Understanding with Models

One of the key philosophical issues facing model-based understanding concerns factivity. The issue is that, as Grimm (2006) observes, philosophers of science tend to agree that scientific understanding is a species of knowledge, and hence factive.⁷ To say that knowledge is factive is to say that, if S knows p, then p is true. Consequently, if S understands p, then p must also be true. Furthermore, if, as some philosophers have argued (e.g., Khalifa 2013; Strevens 2013), all scientific understanding reduces to explanatory understanding, and if understanding results only from explanations based on theories that are (at least approximately) true, then this also would imply scientific understanding must be factive. By contrast, epistemologists have tended to disagree that understanding must be factive in all cases. It is generally accepted in epistemology that there are different kinds of understanding. For example, objectual understanding – which involves having a grasp of the connections between items of information in a body of knowledge – is held to be able to tolerate some falsehoods. A few falsehoods at the margins of one’s objectual understanding might degrade it, but do not undermine it completely (Baumberger 2011: 81). ‘Moderate factivists’ (for example, Kvanvig 2009, Mizrahi 2012) hold that objectual understanding remains possible even with some false propositions, if the core central propositions remain true.

Some philosophers have argued, however, that factivity is far too demanding and restrictive for an adequate conception of scientific understanding. According to Elgin, a factive conception of understanding ‘does not reflect our practices in ascribing understanding and it forces us to deny that contemporary science embodies an understanding of the phenomena it bears on’ (Elgin 2007: 33). Similarly, de Regt (2015) argues that the traditional view of understanding ‘should be replaced by an alternative conception that allows for understanding without truth’ (de Regt 2015: 3794-3795). A key argument for both Elgin and de Regt concerns the use of models in the history and practice of science, and specifically the fact that those models almost invariably incorporate idealized assumptions, fictions and deliberate falsehoods, which do not mirror how the world is. These idealizations are thus, strictly speaking, false, but they ‘can neither be eliminated from scientific theories nor banished to their periphery’ (Baumberger 2011). Thus, a factive conception of understanding is held to be inadequate because the use of idealizations in scientific theorising and modelling is a central and ineliminable feature of scientific research. Elgin uses the Ideal Gas Law as her primary example:

7 See, e.g., Achinstein (1983) and Trout (2002).

Science streamlines and simplifies. It devises and deploys comparatively austere models that diverge from the phenomena it seeks to explain. The ideal gas law accounts for the behaviour of gases by describing the behaviour of a gas composed of dimensionless, spherical molecules that are not subject to friction and exhibit no intermolecular attraction. There is no such gas.

Indeed, there could be no such gas. Nonetheless, scientists purport to understand the behaviour of actual gases by reference to the ideal gas law. (Elgin 2007: 38)

Elgin’s point is that the use of idealized and unrealistic models in scientific practice is compatible with a significant degree of understanding. For Elgin, to deny that idealized models can yield understanding would force one to deny understanding to much of contemporary and historical scientific practice. This, she thinks, would be substantially at odds with the clear cognitive success that the sciences enable.

De Regt, in turn, draws on a range of examples from the life and social sciences to show that the use of idealized and unrealistic models is also compatible with advances in scientific understanding. Economic models, for instance, are highly abstract and idealized, entailing regularities that cannot be found in the real world. Much of classical economics, for example, is founded on the conception of human beings as rational utility maximizers, even if we know from psychology and behavioural economics that this is rarely the case. Nevertheless, it would be controversial to suggest that classical economics provides no understanding of economic reality. As such, de Regt argues that ‘unrealistic models provide understanding that is used in explanations of complex economic reality’ (de Regt 2015: 3787). In the life sciences, the use of ‘model organisms’ (for example, the bacteria E.coli, the fruit fly Drosophila melanogaster, and the mouse cress Arabidopsis thaliana) to understand biological processes are unrealistic in the sense that they idealize and abstract from biological reality. Although model organisms are real organisms, they differ in important respects from organisms ‘in the wild’.⁸ First, model organisms are not typically selected for their representative applicability, but for pragmatic reasons, such as experimental manipulability and tractability, breeding time, and costs.

Second, they are standardised, which ends with them often being ‘extremely distant from those that could be easily found outside the laboratory and in nature’ (Ankeny 2009: 200-201). Thus, even model organisms involve idealizations which are used to make sense of complex biological reality, while not representing it faithfully (de Regt 2015: 3789).

Given that the models and idealizations they appeal to are drawn from examples central to a discipline’s understanding of the phenomena they target, Elgin and de Regt conclude that the cognitive success that we attribute to scientists does not involve attributing success in the sense of knowledge about the truth with respect to a particular domain in nature. What their examples suggest is that scientists will often forego representational accuracy or factive

8 For discussion of model organisms, see Ankeny (2009) and Ankeny and Leonelli (2011).

understanding in favour of computational power or experimental tractability. As such, ‘an approximately true description of the system is no precondition for understanding’ (ibid:

3789). I am sympathetic to Elgin’s and de Regt’s conclusions; I am inclined to agree with them that a factivity condition is too restrictive and demanding for an adequate conception of model-based scientific understanding. However, I do so for different reasons. To see why, let us pause for a moment to consider one of the objections to Elgin and de Regt’s conclusions.

The objection comes from Kvanvig (2009: 342-343) and Mizrahi (2012: 246-249) in defence of moderate factivity. Kvanvig argues that using an idealized model to understand some target phenomenon requires that one knows what the model is like and how it relates to the target. This involves knowing the extent to which the model is an idealization and how this distorts or is unrealistic with respect to the target phenomenon. If a scientist knows all this, Kvanvig contends, then the factivity requirement for understanding is not violated.

Similarly, Mizrahi responds directly to Elgin’s use of the Ideal Gas Law, and argues that we need to distinguish between the Ideal Gas Law, the conditions under which it applies, and the idealizing assumptions necessary to derive the Ideal Gas Law. Mizrahi contends that the idealizing assumptions in the Ideal Gas Law only lie at the periphery of the model, and as such, the fact that they are false does not detract from the central propositions of the gas laws, which must be true if scientific understanding is to be obtained, thus concluding that moderate factivity is preserved (Mizrahi 2012: 250).

Kvanvig’s and Mizrahi’s responses to Elgin and de Regt presume that scientists know what the idealizing assumptions say about the world, how they apply, and the extent to which they diverge from reality. It is thus because of this knowledge that we can say idealized models yield understanding. The difficulty with this claim, however, as Baumberger has pointed out, is that in some cases scientists do not know how their models diverge from reality, or under which conditions exactly that their model gets it right. Nonetheless, this does not seem to undermine their understanding of the target phenomenon. Environmental scientists, for example, do not know exactly how their climate models diverge from reality, but this does not completely undermine their understanding of global warming (Baumberger 2011: 83).

Baumberger treats this point as indicating how understanding and knowledge can come apart. According to Baumberger, Kvanvig and Mizrahi do not succeed in showing that knowledge – and by extension, truth or factivity – is necessary for understanding. However, I think this point reveals something different. What Baumberger, Elgin and de Regt are highlighting, in my view, is the distinction between conceptual meaning and truth. On this interpretation, what Elgin’s and de Regt’s arguments against factive conceptions of model-based understanding point to is the fact that, while reference to truth and factivity can mark out one way we can evaluate model-based understanding, we need to be sensitive to the fact that conceptual meaning and truth come apart. This points to a more specific elaboration of

my discussion of Brandom’s two-dimensional model of the normativity of conceptual understanding. There (Chapter Two, section six), we saw that the normative accountability of our conceptual understanding spans two dimensions. On the one hand, what we say and do can be assessed in terms of the meaningfulness of our claims and actions (whether what we say or do makes sense), and on the other hand, we can determine whether what we say or do is justifiable or true. As Ian Hacking once noted, ‘[w]hether a proposition is as it were up for grabs, as a candidate for being true-or-false, depends on whether we have ways to reason about it’ (Hacking 2002: 160). The distinction between these two distinct but interconnected poles of normativity means that prior to determining whether what we say about the world is true or justified, it must already be understood at the level of conceptual meaning and intelligibility.

From this perspective, Baumberger is right to say that scientists’ understanding is not undermined if they do not know how their models diverge from reality, or under which conditions the model correctly applies. The possibility of settling these issues presupposes that the models and their target phenomena already make sense and are understood. With regards to models and their use in scientific practice, the issue then is making sure not to conflate meaning with truth. Similarly, what Elgin’s and de Regt’s examples reveal is that we can judge whether models provide understanding – whether they enable us to grasp and make sense of the world – without having to conflate that with the issue of whether what models say something that is true about the world.⁹ Put more generally, the point is that this distinction between meaning and truth enables us to distinguish between how we take the world to be from how it actually is.¹⁰ The point is summarised by Rouse: ‘We cannot ask whether a theory, a law, or any other hypothesis is true unless we have some understanding of what it says, and to which circumstances it appropriately applies’ (Rouse 2009: 38).

Therefore, my aim in this chapter is to focus on the way which models provide understanding at the level of conceptual meaning, intelligibility and significance. To do this, I argue that models afford scientific understanding through their role in conceptual articulation. Conceptual articulation with models consists in working out the inferential consequences of our concepts, what they mean, the circumstances to which they appropriately

9 I am not denying here that the truth or justification of what models enable us to say is important to conceptual understanding – it obviously constitutes one pole of the normativity of our conceptual understanding. What I want to emphasise is that while we will evaluate what models say about the world along both poles in practice, it is important not to conflate meaning with truth within our analysis. Ultimately, both conceptual meaning and truth are essential for scientific understanding.

10 Importantly, neither Elgin nor de Regt deny some role for truth in scientific understanding (e.g., de Regt 2015: 3795). They recognise and grant that scientific understanding must be, in Elgin’s words, ‘tethered’ to the world (Elgin 2007: 35) – a point which I agree with. Their point is that focusing solely on the way in which models enable factive understanding risks obscuring the contributions modelling in scientific practice makes to conceptual meaning and intelligibility.

apply and the consequences of their application. I begin in the following section by clarifying the notion of conceptual articulation in more detail before returning to models in section five.