1. Introduction

Traditionally, philosophers of science have denied that understanding is among the epistemic aims of science, or that it is epistemically relevant is some other way. In this article I will argue against this view and defend the epistemic value of understanding. In Section 2, I discuss the traditional objectivist view of the relation between explanation and understanding, as defended by Carl Hempel and J. D. Trout. In Section 3, I challenge this view by arguing that pragmatic aspects of explanation (in particular the role of skills and judgment) are crucial for achieving the epistemic aims of science. Section 4 presents an analysis of these pragmatic aspects in terms of ‘intelligibility’ and a contextual account of scientific understanding based on this notion.

2. Explanation and Understanding: The Objectivist View

It is often suggested that scientific explanations provide us with understanding of the world. However, while scientific explanation has been a legitimate topic for philosophers of science since the publication of Hempel and Oppenheim's 1948 article on deductive-nomological explanation, the notion of understanding has remained outside the focus of philosophical attention until recently. The reason was that logical empiricists drew a sharp distinction between explanation and understanding, emphasizing that only the former is of philosophical interest. Hempel (Reference Hempel1965, 425–426) presented the following argument for this thesis. Notions such as understanding and intelligibility are pragmatic because “their use requires reference to the persons involved in the process of explaining,” and, consequently, they are relative: an explanation may be intelligible to one person and unintelligible to another. By contrast, the hallmark of scientific knowledge is (at least on Hempel's view) its objective nature, and philosophers of science should therefore try to give an objectivist account of science, and of scientific explanation in particular. Accordingly, they should ignore pragmatic aspects such as understanding and intelligibility. Such aspects may be of interest to those who study the phenomenon of science empirically (e.g., historians, sociologists, psychologists), but they are irrelevant to the philosophy of science, or so Hempel argued. To be sure, Hempel was right that the notion of understanding is pragmatic in the sense that it is concerned with a three-term relation between the explanation, the phenomenon, and the person who uses the explanation to achieve understanding of the phenomenon. One can use the term ‘understanding’ only with—implicit or explicit—reference to human agents: scientist S understands phenomenon P by means of explanation E. That understanding is pragmatic in this sense implies that scientist S ₁ may understand P while S ₂ does not, even if they both possess E (the difference in understanding being due to individual differences between S ₁ and S ₂ or between the respective contexts in which they operate). However, as I will argue below, Hempel was wrong when he concluded that for this reason understanding is a philosophically irrelevant notion.

Today, the Hempelian view that understanding should be banned from philosophical discourse is defended by J. D. Trout (Reference Trout2002, Reference Trout2007). According to Trout (Reference Trout2002, 217), philosophical analyses of scientific explanation should be objectivist for the following reason: “What makes an explanation good concerns a property that it has independent of the psychology of the explainers; it concerns features of external objects, independent of particular minds.” Therefore, Trout claims, philosophers of science should eschew allegedly subjective notions such as intelligibility and understanding. The latter are epistemically irrelevant if not dangerous (because experimental research in cognitive psychology shows that feelings of understanding are subject to the overconfidence bias and the hindsight bias and are therefore typically misguided; see Trout Reference Trout2002, 223–229). Trout criticizes philosophers such as Michael Friedman and Wesley Salmon for (unwittingly) relating explanatory power to a subjective sense of understanding. According to Trout, we should not try to justify our theories of explanation by referring to alleged understanding-providing features. The fact that a particular explanation of a phenomenon gives us a feeling of understanding is not a reliable cue to its being a correct or accurate explanation. On the contrary, says Trout: the feeling of understanding will induce us to stop looking for better explanations, but wrongly so because it is a product of the aforementioned biases. In sum, Trout conceives of understanding as a subjective experience that may be induced by explanations and concludes that it should not be regarded as epistemically relevant.

Insofar as objectivists are willing to discuss scientific understanding, they identify it with explanation, thereby making it redundant. Thus, according to Hempel (Reference Hempel1965, 488), explanations provide scientific understanding only in the sense that they show how the phenomena “fit into a nomic nexus.” And Trout (Reference Trout2007, 585–586) states that “scientific understanding is the state produced, and only produced, by grasping a true explanation,” where one “might, for example, treat grasping as a kind of knowing.” (However, Trout does not say of what scientific understanding is a state nor what kind of knowing ‘grasping’ exactly is.)

In the next section I will argue that there is more to understanding than either purely objective explanations or purely subjective feelings, as objectivists such as Hempel and Trout suggest. Between these extremes there exists a nonobjectivist (yet not arbitrary) kind of understanding that has a crucial epistemic function, and that needs to be taken into account in a philosophical analysis of scientific explanation.

3. Challenging the Objectivist View: The Epistemic Relevance of Skills

Let me first make it clear that I agree with Trout that the psychological sense of understanding has no epistemic function: a subjective feeling of understanding is neither necessary nor sufficient for scientific understanding of a phenomenon. Furthermore, I agree with the basic Hempelian idea that explanations are arguments which attempt to fit a phenomenon into a broader theoretical framework. In scientific practice explanation may sometimes conform to Hempel's deductive-nomological model of explanation, but more often it takes the form of model-based explanation. In the present section, I will argue that actual scientific explanation—be it deductive-nomological or model-based—involves a kind of understanding that is pragmatic and hence not purely objective. This type of understanding is based on skills and judgments of scientists and cannot be captured in objective algorithmic procedures. It is therefore incompatible with the objectivist conception of explanation and understanding favored by Hempel and Trout.

The pragmatic kind of understanding that I claim is crucial for scientific explanation is not a product of explanation. Before I substantiate this claim, let us first make a clear distinction between three different ways in which the term understanding can be used in connection with scientific explanation:

1. FU: feeling of understanding = the subjective psychological experiences accompanying an explanation.

2. UT: understanding a theory = being able to use the theory (pragmatic understanding).

3. UP: understanding a phenomenon = having an appropriate explanation of the phenomenon.

UP is generally regarded as an essential epistemic aim of science. It is not at odds with the Hempelian view; as we have seen above, it corresponds to what Hempel calls scientific understanding. UP can be accompanied by FU: explanations may, but do not necessarily, produce a sense of understanding. Accordingly, as Trout has rightly claimed, it is epistemically irrelevant whether or not UP is accompanied by FU. So far I agree with Hempel and Trout. However, contra their objectivist view, I argue that pragmatic understanding UT is a crucial condition for reaching the epistemic aim UP, namely, explanation.

What are explanations and how are they obtained? As stated above, explanations are arguments which fit a phenomenon into a broader theoretical framework. According to Hempel, they do so by deducing the explanandum from covering laws plus boundary conditions. For example, one can explain the fact that jets fly by deducing it from Bernoulli's principle and the relevant background conditions (borrowing an example from Trout Reference Trout2002, 202). Note, however, that merely knowing Bernoulli's principle and the background conditions is not equal to having an explanation: in addition, one should be able to use this knowledge in the right way to derive the explanandum. Thus, a student may have memorized Bernoulli's principle and have all background conditions available but may still be unable to use this knowledge to account for the fact that jets can fly. The extra ingredient needed to construct the explanation is a skill: the ability to construct deductive arguments from the available knowledge.

Harold Brown has shown this convincingly for the comparable case of deductive proofs in formal logic. Brown (Reference Brown and Newton-Smith2000, 195; cf. Reference Brown1988, 169ff) argues that although each step in such a proof is justified by appeal to an explicit rule, “the process of constructing a proof—that is, the process of deciding which rule to apply at each stage—is not governed by any comparable set of rules.” One learns to construct proofs by developing a skill, by practicing guided by someone who already possesses the skill. In other words, one develops the ability to make judgments about how to proceed without an algorithm. It might be thought that judgment is relevant only in the context of discovery, in which one tries to find new proofs. However, Brown (Reference Brown1988, 170–171) observes that also in the evaluation of given proofs logicians typically rely on judgment: “explicit following of rules is characteristic of an unskilled, rather than of a skilled, performance.” While the novice consciously follows rules, the expert immediately recognizes which steps are valid and which ones are not: this “leaps to the mind.” In other words, judgment plays a role in the context of justification as well.

The fact that deductive reasoning—and accordingly deductive-nomological explanation—involves skill and judgment has two important implications. First, skills cannot be acquired from textbooks but only in practice, because they cannot be translated in explicit sets of rules (Brown Reference Brown1988, 164–165). Accordingly, to possess a skill is to have ‘tacit knowledge’ (Polanyi Reference Polanyi1958). It has been argued, most notably by Reber (Reference Reber1993), that tacit knowledge involves implicit learning, that is, the unconscious and unintentional adoption of rule-following procedures. However, Reber's thesis is questionable. In a recent review of the literature, Shanks (Reference Shanks, Lamberts and Goldstone2005, 208–210) observes that, although some grammar learning experiments prima facie suggest that people do achieve unconscious knowledge of rules, the results are equally well explained without recourse to such implicit learning. Moreover, other experiments support the idea that grammaticality decisions are not based on adopted implicit rules but on accumulated information that generates a feeling of familiarity. Shanks (Reference Shanks, Lamberts and Goldstone2005, 216) concludes that “it has yet to be proved beyond doubt that there exists a form of learning that proceeds both unintentionally and unconsciously.” Brown (Reference Brown1988, 171–173) presents an additional philosophical argument against the thesis that developing skills is equivalent to internalizing rules: it would require the assumption of an ‘unconscious mind’ that follows the rules. But the existence of such a mind is implausible from a naturalistic point of view, and, moreover, it does not really solve a problem but rather generates new problems, namely, about the way the unconscious mind would work and about its interaction with the conscious mind and with the nervous system. Instead, Brown (Reference Brown1988, 173, 177) argues that a more fruitful approach is to regard the learning of cognitive skills as analogous to the development of physical skills, and to assume that it involves training of the nervous system in a comparable manner. Interestingly, Trout too (Reference Trout2002, 221–223) emphasizes the role of skills and implicit knowledge and argues that it proves that the psychological sense of understanding (FU) is epistemically irrelevant: if explanatory knowledge can be implicit, a conscious experience like FU cannot be required for it. However, although Trout is surely right that FU is neither necessary nor sufficient for UP and that (implicit) skills are crucially important for achieving UP, it does not follow that the process of achieving UP can be captured in an objectivist account based on internalization of rule-following procedures, as Trout suggests. On the contrary, the arguments of Brown and Shanks render this claim implausible.

Second, the fact that particular skills of the scientist are crucial for constructing and evaluating explanations and for achieving understanding entails that explanation has a pragmatic dimension that is epistemically relevant. Many philosophers of science hold that the pragmatic and the epistemic dimension of science can and should be kept separate. Thus, Hempel (Reference Hempel1965, 426) argues that scientific laws, theories, and explanations are “objective in the sense that their empirical implications and their evidential support are independent of what particular individuals happen to test or to apply them” and that philosophers of science should therefore construct “a nonpragmatic concept of scientific explanation” that “does not require relativization with respect to questioning individuals.” In a similar vein, Bas van Fraassen (Reference van Fraassen1980, 4, 88) explicitly contrasts an epistemic and a pragmatic dimension of theory acceptance. The epistemic dimension contains the relevant beliefs concerning the relation between a theory and the world, while the pragmatic dimension contains reasons scientists may have for accepting a theory independently of their beliefs about its relation to the world; these reasons typically pertain to the use and usefulness of the theory. In contrast to Hempel, van Fraassen (Reference van Fraassen1980, Chapter 5) argues that explanation is not an epistemic aim of science but rather belongs to the pragmatic dimension of theory acceptance. Both Hempel and van Fraassen see the epistemic and the pragmatic as sharply distinguished domains. On their view, the pragmatic dimension pertains to the relation between the theory and its users, that is, to the dimension that seems to be excluded from the epistemic dimension by definition.

The thesis that the epistemic and the pragmatic can and should be kept separate presupposes that the epistemic status of a theory exclusively depends on a direct evidential relation with the phenomena it purports to describe or explain. On this presupposition, pragmatic elements—for example, virtues of a theory that facilitate its use by scientists—are indeed epistemically irrelevant: they do not carry any additional justificatory weight. However, as the previous discussion of the role of skills in deductive reasoning has made clear, this presupposition is false. Skills and judgment are required for the establishing and evaluating relations between theories and phenomena (e.g., deductive-nomological explanations). It follows that, although it is possible and useful to distinguish analytically between the epistemic and the pragmatic, the two are inextricably intertwined in scientific practice: epistemic activities and evaluations (production and assessment of knowledge claims) are possible only if particular pragmatic conditions are fulfilled.

Thus, the pragmatic dimension of explanation is epistemically relevant. This is the case for deductive-nomological explanations but even more so for scientific explanations that do not conform to the deductive-nomological ideal. And the latter are the rule rather than the exception in scientific practice: usually there is no strictly deductive relation between explanans (theoretical laws and initial conditions) and explanandum (the phenomenon or phenomenological laws). Instead, as Cartwright (Reference Cartwright1983), Morgan and Morrison (Reference Morgan and Morrison1999), and others have shown, in scientific practice the connection between theory and phenomena is usually made through models. A model is conventionally taken as a representation of the object or system that one wants to understand scientifically.Footnote ¹ In order to see what the role of models is in achieving understanding, we should first clarify the relation between models, theory, and empirical data. Morgan and Morrison (Reference Morgan and Morrison1999, 10–11) have argued for the ‘autonomy’ of models: models are not derived from theory, but neither do they follow from the empirical data. They typically contain both theoretical and empirical information.

How are such models constructed, and what precisely is their role in scientific explanation? The function of a model is to represent the target system in such a way that the theory can be applied to it. In other words, models replace the bridge principles that traditionally connect theory to empirical phenomena. In the terminology of Morgan and Morrison (Reference Morgan and Morrison1999), models ‘mediate’ between theory and phenomena. The crucial difference between bridge principles and mediating models is that the former establish a strict deductive relation between theory and phenomenon (explanans and explanandum), while the latter connect the two in a looser way. The construction of models and their role in scientific explanation has been analyzed extensively by Nancy Cartwright (Reference Cartwright1983). According to her simulacrum account of explanation, “to explain a phenomenon is to construct a model that fits the phenomenon into a theory” (Cartwright Reference Cartwright1983, 17). In the modeling stage, the target system is presented in such a way that the theory can be applied to it: we decide to describe system S as if it is an M (where M is a model of which the behavior is governed by equations derived from the theory). The construction of models is not a matter of deduction but rather a complex process involving approximations and idealizations. There are no algorithms or formal principles that tell us how to get from the description of a real system to a suitable model: “There are just rules of thumb, good sense, and, ultimately, the requirement that the equation we end up with must do the job” (Cartwright Reference Cartwright1983, 33). This implies that the construction of a model, as well as the assessment of the model as a good (or good enough) representation of the system, is a process in which scientists have to make pragmatic decisions and must accordingly rely on skills and judgment.

Understanding in the sense of UP (having an appropriate explanation of the phenomenon) is an epistemic aim of science, but this aim can be achieved only by means of pragmatic understanding UT (the ability to use the relevant theory). This is the case for deductive-nomological explanations and even more so for model-based explanations that are typically not deductive. Achieving the epistemic aim of science is a complex process that unavoidably has a pragmatic dimension in which skills and judgment play crucial roles. Consequently, the epistemic value of a theory cannot be determined in isolation from its use, and successful use of a theory requires pragmatic understanding.

4. Scientific Understanding, Pragmatic Understanding, and the Intelligibility of Theories

In the previous section, pragmatic understanding UT was defined somewhat loosely as the ability to use the relevant theory. In this section I will give a more precise characterization of the nature of and conditions for pragmatic understanding. Pragmatic understanding is required for constructing models that relate theories to phenomena. As we have seen above, this activity involves making suitable idealizations and approximations: scientists need to make the right judgments regarding idealization and approximation and to possess the right skills to build a model on this basis. What are the right skills? This depends on which theory the scientist is dealing with, in particular on which pragmatic virtues the theory possesses. Particular virtues of theories—for example, visualizability or simplicity—may be valued by scientists because they facilitate the use of the theory in constructing models; in this sense they are pragmatic virtues. But not all scientists value the same qualities: their preferences are related to their skills, acquired by training and experience, and to other contextual factors such as their background knowledge, metaphysical commitments, and the virtues of already entrenched theories.

Philosophers of science have listed and discussed the theoretical virtues that generally play a role in the evaluation of scientific theories, for example, accuracy, consistency, scope, simplicity, unifying power, and fertility (see Kuhn Reference Kuhn and Kuhn1977; Longino Reference Longino1990; Lacey Reference Lacey2005).Footnote ² Many historical studies have revealed that, in evaluations of theories, scientists employ other criteria than accuracy alone, and that there is sometimes a trade-off between accuracy and other virtues. Such evaluations cannot be the result of algorithmic decision procedures, and accordingly judgment plays a crucial role. In addition to the general virtues cited above, scientists in various fields and historical periods have promoted other, more specific theoretical qualities (e.g., visualizability, continuity, and locality; see De Regt Reference De Regt2001 and De Regt and Dieks Reference De Regt and Dieks2005).

Scientists may prefer theories with particular pragmatic virtues because they possess the skills to construct models for explaining phenomena on the basis of these theories. In other words, they have pragmatic understanding UT of such theories. I suggest to rephrase this with the help of the notion of intelligibility. If scientists understand a theory, the theory is intelligible to them. I define the intelligibility of a theory (for scientists) as follows:

It is important to note that intelligibility, thus defined, is not an intrinsic property of a theory but rather a value that is projected onto the theory by a scientist or group of scientists. Moreover, it is a pragmatic, context-dependent value related both to properties (virtues) of a theory and its representation(s)Footnote ³ and to scientists’ skills. Intelligibility is a measure of the fruitfulness of a theory, but it is not an objective measure, because a theory can be more fruitful for one scientist than for another.Footnote ⁴ Which theories are deemed intelligible can vary through time or across disciplines. Scientists prefer a more intelligible theory to a less intelligible one, not because it gives them a psychological sense of understanding but rather because they have to be able to use the theory.

The arguments presented in Section 3 can be summarized by the thesis that scientific understanding of phenomena requires intelligible theories. Only an intelligible theory allows scientists to construct models through which they can derive explanations of phenomena on the basis of the given theory. In other words, understanding scientific theories is a prerequisite for understanding phenomena scientifically. This can be stated as a Criterion for Understanding Phenomena:

First, note that in Section 3 understanding a phenomenon (UP) was defined as ‘having an appropriate explanation of it’, and explanations were defined as arguments that fit a phenomenon into a broader theoretical framework. CUP states that having an intelligible theory T is a necessary condition for scientifically understanding P. Of course, in addition we need to use T to actually construct the explanation that fits P in the theoretical framework. Therefore, CUP also contains a requirement about the actual explanation, in which accepted logical and empirical requirements determine what a good fit is.Footnote ⁵ Accordingly, CUP does not entail that, for example, astrologers understand personality traits of people if only they have an intelligible astrological theory of these personality traits. In addition, explanations on the basis of this theory have to meet accepted requirements such as accuracy and consistency. Second, note that CUP is implicitly pragmatic (i.e., it refers to the scientists involved in the process of explanation) because it involves the pragmatic notion of intelligibility.

Since intelligibility is not an intrinsic property of theories but a context-dependent value ascribed to theories, one cannot specify universally valid criteria for intelligibility. But this does not entail that intelligibility is merely a matter of taste and that no criteria can be formulated at all. Since intelligibility can be regarded as a measure of how fruitful a theory is for the construction of models (by scientists in a particular context), it is possible to determine this measure by means of a criterion or test. There may be different ways to test whether a theory is intelligible for scientists, and not all of them may be applicable in all cases or for all disciplines. As one way of testing the intelligibility of theories, I want to suggest the following criterion:

In Section 3 it was argued that the skills and judgments involved in achieving understanding cannot be reduced to rule-following procedures. Criterion CIT can be regarded as a test of such ‘tacit’ (implicit) skills. The criterion applies specifically to mathematical theories as used in the physical sciences. It is based on a suggestion by Werner Heisenberg about understanding in physics (see De Regt and Dieks Reference De Regt and Dieks2005 for an elaborate defense of CIT). For theories in other disciplines, especially nonmathematical ones, other criteria may apply. Moreover, there may be other ways to determine intelligibility of theories in the physical sciences as well. CIT is a sufficient condition for intelligibility, not a necessary one.

Whether theory T is intelligible depends not only on the virtues of T itself but also on such contextual factors as the capacities, background knowledge, and background beliefs of the scientists in C. Accordingly, CIT can accommodate the variety of ways in which understanding is achieved in scientific practice. Qualitative insight into the consequences of a theory can be gained in many ways, and therefore the criterion does not favor one particular skill or theoretical virtue. Its fulfillment requires an appropriate combination of skills and virtues. The preferred theoretical virtues, to which skills have to be attuned, provide ‘tools’ for achieving understanding. For example, a theory (or a particular representation of it) may possess the virtue of visualizability, which allows for visualization, which in turn may be a useful tool to construct models of the phenomena. Visualization is an important tool for understanding, valued by many scientists, but it is not a necessary condition, and there are also scientists who prefer abstract theories over visualizable ones (see De Regt Reference De Regt2001).

5. Conclusion

Understanding of phenomena (UP) is among the epistemic aims of science, and such understanding is provided by explanations. In this article I have argued, contra the objectivist view of Hempel and Trout, that a pragmatic type of understanding (UT) is a necessary condition for UP. Such pragmatic understanding amounts to the ability to use relevant theories to construct explanations. I have presented a further analysis of UT, based on the notion of intelligibility, and provided criteria for understanding phenomena (CUP) and for pragmatic understanding UT (the criterion for intelligibility CIT). Scientific understanding of phenomena (UP) requires intelligible theories, where intelligibility is defined as the positive value that scientists attribute to the theoretical virtues that facilitate the construction of models of the phenomena. Intelligibility is not an intrinsic property of a theory but rather a value projected onto the theory by scientists. It is a pragmatic, context-dependent value related both to the theoretical virtues and to the scientists’ skills (see De Regt Reference De Regt, de Regt, Leonelli and Eigner2009 for a more detailed defense of this account and application to a concrete example).

The conclusion that intelligibility has epistemic relevance is in direct opposition to the objectivism of Hempel and Trout: it implies that of two people who possess exactly the same theories and background knowledge, one may achieve understanding of a phenomenon while the other does not. Accordingly, scientific understanding is not completely objective, that is, it is not fully independent of the subject. It might be objected that this implies a relativist view of scientific understanding and hence of science itself. But that worry is unfounded. Skills are acquired within a community and assessed by that community, which guarantees that judgments based on skills are not arbitrary. As Brown (Reference Brown and Newton-Smith2000, 201–202) observes, “Scientists develop judgment in the specific fields that they have mastered, and this results in the existence of a set of cognitive skills in the scientific community. These skills are fallible, but their fallibility does not make them epistemically worthless.”

The thesis that pragmatic understanding of theories (UT, intelligibility) is a necessary condition for understanding phenomena (UP) undermines traditional objectivist conceptions of science. But abandoning such conceptions does not necessarily open the door to relativism: intelligibility is necessary but insufficient for scientific understanding. Criterion CUP includes accepted logical and empirical requirements to which explanations have to conform. These requirements can be listed as a set of theoretical virtues that generally play a role in the evaluation of scientific theories, which together provide a shared basis for assessing explanations (cf. Kuhn Reference Kuhn and Kuhn1977, 322). Intelligible theories can be fruitfully employed in the construction of explanatory models, but the resulting explanations are scientific explanations if and only if they conform to the shared virtues to a sufficient extent. Intelligibility is not the only requirement for scientific theories but is an essential one if one wants to understand the phenomena.