How Persuasive is Wilby’s Solution to the Problem of Common Knowledge in Joint Attention?

I attend to a candle. You attend to the candle. We know of each other doing just that. We jointly attend. Simple enough, right? Unfortunately, philosophically conceptualising this concept is rather difficult. It would have to be some action-enabling, open epistemic notion that is at the same time compatible with empirical evidence from psychology. Here I argue against one such notion from Wilby of shared mental states in joint attention. I also consider Tomasello’s critique of the applicability of philosophical accounts to psychology altogether.

Joint attention is a psychological phenomenon that we encounter daily and is hence important to psychologists and philosophers. It is a process wherein two or more agents simultaneously attend to an object and have common knowledge of each other doing so. For this to be initiated, we want to except the premise of openness, which states that our own mental states are transparent to other agents. This is important because it means that if one agent (say, Amalia) follows the gaze of a second (Gudrun), her experiences need to be accessible to Gudrun, otherwise propositions of the form “Gudrun knows that the Amalia knows” could not be formed, which we think are necessary for common knowledge in joint attention (Wilby, 2010: 84). We can observe this knowledge already in one year olds, who after having initiated joint attention, are able to “track their shared experiences with specific individuals” over time (Carpenter & Liebal, 2011: 164; see also Liebal, Carpenter and Tomasello, 2010: 545). Here the specific referent is important. It is not the case that joint attention merely means looking in the same direction (see Liszkowski, Carpenter & Tomasello, 2007: 1; in Carpenter & Liebal, 2011: 163), but engaging in it is a “premeditated” (Franco & Butterworth, 1996: 307;Franco & Gagliano, 2001: 289; see also Liszkowski, Albrecht, Carpenter & Tomasello, 2008: 157), goal oriented (see Gomez, Sarriá & Tamarit, 1993: 397) action that specifically aims to capture the interest of another agent (see Liszkowski, Carpenter & Tomasello, 2007: 1; in Carpenter & Liebal, 2011: 163). When one agent initiates joint attention, the “communicative looks” usually take the following form: Amalia looks at Gudrun, Gudrun at Amalia, Amalia at object, Gudrun at object, both at each other (sharing look) (see Brink, 2003; Tomasello, 2008).

The following problem now arises: As we have seen, the evidence suggests that 1) common knowledge exists and is action-enabling and that 2) our mental states are open. Finding an account of what common knowledge looks like however has presented us with many difficulties (see Eilan, 2005: 25; Heal, 2005: 39 in Wilby, 2010). One of them is that excepting both premises leads to an infinite regression of mental states: Let us say Amalia and Gudrun jointly attend to x, hence “Amalia knows x” and “Gudrun knows x”. Now, to be aware of the other person’s attention, we may add “Gudrun knows that Amalia knows x”; as well as “Amalia knows that Gudrun knows x”. It could still be the case that both know the other is observing x but do not jointly attend, so also “Amalia knows that Gudrun knows that Amalia knows x” and Gudrun knows that Amalia knows that Gudrun knows x”. Still, it may be that the above are true yet neither of the two knows that they are watching each other, so another layer of propositions must be added ad infinitum (Wilby, 2010: 85). This is unacceptable, since psychological evidence suggests that an infinite regress would be cognitively implausible. However, as Wilby pointed out, a simple appeal to psychological plausibility does not constitute a solution, since just ignoring the above propositions beyond some level of adding layers, will not satisfy the previously outlined openness requirement (2010: 87).

Schiffer famously tackled this problem by showing that a finitely defined situation can bring about this infinite regress (1972; in Wilby, 2010: 88-92). This is accomplished by ascribing a property of “normality” to the agents. Amalia and Gudrun commonly know x iff there are properties F and H and the following are true: 1) Amalia is F, which is a property that describes her normality as agent; 2) Gudrun is H, which is a similar property for her; 3) having either property suffices for knowing x as well as knowing that both have these properties; and 4) for “any proposition”, if having either property suffices for knowing it, than having such a property also suffices for knowing that such a property suffices. What follows, is that Amalia and Gudrun still need an infinite regression to commonly know x, however, if they have the properties F and H respectively, then 3) can be put into 4) in place of “any proposition”. What comes out of 4) can again be put into that same place, ad infinitum (This version of the argument is extremely abridged, for a more elaborate account see Schiffer, 1972; Wilby, 2010; or Peacocke, 2005: 308-310). This property of normality could be something like unhindered perception, the absence of disorders, et cetera (see Schiffer, 1972: 35). In essence, what Schiffer offers here is not a solution to the problem of infinite regress, but rather he has shown that common knowledge can be conceptualised with a finite set of premises.

This is where Wilby comes in. He argues that instead of embracing the regress by means of a finite base, one ought to use that very base to account for common knowledge (2010: 88). He starts this project by attacking Schiffer’s concept of the properties F and H in terms of normality, which he states are “remarkably underspecified” (Wilby, 2010: 89). Normality does not “guarantee” getting us even as far as 3) since it is possible for both agents to be normal, yet not know that the other possesses that property (Wilby, 2010: 90). More specifically, Wilby presents counterexamples that seem to show that when normality is put into Schiffer’s analysis, under certain circumstances the truth values do not turn out expectedly (see mirror and candle example in Wilby, 2010: 90). In order to avoid that, he speculates that a finer, scenario-specific grain to the properties F and H is required.

This has a logical consequence: Under Schiffer’s account eventually we are able to derive the biconditional between “Amalia is F iff Gudrun is H”. This biconditional is justified because under Schiffer’s assumption that both have some property of normality, being normal for Amalia means being at least somewhat similar to the other agent, Gudrun. If we now make the properties more specific to a situation, we can only justify the claim that in a case of common knowledge, property F of Amalia is necessary and sufficient for the distinct property H of Gudrun. This is problematic because it means that suddenly two ontologically separate properties are “necessary conditions for each other” (Wilby, 2010: 91) To overcome this problem, Wilby proposes an unusual idea: Instead of the biconditional connecting two distinct properties, we ought to pair the two in an identity relation, i.e. essentially replacing F and H with one property J that must be true for both agents. This can be fed back into Schiffer’s analysis where 1) and 2) just become “Amalia and Gudrun are J”, and this new property replaces F and H in 3) and 4) (For a complete analysis see Wilby, 2010).

Let me summarise where we are: We started with experimental evidence of what we think joint attention needs to account for. This task led us to the problem of common knowledge and the infinite regression. Schiffer proposed that this regression can be derived from a finite base, which Wilby now adapted to show a finite solution to the entire problem, that entails that there is some property both agents share, that is “just there” and not reducible to individual properties or mental states of the agents involved. This essay shall not examine Wilby’s logic, but suffice it to say that the solution is neat. The next step must now be to question whether it is able to account for the phenomena we previously listed.

Wilby claims that his notion is not just just useful, but “indispensable” in doing so (2010: 96). Since common knowledge is a cornerstone of social cognition also beyond joint attention, having a primitive notion of common knowledge means that many phenomena can be explained in terms of that primitive notion leading to a much more tidy theory of social cognition. One possible problem where this idea may help according to Wilby are false-belief tasks (2010: 97, for such a task see exemplary Wimmer & Perner, 1983) since here standard theory-theory fails.

I believe that this is a very nebulous argument. From his article it is not at all clear how this is supposed to follow. What Wilby merely offers is a formal logical solution to an epistemological problem. He explains a missing biconditional with appeal to a shared mental state and as neat as the resulting logical explanation for common knowledge may be, it seems premature to derive explanatory power in regard to experimental evidence at this point. Let me make this point clearer by side-tracking to Tomasello’s critique against any characterisation of common knowledge that leads to an infinite regress on the grounds that it could not reflect the cognitive processes involved in joint attention (2008: 96). Philosophers are hence engaging in a pointless activity of accounting for an “idealised notion” of common knowledge that is inherently unable to incorporate our “psychological limitations” (Wilby, 2010: 86). Tomasello then proposes to solve the problem by simply ignoring propositions of the type “Gudrun knows that Amalia knows x” beyond a certain level of complexity. As we have previously seen, this cannot be a solution since it guarantees not the openness requirement for common knowledge. Even though Tomasello’s critique is a bit clumsy in this respect, I believe that he is on to something: He concedes that common knowledge is an integral part of joint attention (Carpenter & Liebal, 2011: 164; see also Liebal, Carpenter and Tomasello, 2010: 545) which he cannot completely account for, but at the same time he questions the applicability of philosophical solutions to empirical problems. In this specific example, Wilby may want to argue that his account for common knowledge is a solution to the infinite regress problem and not a restatement of it, but I would like to expand on this puzzle of how promising Wilby’s account can effectively be for explaining the empirical evidence.

If we accept “Gudrun and Amalia are J”, with J being a shared property that hints towards a shared mental state, then the following puzzle presents itself: Schilbach (et al, 2009) has shown that areas of the brain associated with reward were stimulated when a participant engaged in gaze-following with a computer screen. Hence we can abstract that the cognitive processes that are involved in joint attention where active, otherwise no reward would have been warranted. Understanding these processes entails understanding how common knowledge can arise. If however, those processes were active when engaging in joint attention with an inanimate screen, it seems plausible to assume that the partners in this interaction are not similar in any relevant respects, hence the property J is violated. Moreover, we can potentially analyse all cognitive processes that the participant utilised in this study. If it is possible to explain all cognitive processes required with a single individual, then multiplying these processes with more people should give the explanation for common knowledge that we desire without introducing anomalous shared mental states the way Wilby suggests. Therefore I submit that Wilby’s account for common knowledge is superfluous.

Wilby would have a forceful way of responding to this critique: He might claim that I misconstruct his argument. After all, what he hints towards is not some form of telepathy wherein the cognitive processes of Amalia and Gudrun merge, but rather a primitive account for common knowledge. Hence, the idea that I cannot engage in joint attention with a screen entails not the falsity of his account, but rather the need to find a solution that explains why that is not joint attention, which his notion of a shared property can do. Still, I would argue that in order to be rewarded, one first has to accomplish; and that Schillbach as well as other previously mentioned experimental evidence seems to indicate that agents use very complex cognitive processes to arrive at the common knowledge required to initiate joint attention on their own (see examplory “communicative looks” in Brink, 2003; or theories of the “circular reactions model for imitative behaviour” paired with mirror neurones in initiating joint attention in Grossberg & Vladusich, 2010: 940), not the other way round.

In conclusion, I have to concede that the Schillbach counterexample has to overcome the explanatory limitations of the experiment. Still, I would stick to the weaker claim that since children need a sequence of communicative looks to engage in joint attention, it seems intuitive to assume that that sequence is accompanied by propositions in the form of “Amalia knows x”; and that all cognitive facilities needed for joint attention are present in every participants own mind. Therefore, finding an account of joint attention that begins with a shared mental state from which individual mental states follow still seems suspicious and a challenge Wilby will have to respond to in greater detail.

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