is that if one does not have any grasp of how p depends on q, then one cannot acquire via testimony exactly the same beliefs as the testimony giver (who is an expert and understands why p) has – in particular, one cannot genuinely believe that p is the case because of q. Put differently, genuinely believing the truth that p is the case because of q requires having at least a rudimentary grasp of how p depends on q. If it is not always easy to have a rudimentary grasp of how p depends on q, then transmission of belief and knowledge is not always easy, pace Zagzebski (Reference Zagzebski and Steup2001, Reference Zagzebski2008) and Hills (Reference Hills2016). The apprentice might fail to believe what the expert tells her even if she epistemically defers to the expert and is willing to believe whatever the expert says.Footnote ⁸

4. A new objection and why it also fails

Some might agree with my analysis above but think the objection from testimony can be strengthened. Specifically, given that grasping comes in degrees, one might acquire via testimony exactly the same beliefs as the testimony giver has, but have less understanding-why than the testimony giver has, for one might have less grasp of how p depends on q than the testimony giver has. In the case offered by Ahlstrom-Vij and Grimm, the apprentice, unlike the investigator, cannot read a similar new fire scene. The best explanation of this difference is not that the apprentice has no grasp of the relevant causal dependency, while the investigator has. Rather, the best explanation is that the apprentice has some grasp of the relevant causal dependencies, while the investigator has more grasp. The more grasp one has, the more understanding one has. Now the person who has more understanding-why is doing finally epistemically better (ceteris paribus). Thus, one might be doing finally epistemically better than the other even though they share exactly the same beliefs. It follows that veritism is false.

Interesting as this objection sounds, it cannot stand close examination. Here is why:

1. 1. Understanding-why entails not only grasping the relevant dependency relations but also assenting to what is grasped.

2. 2. To assent to what is grasped is to believe that what is grasped is accurate (or accurate enough).

3. 3. If S1 (e.g., the testimony giver) has more grasp of how p depends on q than S2 (e.g., the testimony receiver), then S2 does not have an exact idea of what S1 grasps.

4. 4. If S2 does not have an exact idea of what S1 grasps, then S2 cannot fully believe the proposition that what S1 grasps is accurate (or accurate enough).

5. 5. Therefore, if S1 has more understanding than S2 because S1 has more grasp of how p depends on q than S2, then they cannot hold exactly the same beliefs.

Let me explain each premise in turn. To appreciate Premise 1, it is important to see that one might grasp dependency relations without assenting to what is grasped. Consider a Pyrrhonian skeptic who does not believe any propositions or theories about fire. Yet this does not prevent her from grasping how the relevant true theories work: She might still be able to apply them to different particular cases and draw the correct conclusions about the cause of each fire. Thus, a Pyrrhonian skeptic might grasp real worldly dependence relations via grasping how a true theory works. But since she does not assent to the true theory and the propositions about particular circumstances, she does not assent to what is grasped. (N.B., this would not prevent a Pyrrhonian skeptic from living a normal life or teaching apprentices how to analyze a fire scene like a non-skeptic.)

I'd like to further suggest that grasping dependency relations without assenting to what is grasped is analogous to entertaining/considering a proposition without believing that proposition. Many philosophers (e.g., Strevens Reference Strevens2008; Grimm Reference Grimm, Bernekjer and Pritchard2010a; Greco Reference Greco, Timpe and Boyd2014; Hills Reference Hills2016) hold that we do not directly grasp real worldly dependency relations: We grasp real worldly dependency relations via grasping relations that hold among the propositional contents of our beliefs.Footnote ⁹ Put differently, what we directly grasp is a representation, i.e., the dependency relations between various propositions. We indirectly grasp real worldly dependency relations when the dependency relations between various propositions we grasp accurately represent or mirror the dependency relations between various facts (I will return to this point in section 6). This is just like we do not directly entertain/consider the facts. What we directly entertain/consider is a representation, i.e., a set of propositions. We indirectly entertain/consider the facts when the propositions we consider are true. Now we might entertain/consider a set of true propositions without believing them. Similarly, we might grasp an accurate representation of real worldly dependency relations without assenting to what is grasped. (Perhaps here is a better analogy: In order to believe a proposition, one must grasp the proposition. But one might grasp the proposition without believing it. To grasp a proposition is to see how some elements of the proposition are connected to other elements, that is, to grasp dependency relations between various elements of the proposition. Thus, in the case of grasping a proposition, one might grasp dependency relations without assenting to what is grasped. Grasping dependency relations between propositions is similar.)

In fact, some anti-veritists like Grimm note the possibility of grasping dependency relations without assenting to what is grasped. Grimm (Reference Grimm2010b: 341) makes a distinction between what he calls “simple grasp” and “conditional grasp.” Simple grasp is the case where “we grasp a representation in a straightforwardly assenting way, as when we take the representation to be the sober truth about the system it represents” (Grimm Reference Grimm, Bernekjer and Pritchard2010a: 89, my italics). By contrast, we conditionally grasp a representation when we do not straightforwardly assent to what is grasped, e.g., when we say “Supposing that Priestley was right, the lighting of the tinder was due to the presence of phlogiston.” Thus, for Grimm, simple grasp = conditional grasp + assent to what is grasped. I think the distinction between simple grasp and conditional grasp unnecessarily complicates the matter, for in the case of the so-called “conditional grasp,” we simply do not take the representation to be the truth about the system it represents, that is, we do not assent to what is grasped. Given this, I suggest what Grimm calls “conditional grasp” is better called “grasp per se” and what he calls “simple grasp” better called “grasp with assent.”

Intuitively, a Pyrrhonian skeptic who grasps how p depends on q without assenting to what is grasped does not understand why p, just like a Pyrrhonian skeptic who is able to ride a bike without believing what she rides is a bike does not know how to ride a bike.Footnote ¹⁰ This point is recognized by many philosophers. For example, Baumberger et al. (Reference Baumberger, Beisbart, Brun, Grimm, Baumberger and Ammon2017: 6) claim that understanding requires individuals to “possess a representation of what is understood” and that “the representation must in some way be accepted by the agent.”

So much for Premise 1 of my response. Premise 2 states that to assent to what is grasped is to believe that what is grasped is accurate (or accurate enough). Specifically, assenting is a doxastic/propositional attitude. To assent to a certain proposition is to believe that the proposition is true (or true enough).Footnote ¹¹ To assent to a certain non-propositional representation is to believe the proposition that the non-propositional representation is accurate (or accurate enough). Grimm and Hills suggest that what is grasped in the case of understanding-why is non-propositional representation. Let's grant this view for the sake of argument. Then to assent to what is grasped is to believe the proposition that what is grasped – a non-propositional representation – is accurate (or accurate enough).

A few clarifications. (1) First, the phrase “accurate enough” in the parentheses means something similar to what Catherine Elgin means by “true enough.” Elgin (Reference Elgin2004: 119) makes a distinction between belief and acceptance: “to accept a claim is not to take it to be true, but to take it that the claim's divergence from truth, if any, is negligible. The divergence need not be small, but whatever its magnitude, it can be safely neglected.” Simply put, “We accept a claim … when we consider it true enough.” However, this distinction between belief and acceptance seems unnecessary, for to take p to be true enough is just to believe that p is true enough. What Elgin actually draws is a distinction between believing that p is true and believing that p is true enough. Such a distinction can make sense of certain cases of understanding where the agent grasps dependency relations through an ideal model. Elgin claims that in such cases, the agent accepts the model without believing it is true. But this claim is essentially the same as the claim that the agent believes that while the model is not true, it is true enough.Footnote ¹² (2) In addition, the claim that the person with understanding-why believes the proposition that what she grasps is accurate (or accurate enough) is consistent with the claim that it can be difficult for her to express what is grasped in words/propositions (and thereby difficult for her to transmit what is grasped to others via testimony). This is just like one can believe the proposition that a certain map is accurate without being able to describe everything of the map in words.Footnote ¹³ (3) Further, there is no denying that, in the case of understanding-why, one might assent to what is grasped without being aware of the proposition that what one grasps is accurate. But again, this is consistent with the claim that one actually believes what one grasps is accurate. This belief might be simply unconscious.Footnote ¹⁴

Now let's move on to Premise 3, which states that if S1 has more grasp of how p depends on q than S2, then S2 does not have an exact idea of what S1 grasps. For if S1 has more grasp of how p depends on q than S2, then S1 grasps more relevant dependence relations than S2 (as we have seen above). But if S2 has an exact idea of what S1 grasps, then S2 has an exact idea of all the dependence relations that S1 grasps and thereby grasps exactly what S1 grasps. Thus, Premise 3 is true.

Premise 4 states that if S2 does not have an exact idea of what S1 grasps, then S2 cannot fully believe the very proposition that what S1 grasps is accurate (or accurate enough). To see this, consider an analogy: Suppose you saw an exotic animal that I never saw. Suppose you try to explain what the animal looks like to me. I learned via your testimony that the animal has certain properties F. So, in a sense I have a mental representation of the animal. But F is not everything you noticed about the animal. You also noticed many other properties, which it is difficult for you to describe or explain to me. In this case, your mental representation of the animal is more complex than mine. I do not have an exact idea of what is on your mind. Suppose you tell me that you believe the proposition that your mental representation of the animal is accurate. I cannot fully believe this very proposition, however. For me, your mental representation of the animal consists of your belief (that the animal has certain properties F) + X, where I do not have the faintest idea of what X is. I can believe that your belief that the animal has certain properties F is true, but I cannot genuinely believe that X is accurate. So, I can only half-believe the proposition that your mental representation of the animal is accurate. Put differently, you and I cannot share exactly the same beliefs. Premise 4 is true for similar reasons.Footnote ¹⁵

It is worth noting that Premise 4 can be generalized: if one does not have an exact idea of what W refers to, then one cannot fully believe a proposition formulated in terms of W. Dennett (Reference Dennett2013: 68) offers the following example:

Such half-belief is often called quasi-belief. Dennett and some other philosophers (e.g., Stalnaker Reference Stalnaker1984; Recanati Reference Recanati1997) seem to think that belief and quasi-belief are not different in kind. Rather, their difference is merely a matter of degree. But some (e.g., Sperber Reference Sperber, Hollis and Lukes1982) argue that quasi-belief is an attitude different in kind from belief. I will not take sides on this issue. It is enough to point out that on either side, if S1 believes p, and S2 can only half-believe or quasi-believe p, then S1 and S2 cannot share exactly the same beliefs.

So far, I have explained each of the four premises of my response. If all these premises are true, then it follows that if S1 has more understanding than S2 because S1 has more grasp of how p depends on q than S2, then they cannot hold exactly the same beliefs. The strengthened version of the objection from testimony fails accordingly.

5. A new veritist account of the value of understanding

At the beginning of this paper, I noted that veritists can agree that understanding-why is of final epistemic value: Veritists would say understanding-why is of (non-basic) final epistemic value because it partly consists of true beliefs: Understanding why p requires believing a set of true propositions such as that p, that q, and that p is the case because of q.

Here I'd like to propose a new version of the veritist account by adding a few details. First, as the case of the Pyrrhonian skeptic shows, understanding why p requires not only (i) grasping the relevant dependence relations but also (ii) believing the truth that what one grasps is accurate (or accurate enough).Footnote ¹⁶ Understanding-why is of final epistemic value partly because of (ii) rather than (i). (I shall say more about this in section 6.2, where I argue against Grimm and Hills’ double mirroring account of the value of understanding.)

Second, veritism does not imply that all true beliefs are of equal final epistemic value, for veritism merely states that only true beliefs are of final epistemic value (cf. Hu Reference Hu2017). Thus, veritists may hold that fully believing a certain truth p is of more final epistemic value than half believing p (if half-belief is a kind of belief). Suppose a biologist fully believes the truth that living organisms have descended with modifications from species that lived before them, while a middle school student can only half-believe the same truth. Then the biologist is doing finally epistemically better than the student with regard to the truth. In the case of understanding why the fire happened, the investigator fully believes the true proposition that what she grasps is accurate enough. But her apprentice can only half believe the same proposition. Thus, the investigator is doing finally epistemically better than the apprentice with regard to this proposition.

On top of that, veritists may incorporate our intuition that some truths are more significant than others by claiming that fully believing some truths is of more final epistemic value than fully believing some others. For example, fully believing a truth about how the solar system works is of more final epistemic value than fully believing a truth about the number of blades of grass in my backyard. This point has an implication on the value of understanding-why. Suppose the investigator has more understanding-why than the apprentice because the investigator has more grasp of how the fire causally depends on faulty wiring than the apprentice. Suppose the investigator fully believes the truth that what she herself grasps is accurate enough. And the apprentice also fully believes the truth that what she herself grasps is accurate enough. What the investigator grasps is different from what the apprentice grasps. So, they believe different truths. Veritists may say that fully believing the truth that what the investigator grasps is accurate enough is of more final epistemic value than fully believing the truth that what the apprentice grasps is accurate enough. This partly explains why the investigator is doing finally epistemically better than the apprentice.

Admittedly, veritists will have to do a lot of work to spell out what exactly makes some true beliefs more finally epistemically valuable than others (for preliminary discussions, see Grimm Reference Grimm2011 and Hu Reference Hu2017). But it is plausible to say that veritism can incorporate the idea that some true beliefs are of more final epistemic value than some others, just like hedonism can incorporate the idea that some pleasures are more finally valuable than others.

6. Against two anti-veritist accounts

In this section, I will further defend the veritist account of the value of understanding-why by arguing against two anti-veritist accounts in recent literature: the double mirroring account and the achievement account.