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The Question

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For a process to track an attribute is for how the process unfolds to nonaccidentally depend, perhaps within limits, on the presence or absence of the attribute.

The ability to track a variety of instrumental actions and mental states is widespread not only in human adults but also infants and nonhuman animals.[1] Within limits, you can change how they respond to situations by changing some facts about someone’s mental states.

This fact about tracking invites two questions.

  1. Which processes are involved in tracking instrumental actions and mental states?

  2. Which models are involved in tracking instrumental actions and mental states?

Processes and Limits

Although the first question is not very puzzling, it has received little sustained attention. Let me illustrate a strategy for answering it.

Consider first the abilities of infants, from around three months of age, to track the goals of instrumental actions (Sommerville, Woodward, & Needham, 2005). One hypothesis about the first question above is that this early-developing ability to track goals involves motor process (Woodward & Gerson, 2014).

Support for this hypothesis comes from considerations about limits. First, limits on infants’ abilities to track goals line up, roughly, with limits on their abilities to act (e.g. Kanakogi & Itakura, 2011; Ambrosini et al., 2013). Second, intervening on infants’ abilities to act—both enhancing them through training (Sommerville, Hildebrand, & Crane, 2008; Gerson & Woodward, 2014) and impairing them through restraining (Bruderer, Danielson, Kandhadai, & Werker, 2015)---has a corresponding effect on their abilities to track the goals of actions.

I am not suggesting that the evidence is decisive,[2] but I do think the focus on limits is fruitful.

In fact we can use limits in the same way to defend the hypothesis that some belief tracking involves motor processes. In testing this hypothesis, Jason Low and Katheryn Edwards generously let me join them to follow up on some of their earlier work (Edwards & Low, 2017; Edwards & Low, 2019). They had adapted a paradigm first introduced by Kovács, Téglás, & Endress (2010) which builds on an object detection task. Simplifying,[3] Kovács et al. (2010) found that how long it takes for participants to respond to the objects’ presence by pressing a key is influenced by a protagonists’ task-irrelevant belief about whether it is present or absent. We wondered:

Why do another’s task-irrelevant false beliefs ever influence my reaction times?

Our conjecture was that the influence is a consequence of me tracking the other’s apparent action possibilities. Not their actual action possibilities but the action possibilities they would have if the other’s beliefs were true. Anticipating that the other could act speeds up my own action.

Since tracking another’s action possibilities often involves motor processes, you can impair tracking by temporarily limiting both the other’s ability to act (Costantini, Committeri, & Sinigaglia, 2011) and by temporarily limiting my ability to act (Ambrosini, Sinigaglia, & Costantini, 2012).

Our conjecture therefore generates the prediction that constraining either my own, or the other’s, action possibilities will reduce or even eliminate the influence of the other’s task-irrelevant false beliefs on me. And so far we found quite promising evidence for the second part of this prediction (Low, Edwards, & Butterfill, 2020).

We would not expect, of course, that all abilities to track mental states are explained by a single type of process. There may be variation between species or ages. And there may even be two or more processes for tracking mental states at work simultaneously in a single individual—or so the ‘two systems’ theory of mindreading postulates.

If there are multiple processes involved in tracking instrumental actions and mental states, then they probably also rely on different models.


A model is a way that some part of the world could be. The point of specifying a model is to capture the point of view of the agent or process that is tracking mental states. How, from their point of view, does the world appear?

Or, to put this less metaphorically, the model is the world as it would have to be for the tracking to be free of errors.

Specifying a model is a key part of providing a computational description of a mindreading process.

Why Not Representations?

Why ask about models instead of representations? A claim about what a mindreader represents answers, in effect, two questions simultaneously:

  1. Which model characterizes this mindreading process?

  2. What links this model to the mindreading process?

The second question (about links) can sometimes be answered by saying that the mindreader represents the model, or represents a theory that specifies the model. But this is not always the right answer because sometimes the model is merely implicit in constraints on how a process operates.[4]

This is why it is useful to focus on models rather than representations: doing so allows us to answer the first question without committing on how the second question will be answered.[5]

Why Not Theories?

To specify a model, we as theorists might use a theory or a set of equations; or we might specify the model less formally. Note that the theory or equations are distinct from the model. They are tools that we theorists use and might be entirely unknown to those who rely on the model.

Why Models?

The importance of models is easy to see in the case of the physical. Suppose we are interested in commonsense physical thinking. We notice that our subjects are able to track the movements of objects, but also that this ability is subject to some odd limits. For example, they are fine at tracking objects launched horizontally but struggle when objects are launched vertically. This and other limits on their tracking might move us to postulate that their tracking involves an impetus model of the physical.[6]

It is important to notice that you can track things without having a very accurate model of those things. An impetus model of the physical has all kinds of limits but remains useful in a range of everyday situations. In some cases you can even track things without having any model of them at all. For example, you might track toxicity by with a model of the world which involves only odors; or you might track what others can perceive with a model of the world which involves only lines of sight.

The Question

In the past I focussed on the problem of identifying the models that are involved in the most basic forms of mindreading, those that are common to several species and occur early in development.

I took for granted that we are all acquainted with the models that are involved in the most sophisticated forms of mindreading.

Today I want to argue that this was a mistake. We face as significant problem in identifying the models involved in the most sophisticated forms of mindreading. And failure to recognize this problem is impairing even the most prominent recent debates about mindreading (see We Lack a Shared Understanding). But it is a problem that we can work around, and I will attempt to outline how we can do so (in But One We Can Work Around).


computational description : A computational description of a system or ability specifies what the thing is for and how it achieves this. Marr (1982) distinguishes the computational description of a system from representations and algorithms and its hardware implementation.
heuristic : A heuristic links an inaccessible attribute to an accessible attribute such that, within a limited but useful range of situations, someone could track the inaccessible attribute by computing the accessible attribute.
inaccessible : An attribute is inaccessible in a context just if it is difficult or impossible, in that context, to discern substantive truths about that attribute. For example, in ordinary life and for most people the attribute being further from Kilmery (in Wales) than Steve’s brother Matt is would be inaccessible.
See Kahneman & Frederick (2005, p. 271): ‘We adopt the term accessibility to refer to the ease (or effort) with which particular mental contents come to mind.’
instrumental action : An action is instrumental if it happens in order to bring about an outcome, as when you press a lever in order to obtain food. (In this case, obtaining food is the outcome, lever pressing is the action, and the action is instrumental because it occurs in order to bring it about that you obtain food.)
You may encounter variations on this definition of instrumental in the literature. For instance, Dickinson (2016, p. 177) characterises instrumental actions differently: in place of the teleological ‘in order to bring about an outcome’, he stipulates that an instrumental action is one that is ‘controlled by the contingency between’ the action and an outcome. And de Wit & Dickinson (2009, p. 464) stipulate that ‘instrumental actions are learned’.
model : A model is a way some part or aspect of the world could be.
motor process : A process featuring motor representations.
motor representation : The kind of representation characteristically involved in preparing, performing and monitoring sequences of small-scale actions such as grasping, transporting and placing an object. They represent actual, possible, imagined or observed actions and their effects.
Principles of Object Perception : These are thought to include no action at a distance, rigidity, boundedness and cohesion.
Teleological Stance : To adopt the Teleological Stance is to exploit certain principles concerning the optimality of goal-directed actions in tracking goals (Csibra & Gergely, 1998).
tracking an attribute : For a process to track an attribute or thing is for the presence or absence of the attribute or thing to make a difference to how the process unfolds, where this is not an accident. (And for a system or device to track an attribute is for some process in that system or device to track it.)
Tracking an attribute or thing is contrasted with computing it. Unlike tracking, computing typically requires that the attribute be represented.


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Ambrosini, E., Sinigaglia, C., & Costantini, M. (2012). Tie my hands, tie my eyes. Journal of Experimental Psychology: Human Perception and Performance, 38(2), 263–266.
Bruderer, A. G., Danielson, D. K., Kandhadai, P., & Werker, J. F. (2015). Sensorimotor influences on speech perception in infancy. Proceedings of the National Academy of Sciences, 112(44), 13531–13536.
Butterfill, S. A. (2020). The Developing Mind: A Philosophical Introduction. London: Routledge.
Butterfill, S. A. (2021). Goals and targets: A developmental puzzle about sensitivity to others’ actions. Synthese, 198(1), 3969–3990.
Carey, S., & Xu, F. (2001). Infants’ knowledge of objects: Beyond object files and object tracking. Cognition, 80, 179–213.
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Edwards, K., & Low, J. (2019). Level 2 perspective-taking distinguishes automatic and non-automatic belief-tracking. Cognition, 193, 104017.
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  1. See, for example, Kovács et al. (2010); Kano et al. (2019); Kaminski et al. (2009); Superman, 1978. ↩︎

  2. Not all goal tracking in the first year of life can involve motor processes only (Butterfill, 2021). ↩︎

  3. This is the ‘P-A+ > P-A-’ effect. ↩︎

  4. To illustrate, it is plausible that Spelke’s Principles of Object Perception specify the model that characterizes object cognition in early infancy—but rather than being represented by infants, it seems that they characterise how a system of object indexes operates (Leslie, Xu, Tremoulet, & Scholl, 1998; Carey & Xu, 2001). Similarly, it may be that the Teleological Stance provides a model of goals from an infants’ perspective even though infants do not represent any of the principles. Butterfill (2020) discusses both examples. ↩︎

  5. This is probably over-cautious. It is unlikely that many readers will care at this stage. I should probably frame things in terms of representation (more familiar)? ↩︎

  6. See Kozhevnikov & Hegarty (2001) and Hubbard (2013), for example. White (2012) offers an opposing view. ↩︎