An Inferential Model of Scientific Understanding

Abstract

In this article I argue that two current accounts of scientific understanding are incorrect and I propose an alternative theory. My new account draws on recent research in cognitive psychology which reveals the importance of making causal and logical inferences on the basis of incoming information. To understand a phenomenon we need to make particular kinds of inferences concerning the explanations we are given. Specifically, we come to understand a phenomenon scientifically by developing mental models that incorporate the correct causal and logical properties responsible for the causes or logical properties of the phenomenon being explained.

Acknowledgements

Thanks to two anonymous referees of this journal and Meghan Newman for helpful comments on this paper. Also thanks to Andrew Terjesen, Jason Ford, Sean Walsh, and Tristram McPherson for useful discussions on this topic.

Notes

In this article I am specifically addressing scientific understanding, rather than understanding more generally construed. That there is a difference between the two will be argued shortly, and plays a crucial role in my argument.

Trout is not offering these conditions as part of a semantic analysis, so these should not be taken as individually necessary and jointly sufficient conditions on understanding. They are a hedged description of the properties contingently accompanying understanding. Nevertheless, I argue they are an inaccurate characterization.

On the other hand, one might argue that since theories in science often appeal to modeling techniques that deliberately incorporate idealizations and abstractions, we are asking too much of our theory of understanding if we require explanations be even approximately true. Elgin (2004) has argued that acquiring scientific understanding is often orthogonal, or even directly conflicts with acquiring truth. This would be correct if we didn't replace the aim of truth for that of approximate truth, but once this replacement is made, I believe her concerns are diminished.

As one reviewer pointed out, most leading externalist philosophers offer a synthesis by supplementing their accounts of knowledge with an internalist ‘no-defeater’ clause. However, this fact does not show how an internalist condition like (2) can be reconciled with (3), since even with such a clause, one would still have to externalize the necessary ‘supporting beliefs’ in Trout's account.

The idea of course is that ‘mere’ knowledge is the concept traditionally analysed in epistemology—something like justified true belief, and that understanding, we generally think, goes beyond this concept. Grimm (2006) provides a nice analysis of why understanding might still be ‘mere’ knowledge, arguing amongst other things, that Kvanvig's (2003) view must be in error. Kvanvig thinks understanding requires making the appropriate connections between our beliefs, whereas Grimm sees the focus more as being on our ability to answer questions. In this article I focus on the views of Trout and de Regt because they specifically concern scientific rather than general understanding.

Bernoulli's principle states that for a fluid in an ideal state, pressure and density are inversely related, which entails that a moving fluid exerts more pressure when its velocity is low, and less pressure as the velocity increases.

Notice in this explanation there is no mention of Bernoulli. That is because this explanation has been given in terms of pressure distribution with no reference to velocity distribution. Here's how we can relate the two: Newton's laws of mechanics can be expressed either as a set of simultaneous differential equations or as a set of integrals. Using differentials for aerodynamics is useful if one wishes to determine the behavior of the fluid at specific locations or many locations while mapping the flow-field. This is where one would instead use Bernoulli's law, which is a version of the conservation of energy: P _T  = constant = P _S  + ½ρ V 2 = P _S  + q. This says that total pressure (P _T ) equals static pressure (P _S ) plus dynamic pressure (q), where this dynamic pressure is one-half fluid density (ρ) times velocity (V) squared. This latter approach to describing lift gives one the pressure distribution for a known velocity distribution. In order to determine this velocity distribution for the streamlines of the fluid one does however need to solve equations for conservation of mass, momentum and energy as the fluid passes the aircraft (Navier-Stokes equations). In simpler accounts at the macroscopic scale integrals that more closely resemble Newton's laws are used to describe changes in momentum and energy in regions of fluid flow. Both approaches are equally valid for describing lift, it is just that Newton's is simpler, and loses nothing provided one does not need to evaluate details of fluid flow. Also notice that use of Bernoulli's equation should avoid a popular but incorrect explanation of lift, which suggests conservation of energy entails that fluid travelling over the top surface of an airfoil must move faster than that moving below in order to ‘catch up’ with the lower air.

I am not here committing to a strong distinction between scientific and non-scientific explanations. In fact I consider this a false distinction. All I require though is that even if explanations lie on a continuum between common sense and informed science, most explanations we find in science are far more complex than their common-sense counterparts.

For an introduction to the discourse and comprehension literature, Kintsch (1998) and Tapiero (2007) are good places to start. Otero, Leon, and Graesser (2002) is a useful anthology regarding comprehension of specifically science texts.

Notice that although in this literature comprehension is characterized in terms of knowledge, this does not lend much philosophical support to the claim that understanding is a form of knowledge. It doesn't undermine the claim either though.

There are other means of representing the propositional content of an explanation of course, but here I illustrate merely that used most prominently in the literature.

The last level of representation studied in the literature is that of pragmatic communication. This level reflects the primary message being conveyed by the explanation being given in the text. The pragmatic component of scientific explanation is well appreciated in the work of van Fraassen (1980) and Achinstein (1983), and can plausibly be thought to capture an important part of what it means to understand the world scientifically. It is less uncontroversial to suggest that this level of representation captures what we mean when we say we understand p. Consequently, I shall side-step the interesting question of how the pragmatics of explanation contributes to a cogent theory of scientific understanding. This covers the levels of representation, but representations themselves also come in many different types. I won't spend time explicating the wide range of representations used in the sciences, but at least a few recurrently play important roles: class inclusion; temporal and spatial relations; composition of parts into subparts; step-wise procedures; causal chains and networks; and intentional action. There is an important property of this list, and it is that the more fine-grained are these types of representation, and the greater their coherence (their conceptual interconnections), then the deeper is the knowledge one acquires of an explanation—or at least this seems to be indicated by studies (Graesser, Gordon, and Brainerd 1992).

There are many ways of characterizing this taxonomy. For recent accounts, see Anderson and Krathwohl (2001) and Marzano and Kendall (2007).

It is of course a common complaint amongst physics professors that students frequently fail to check that their answers cohere with common sense.

The ordering I have given actually is traditionally thought of as being a ranking which originated with Bloom's (1956) taxonomy of educational objectives. I am not committed to it however.

Like Kvanvig, I appreciate the importance of developing a coherent network of beliefs in order to achieve understanding. Unlike Kvanvig, I also think these beliefs must constitute knowledge.

I omit the derivation because it requires graphics, which would consume too much space here. For a clear exposition of how to derive the angular radius of a rainbow, see Tipler (1991), 993.