12 June 2002
Joint Attention: Its Nature, Reflexivity and Relation to Common Knowledge
Two parents are watching their son take his first upright steps in learning to walk. Here we have a paradigm of joint attention. The two parents are attending to their son; they are aware of each other’s attention to their son; and all this attention is wholly overt. Everything is in the open, nothing is hidden. In what does this openness or overtness consist? Can we characterize it explicitly, without using metaphors?
The parents are likely to switch their attention to each other and smile during this episode. This would be a case of what is sometimes called ‘contact attention’; and here too everything is in the open. Again, we can ask: what is a literal, explicit characterization of this openness?
As a stipulation, and following some but not all writers in the field, I will restrict the terms ‘joint attention’ and ‘contact attention’ to episodes which fully possess this openness. So our first task is to say what, constitutively, joint attention and contact attention are. We cannot hope to be clear about the relations of joint attention and contact attention to other phenomena and capacities until we have an answer to this foundational question. The question is not one of giving an analysis of the meaning of some word in English which has a determinate sense which is hard to make explicit. We use such metaphorical terms as ‘openness’ precisely because there is no such English term. So our task here is not conceptual analysis: it rather that of characterizing properly a complex psychological phenomenon, of saying what it is.
After offering such a characterization, I will go on to consider the relation of joint attention to common or mutual knowledge. I will argue that joint attention is more fundamental than mutual knowledge; that in many cases it makes mutual knowledge possible; and that a range of phenomena that have been characterized in terms of mutual knowledge should rather be elucidated in terms of joint attention. If these points, joint attention and is properties should be accorded a much more prominent position in the philosophy of mind and language than it has given hitherto.
1. Characterizing Joint Attention
Joint attention involves much more than two subjects attending to the same object. Two subjects could each be attending to the same object without being aware that the other is attending to the same object. More strikingly, two subjects could each be aware, and it could also be part of the content of their experience, that the other is attending to the same object, without the episode having the openness of joint attention and contact attention.
Consider two people who are standing facing each other, separated by a thick pane of glass. Suppose each person falsely believes that this glass is a one-way mirror, allowing him to see the other, but preventing the other from seeing him. So each really sees the other, and may see the other attending to him, while believing the other cannot see him. This is far from having the openness of contact attention. Similarly, we can suppose that in this situation, both are attending to something – an animal, say - in their common field of view, off to one side of the glass between them. Each may have a genuine perception of the other attending to exactly the same thing as he is attending to, viz. the animal. But because each believes the other cannot see him, this too is far from having the overtness present in our paradigm cases of joint attention.
It might be suggested that these are not cases of joint attention because each person does not perceive that the other is jointly attending with him in our strong, favoured sense of joint attention. That is a true statement about these cases. It is indeed true that in joint attention, subjects do perceive, or can be aware, that they are jointly attending. But this point cannot answer our original question, for it embeds the notion of joint attention within the content of psychological states such as attention, perception and awareness. If our task is to say what joint attention and contact attention are, we do not fully answer that question by giving a condition which embeds that very notion within certain mental states.
The point bears upon the suggestion that what is distinctive of joint attention is that the co-attender figures, as someone who is co-attending to the same object, as a constituent of the subject’s perceptual experience. What does ‘co-attender’ mean in such a condition? If ‘co-attender’ means just ‘attends to the same object’, that condition will be met in our example of the glass barrier that is falsely believed to be a one-way mirror, in the case in which both subjects attend to the animal off to one side. In that example, each perceives that the other is co-attending in that sense. If ‘co-attender’ means something stronger, and implies full joint attention to the object to which both are attending, the notion of a co-attender simply embeds the property which is to be explained, the overtness of joint attention. This is not to say that such embeddings do not provide an important constraint upon what joint attention is. It is just to say that they cannot be the full account. Compare: to be fashionable, something must be believed to be fashionable. But this cannot be a complete account of what it is to be fashionable. We cannot fully or completely individuate the property of being fashionable by saying that it is that property P such that to have P, something must be believed to be P. Too many other properties besides that of being fashionable meet this condition; and correspondingly it intuitively leaves out too much of what is involved in being fashionable.
How then are we to say, in a more informative way, what is missing in the glass-barrier examples, and is present in paradigm cases of genuine joint attention?
One of the challenges in carrying out this task lies in a difference between the joint attention, and the much-discussed phenomenon of mutual or common knowledge, so carefully identified and discussed by David Lewis and Stephen Schiffer. Let us follow Schiffer and take this as our definition of x and y’s having mutual knowledge* that p:
x knows that p
y knows that p
x knows that y knows that p
y knows that x knows that p
x knows that y knows that x knows that p
y knows that x knows that y knows that p
It is part of any plausible defence of the view that this definition actually applies to a particular pair of individuals that for a person to have a belief captured in one of the longer iterations of belief, it is only required that the believed content is something the person could infer to from what he indisputably currently believes. The thought of the believed content in a complex embedding does not have to enter his consciousness for the attribution of the belief to be correct. Many other beliefs are like this, as Schiffer notes: “I trust that it is true of each philosophy don in Oxford that he knows that his maternal grandmother was never married to Benito Mussolini” (Meaning, p.36).
Now intuitively, the overtness of joint attention is specifically a perceptual phenomenon. So could we write down this as involved in joint attention?
x perceives that x and y are attending to o
y perceives that x and y are attending to o
x perceives that y perceives that x and y are attending to o
y perceives that x perceives that x and y are attending to o
x perceives that y perceives that x perceives that x and y are attending to o
The problem is that the observation which defends the applicability of the definition of mutual knowledge* does not carry over to the perceptual case. The sense in which each philosophy don in Oxford has the belief about his maternal grandmother is a counterfactual sense. It is something he would infer from currently stored beliefs by principles he already accepts. But perception is not something counterfactual at all. Someone perceives something to be the case only if in the actual world he is in a conscious state with the representational content of what he perceives to be the case. And it is quite implausible that in all cases that display the overtness of joint attention, subjects are in the perceptual states mentioned above, with arbitrarily complex embeddings of the ‘perceives that’ operation.
The situation is yet more demanding. The overtness of genuine joint attention is not something merely dispositional or counterfactual either. In fact intuitively, what we are still characterizing metaphorically as the overtness of the situation of joint attention and of contact attention is not merely something which exists: it also seems to be present to the consciousness of the participants. How are we to account for this combination of characteristics, the presence of such overtness in consciousness, combined with the absence of arbitrarily complex embeddings within ‘perceives that…’?
We can begin by characterizing what it is for a state of affairs to have what I will label ‘mutual open-ended perceptual availability’ to two subjects. To be thus available, a state of affairs must meet the following condition:
if its obtaining, and the operation of perceptual and attentional mechanisms in the two subjects, bring it about that one of them perceives that it obtains, or perceives that the other perceives that it does, or perceives…etc., then the state of affairs of his so perceiving is available for the other to perceive.
The other does not actually have to perceive it for this condition to be met. Availability suffices. For the perceptual state of one person to be available to a second is for there to be information in the public environment of the second person which permits a sound computation to the content that the first person is in the perceptual state, using computational principles of the same kind (possibly differing only in complexity of the contents involved) as those already employed by the second person. In the case of joint attention, the state of affairs of the two subjects each attending to a given object is one which has mutual open-ended perceptual availability to them.
No finite mind can accommodate arbitrarily long embeddings of perceives that in its representational contents. What is available for a subject to perceive will eventually not be capable of entering the content of the perceiver’s states, because of some cognitive and computational limitations in the perceiver’s psychological economy. These limitations, however, should not be taken as limitations on the openness or overtness of the situation of full joint attention, but as limitations on the ability of the subject to take advantage of what is made available by such openness. If we were to have a definition of openness which can be satisfied only by infinite minds, it could not capture the openness which is enjoyed in joint attention by ordinary finite human beings.
Mutual open-ended perceptual availability of x and y’s attending to a particular object seems to be a necessary condition for the overtness of their joint attention to the object. It does not seem to be sufficient. Consider someone who is surprised and delighted when he discovers that when he is attending to an object, the other notices it, and he perceives the other noticing it. This can be the situation of someone who is just coming to appreciate the possibility of joint attention, but is not yet fully engaging in it. This is a case of incipient joint attention. Yet this person and his partner’s attention to an object may have the property of mutual open-ended perceptual availability. Having this property is consistent with merely incipient joint attention. It is one thing for a state of affairs to have that property; another for the participants to have some awareness that it does. I think that awareness that it has that property is essential to the full overtness of joint attention. In our example of false belief about the presence of one-way glass between the two subjects, those subjects did not have awareness of the mutual open-ended perceptual availability of their situation.
Mutual open-ended perceptual availability is a notion that it takes some intellectual reflection to formulate. It might be doubted for this reason whether it can really enter the content of perceptual experience. I would contest the objection. There are other clear cases in which a person experiences something as being a certain way, does not necessarily have a word or recognitional concept for that way, and in which his experiencing it as being that way consists in his experiencing it as having other features, which he may find it quite hard to articulate. To take a familiar example, someone may experience something as diamond-shaped. Someone can have this experience without having formed a recognitional concept diamond-shaped. To experience something as diamond-shaped is to experience it as a shape which is symmetrical about the bisectors of its angles. Even quite sophisticated thinkers find it hard to say what it is about something that is diamond-shaped that makes them experience it as so. All the same, the experience of symmetry about the bisectors of the angles is real and effective in producing the distinctive way the whole shape is experienced as being. At a much greater level of complexity, there is no difficulty of principle in two people experiencing their joint attention to an object as having a certain feature, a feature which consists in certain other properties as being experienced, properties they may find it hard to articulate despite the familiarity of the experience.
Is awareness by two people, attending to the same object, of the mutual open-ended perceptual availability of their situation sufficient for the intuitive openness which is characteristic of joint attention? Considering the possibilities in the abstract, we would have to say that this is still not sufficient for full openness. For someone could be aware that his situation has the property of mutual open-ended perceptual availability, without being aware that the other had the same awareness. One could think of cases in someone is told that the other, unlike oneself, does not have such awareness, and in which one has come to internalize this, so that it affects one’s perceptions of the other.
In actual cases of joint attention, each is aware of the mutual open-ended perceptual availability because he sees the other, he sees the object to which both are attending, and sees the spatial relations between these three things, and the other’s perceptual organs. So does it suffice to add to these conditions
x and y are jointly attending to o in our special sense iff
(a) x and y are attending to o;
(b) x and y are each aware that their attention in (a) has mutual open-ended perceptual availability;
this further requirement:
the awareness in (b) results from x and y’s perception of their spatial relations to o, and to one another, and to the sense organs involved in their attention in (a)?
That would certainly not suffice: if a person who informs each of x and y that their attention in (a) has mutual open-ended perceptual availability (or, as I shall sometimes abbreviate it: is open-ended) does so only when he has checked on the spatial relations of x,y and o, and the properties of their sense organs, the ‘results from’ relation in the proposed third requirement could hold. But this would not be case of full joint attention. But besides being wrong in detail, such a style of modification is taking a wrong turning. We are aiming to characterize the experience of openness itself, not what makes it available.
I suggest that one distinctive feature of full joint attention is as follows. Suppose you are a participant in a situation of full joint awareness. Concerning the total awareness which is involved in your joint attention, you are aware that: both you and the other person are aware that this total awareness exists.
On this view, the total awareness has an indexical intentional content which makes reference to the total awareness itself. Is this coherent and intelligible, and if so, what does it involve?
There are many examples of mental states and events whose intentional contents contain indexical components that make reference to those very same mental states and events. Suppose I am being lazy, and my friend encourages me on urgent practical grounds to start thinking. I may then think:
This thinking is coming too late.
My thought is about the very event of thinking itself; and the thought may very well be true. Mental events and states, like linguistic items, can sometimes refer to themselves indexically.
The phenomenon is to be distinguished from alleged cases falling under two other descriptions, whose coherence is doubtful. It is prima facie plausible that awareness of something is always distinct from what it is awareness of. (A closely related claim would be that awareness that something is the case is always distinct from the holding of the proposition of which it is awareness.) If that is so, no state can be or consist in part in awareness of itself. But the indexical mental self-reference of which I have been speaking does not involve such incoherence. To say that a mental state of awareness has an intentional content which refers to that awareness is not to say that it is an awareness that consists in part in an awareness of itself. The indexical component this awareness can refer to an awareness without the awareness referred to having itself as an individuating component. Such reference no more involves a regress of individuation than does the reference this thinking in ‘This thinking is coming too late’. Such a self-referential thought does not require that some event of thinking be a constituent of itself. For something to have an intentional content which refers to itself is not for it to be individuated by its relations to itself. There is no kind of objectionable ungroundedness here.
Indexical mental self-reference is also distinct from the use of such vacuous contents as ‘This intentional content is thus-and-so’. That last purports to refer to an intentional content; and arguably it cannot succeed in doing so. The indexical intentional contents with which I am concerned refer, by contrast, not to intentional contents but to mental events or states. So they do not have this second kind of ungroundedness either.
Indexical self-reference can generate iterations. The extent to which this possibility is realized depends upon what notions feature in the content in which the indexical self-reference is made, and on what principles hold for those notions. To illustrate how indexical self-reference can generate iterations, I will first consider a linguistic case, since it shows the phenomenon in relatively pure form, free of extraneous complications. The basic structures illustrated in this simple case are present also in much more complex examples.
Suppose we have a rather powerful encyclopedia E. It contains not only first-order information about the world, but also contains information about encyclopedias, including itself. In particular,
(i) The encyclopedia E says:
(C) Rome is Italy’s capital and this encyclopedia E contains this conjunction.
We can discuss the question of which propositions this encyclopedia is committed to. There is a notion of commitment, and an entailment-like notion of implication for which the following principle holds:
(Principle) If E is committed to A, and A implies B, then E is committed to B.
From E’s containing the self-referential information (C) and (Principle), we can obtain arbitrarily complex iterations of ‘E is committed to E is committed to E is committed to….C’, as follows.
From the statement of the example, proposition (i), we have
(ii) E is committed to C.
(iii) C implies E is committed to C.
We can now apply (Principle), taking the proposition C as the value of ‘A’ and the proposition ‘E is committed to C’ as the value of ‘B’. From (Principle), (ii) and (iii) it follows that
(iv) E is committed to: E is committed to C.
That gives our first iteration. We have also just shown:
(v) (ii) implies (iv).
We can now apply (Principle) again, taking the proposition (ii) as the value of ‘A’, and the proposition (iv) as the value of ‘B’. By (Principle), (iv) and (v), we can conclude:
(vi) E is committed to: E is committed to: E is committed to C.
It is clear that this pattern of argument can be repeated to obtain arbitrarily long iterations of ‘E is committed to’ preceding C. It should also be clear that the self-reference within (C) is wholly essential to obtaining these iterations. Suppose we had only this information about a variant encyclopedia F:
(i') The encyclopedia F says:
(D) Rome is Italy’s capital, and this encyclopedia F contains the information that Rome is Italy’s capital.
Arbitrarily high iterations do not follow from this. F says that it says that Rome is Italy’s capital; but it leaves it open (on the basis of the information given) as to whether it is committed to saying that it says it. (iii) in our little derivation above was crucial in arguing for the iterations. The analogue of (iii) does not hold in this case. (D) itself does not imply that F contains (D). (D) implies only that F contains the information that Rome is Italy’s capital, and not that it contains the information (D) itself.
Now we can return to mental states and events with indexical self-referential contents. Do they generate arbitrarily high iterations? To paraphrase a remark of Barwise, in the example of the encyclopedia, commitment travels at the speed of logic, but awareness and knowledge travel at the speed of the mind (and sometimes that speed may be zero.) Consider someone who has a genuinely reflexive awareness of his own pain. He is not merely aware that he is in pain. He rather meets the condition (vii):
(vii) he is aware that he is in pain, and he is aware this whole awareness exists.
Do arbitrarily high iterations of ‘he is aware that’ applied to ‘he is in pain’ follow from (vii)? They would if we had the following unrestricted principle:
If our subject is aware that an awareness exists, and this latter awareness involves his being F (for a suitably tight notion of involvement), then he is aware that he is F.
This unrestricted principle does not hold, if humans are not capable of arbitrarily complex states of awareness – as, to say it again, they cannot be if their minds are finite. But there is a clear sense in which the materials are available for a subject to rise to any particular level of iteration once he meets the reflexive condition (vii). (vii) is stronger than any finite iterations of ‘he is aware that’ applied to contents that do not refer to the mental state of awareness in question.
So it is with full joint attention. The account of full joint attention by x and y to o that I am now suggesting is this:
(a) x and y are attending to o;
(b) x and y are each aware that their attention in (a) has mutual open-ended perceptual availability; and
(c) x and y are each aware that this whole complex state of awareness (a) – (c) exists.
For any particular level of iteration of ‘x is aware that y is aware that…’, it could in principle be reached by x and y, if each co-operates and each extracts everything from the state of awareness that is required to reach that level. No finite mind can reach every level. But (a) – (c) remain very different from a non-self-referential state of awareness with finitely many iterations and a cutoff point. The elements of the finitely many iterations which do hold in a particular case of full joint attention also have a single common explanation, awareness with a indexically self-referential content. Just as (vii) is a case of individual genuinely reflexive consciousness, this account (a) – (c) of full joint attention can be regarded as treating it as a simple two-person case of genuinely reflexive social consciousness.
Important questions arise at this point about the relation of awareness with self-referential intentional contents to the possibility of self-involving situations, and to other self-referential mental states. I defer these metaphysical issues to an Appendix, in order not to lose the main thread of argument in the philosophy of mind relating the proposed nature of joint attention to issues about mutual knowledge.
2. Joint Attention and Mutual Knowledge
I am going to argue that the classical account of common or mutual knowledge developed by Lewis and Schiffer does not capture the openness of some of the situations to which it has been applied in the literature.
Lewis’s and Schiffer’s accounts, which are in their essentials identical, are justly famous and beautiful accounts of a phenomenon with which previous writers had grappled and failed. I do not question that the Lewis-Schiffer account gives a good philosophical explanation of mutual knowledge as (say) Schiffer defines it. I also think that it gives the correct explanation of mutual or common knowledge of such truths as that Bush is currently President of the US, and that people around here in New York drive on the right, speak English, and use dollars and cents as money. But I think there is a class of cases to which the Lewis-Schiffer account does not apply, even though these cases nevertheless display a distinctive kind of mutual overtness. This class includes even some examples by reference to which the notion of mutual knowledge introduced in this literature. The class of cases in question is that in which there is a kind of knowledge made available by joint attention.
To substantiate these claims, we need to look in more detail at the classical account. I will use Schiffer’s formulation (points corresponding to those I will make could be set out pari passu for the Lewis formulation). First, here is Schiffer’s development of an example, a case in which we “Suppose that you and I are dining together and that we are seated across from one another and that on the table between us is a rather conspicuous candle.” (31). He continues (I will change his notation for uniformity with the preceding, but otherwise this is verbatim):
“Clearly I know that there is a candle on the table. So
I also know that you know that there is a candle on the table. How do I know this? First, I know that if a “normal” person (i.e. a person with normal sense faculties, intelligence, and experience) has his eyes open and his head facing an object of a certain size (etc.), then that person will see that an object of a certain sort is before him. Secondly, I know that you are a “normal” person and I see that your open-eyed head is facing the candle. […] So
Further, I do not presume to be the only person aware of the above-mentioned law about normal people in certain circumstances; I also know that you know that normal people see things that are in their line of vision when their eyes are open, etc. And I have seen that you see that my open-eyed head is facing the candle. So I know that you know that I know that there is a candle on the table; i.e.
Schiffer’s account relies on what we can call generating properties (my terminology) and iterated inferences from these generating properties and their characteristics. In the example of mutual knowledge about the candle, the person x has the following generating property: that of being a visibly “normal”, open-eyed, conscious person who is identical with x and who, at a close distance, is directly facing the candle and y, who has the same properties vis-ŕ-vis x (cp.35). The idea is that in a case of mutual knowledge between x and y that p, if F is the generating property for x (with respect to p), and G is the generating property for y (with respect to p), F will have two crucial characteristics:
First, being F is sufficient for knowing that p, for knowing that x is F, and for knowing that y is G. The same holds for G correspondingly.
Second, for any proposition q, if being F and being G are each sufficient for knowing that q, then both being F and being G are sufficient for knowing that sufficiency condition.
Schiffer provides a finite basis for cases of mutual knowledge in terms of such generating properties. His theory is then that x and y mutually know that p iff there are generating properties of x and y with respect to the proposition p. The hierarchy of iterations of knowledge on the part of the each mutual knower is attained by that knower by inference from his knowledge that he and the other have the relevant generating properties. These iterations really do follow from this simple theory. The elegance of the approach is undeniable.
I will be arguing for three points. The first point, a negative claim, is a Thesis of Non-Necessity, that the Schifferian conditions are not required for the openness distinctive of many of the examples discussed. The second point, more positive, is that an Alternative Account can be given of a kind of openness and the knowledge it generates, an account which does not require mutual knowledge. The third claim is that this openness and knowledge of a sort characterized in the Alternative Account is in fact what characterizes a significant range of the phenomena for which mutual knowledge was invoked by earlier writers.
The Thesis of Non-Necessity says, then, that in some basic cases of joint attention, there is no such generating property and there are no such iterated inferences. That is, the overtness or openness of the situation is not an inferential matter. It is rather perceptual. The overtness of the situation is not captured by any finite basis for inference, because it is not a (personal-level) inferential matter at all. As a further elaboration of this Thesis, I also suggest that the cases in which there is no such inference are in a certain sense basic; and that the existence of these cases makes possible examples of mutual knowledge as characterized by Schiffer’s theory.
Two people, one or both of whom may be six years old, can jointly attend to a candle without so much as having the conception of a normal person, let alone beliefs or knowledge about the psychological capacities of normal people. Each person may simply see that the other sees the candle. They can also have the more complex forms of mutual awareness involved in our characterization of joint attention without engaging in inference at all, and a fortiori without employing a finite basis for inference.
Could it be replied that the finite basis, the relevant generating properties, are actually merely tacitly known, and that there is tacit inference from this tacitly known finite basis? Maybe so: but tacit knowledge and tacit inference, or computation, therefrom is entirely compatible with the finally attained state being a perceptual state, rather than being a personal-level inferential state. This is precisely our conception of tacit knowledge of the rules of a grammar for English. Unconscious operations which draw on the information stated in grammatical principles result in perceptual states, of finding a sentence grammatical or otherwise, or of hearing it as having a certain semantic and syntactic structure. But this is not personal-level inference, under rational control. Far from being an alternative to a perceptual account of the openness involved in joint attention, merely tacit knowledge is rather one particular kind of account of how a perceptual phenomenon might arise.
How, as things actually are, do people ever come to know that in general, normal people see things that are in front of them, that normal people know this, and so forth? It seems to me that this knowledge is attained by generalization from experience with particular situations in which one sees that someone is seeing something, and in which this is wholly overt in the way in which we have tried to characterize joint attention. Experience with and knowledge of the particular situation is rationally prior to knowledge of generalizations about normal persons. It is not clear that there is a plausible alternative way, as things actually are, in which knowledge about normal people could be acquired. Further, for the relevant properties of normal people to have the distinctive characteristics of Schiffer’s generating properties, one needs not merely experience of others seeing things, but of the openness of such situations. Common knowledge of such matters of driving conventions, and geographic and political matters, all relies on common knowledge of facts about perception; which in turn relies on the phenomenon of joint attention.
In fairness to Schiffer, I should add that his intention may simply have been to show that a finite basis for mutual knowledge is a genuine possibility. His concern may not have been the correct treatment of the particular example of the candle, but simply to show how mutual knowledge is so much as possible for finite minds. He did make clear one way in which mutual knowledge can be attained. All the same, we still do need a correct treatment of the example of the candle.
We cannot simply leave the matter with this Non-Necessity Thesis, resting content to note that not all cases of joint attention meet the conditions for mutual knowledge as characterized in Schiffer’s theory. For it is highly intuitive to say that there is some kind of openness to the knowledge that there is a candle on the table when there is joint attention to the candle. That is, there is a kind of openness to the knowledge that there is a candle on the table, an openness which is captured neither by the classical theory nor by the definition of mutual knowledge.
At this point, in attempting to characterize this openness, we have at least two options. One option is to seek to modify the classical theory of mutual knowledge. We might try to change some of the parameters of the classical theory, in a way that respects the perceptual character of this openness. It is not easy to see how this might be done. We cannot simply replace ‘knows’ by ‘perceives’ throughout Schiffer’s theory. Recall that in a case of mutual knowledge that p, the generating property F for x had to be such that if it is sufficient for knowing an arbitrary proposition, it is also sufficient for knowing that it is so sufficient. We cannot simply replace ‘know’ by ‘perceive’ here, and obtain something true. When we consider the sort of generating properties with which Schiffer was concerned – being a ‘normal’ perceiver, awake where there is light, etc. – it is implausible that when those conditions are sufficient for the subject knowing some given proposition, it is also literally perceived, rather than known, that they are so sufficient. If one says merely that this sufficiency is known, nothing follows about the availability of higher-order perceptions. Perceptual content is, as we have in effect commented before, not closed under a priori operations on its contents. Actually this point would apply even if it were maintained that in some cases the sufficiency of the generating property for perceiving certain propositions to hold could itself be perceived. From the facts that a given thinker perceives A to be the case, and perceives B to be the case, and the fact that A and B together trivially entail C, it does not follow that our subject perceives C to be the case. I will not pursue the option of modifying the Schifferian account in any more detail, because I think that account is suited only to the inferential case. Its essentially inferential structure is not well-suited to perceptual cases.
The other theoretical option is to say that there is an openness of knowledge in cases of joint attention that is not captured by the classical theory of mutual knowledge and its inferential mechanisms. At this point we aim to develop the Alternative Account. Let us speak of open knowledge in its own right. In particular, we consider open perceptual knowledge. We can say that
x and y have open perceptual knowledge that p iff
(a’) x and y both perceive that p;
(b’) x and y are both aware that their perceptions that p are mutually open-ended; and
(c’) x and y are aware that they are both aware of this very awareness (a’)-(c’).
Two people jointly attending to a candle between them may have open knowledge that the candle is flickering, even if they do not meet Schiffer’s finite basis for mutual knowledge that the candle is flickering. The more general case of open knowledge, perceptual or non-perceptual, could be characterized in terms of open perceptual knowledge and what is mutually known about each other’s memory and inferential procedures. This more general case would be a mixture of the perceptual character of joint attention and the inferential character of Schifferian mutual knowledge.
What are the properties of open perceptual knowledge? Open knowledge that p does not imply arbitrarily high iterations of knowledge, since, as we saw, arbitrarily high iterations of awareness are not implied by our description of joint awareness. Failure to imply arbitrarily high iterations of knowledge is not, however, the most fundamental difference between open knowledge and common knowledge. Indeed, Lewis notes that his particular formulation of common knowledge does not imply arbitrary iterations of actual knowledge or expectation, since the rationality assumptions required on his account for such a derivation become more demanding and implausible as we rise through higher levels (pp.55-6). What is distinctive of cases of open knowledge is not the absence of arbitrary iterations of knowledge, but rather the means by which such finite iterations as do hold are reached. Suppose that in the case of joint attention to the candle, x does reach this state:
x sees that y sees that the candle is flickering.
Since seeing that p is a form of knowledge that p (‘seeing that’ is a factive mental state operator with the properties noted by Williamson), it follows that
x knows that y sees that the candle is flickering.
This is something that follows from the nature of x’s state: it is not a matter of x making any transition in thought. By contrast, the final step is a matter of x himself making some transition in thought. Suppose also that x has some appreciation that seeing is a form of knowledge. Then from that fact, some minimal inferential competence, and the last displayed sentence we have that
x knows that y knows that the candle is flickering.
There are two notable features of this derivation of second-level iterated knowledge. One feature is that the iteration has not been derived from a Schifferian finite basis. It has instead been extracted from a complex state of awareness present in a case of joint attention. It has not been reached by any inferences about ‘normal’ people. The openness of a situation of joint attention consists in the facts, perceptual facts, given in our characterization of joint attention. Open knowledge is a byproduct of that perceptual openness.
The other notable feature of the derivation is that it requires x to appreciate that seeing something to be the case is a way of coming to know that it is the case. Autistic children, even able ones, do not in general have this knowledge. A study by Josef Perner, Uta Frith, Alan Leslie and Susan Leekam suggests that only one third of able autistic children realize that seeing that something is the case is way of coming to know that it is so. If their figure is roughly right, it follows from their work and the present account that most autistic children will not be capable of attaining open knowledge. Even if an autistic child sees that someone else is seeing something, he does not thereby gain knowledge of what the other knows. This may greatly reduce the interest, for the autistic child, of situations in which he sees that he and another are seeing the same thing.
My third claim was that there is a range of phenomena for which the Alternative Account, in terms of open knowledge and its source in joint attention, does better than mutual knowledge. Before generalizing, I take first the openness of linguistic communication. Suppose I say to you “It’s time for lunch”. My utterance is successful if we are jointly aware that I am saying that it is time for lunch. More generally, the paradigm of a successful indicative utterance in which one says that p is an utterance of which utterer and audience are jointly aware that it is a saying that p. A similar point applies pari passu for moods other than the indicative. The utterer aims to bring about a state of joint awareness whose content involves the meaning or, better, the intentional content of the utterance itself.
It is essential for this account that the intentional content of the utterance be part of the representational content of the experiences of utterer and listener. If the assignment of meaning to the utterance were merely a matter of personal-level inference, then joint awareness that I’ve said that it’s time for lunch would not be purely perceptual. But it is so.
It seems to me that the openness of communication does not require the inferential structures in Schiffer’s account of mutual knowledge. The openness of my communication consists rather in the fact that you and I have full joint awareness that I am saying that it’s time for lunch. We equally have open knowledge that I said it’s time for lunch.
I don’t need to have any beliefs about what normal people in our linguistic community do, or how they interpret utterances, to perceive you as saying that it’s time for lunch. Nor do I need such beliefs for us to be jointly aware of this fact about what you are saying. In fact in the cases in which I do have such knowledge, it seems to me to be based on experience of communications with relatives and acquaintances which already involve the kind of joint awareness I am identifying, in advance of any knowledge about the community. Even if some of my beliefs about what the wider community would mean by utterances of certain expressions are false, that need not prevent me from hearing your utterance correctly, and from our having full joint awareness of my saying that it’s time for lunch. Just as false beliefs about the mechanisms of perception does not prevent one from having ordinary perceptual knowledge about the world - since that knowledge does not rest on beliefs about the nature of perceptual mechanisms - so also having false beliefs about language in the community does not prevent one from being aware of what someone has said on a particular occasion.
Sometimes, when an expression or a surface syntactic structure has to be disambiguated, beliefs about one’s circumstances, and the likely topic of conversation, will affect how one hears one’s interlocutor’s utterance. But this does not mean that knowledge of meaning is purely inferential. The point is analogous to perceptual cases outside those of linguistic communication. Your knowledge of your peaceful circumstances means that you will discount an apparent perception as of a machine gun firing as incorrect. You may realize that, say, some ball-bearings have tumbled in rapid succession on a metal surface; and you may (but need not) come to hear the continuing event as such a tumbling. Perception remains distinct from judgement and belief; but it is false to say that it cannot be influenced by it, or by hypotheses entertained by the thinker. Sometimes also disambiguation itself is not a matter of conscious inference. The continuing context disambiguates without any entertaining or thought of alternative readings.
Joint attention is rarely a matter of one-off single events of joint attention. Joint attention and contact attention between two people is commonly extended over time. Examples are ubiquitous, and so important that one is inclined to say that their possibility is part of what it is to be distinctively human. Cases range from temporally extended games and interaction with a child, to adult games and interactions. In an extended encounter involving joint attention and contact attention, we can speak of the world which is created between the participants. This would involve the events which are jointly attended to, the participants’ relations to them, the development of both of these over time, and what is known at each stage about what has happened earlier in the world of joint attention. Nagel’s well-known paper ‘Sexual Perversion’ was right to emphasize the role of iterated psychological states in mutually open sexual interactions between two people. Here too I believe the phenomena are best characterized in terms of full joint attention and full contact attention. In such encounters too, a joint-attentional world is created between the participants.
Extended discourse between two people creates such a joint-attentional world. Some of the matters that David Lewis calls score-keeping in a language-game concern the created world of joint attention constructed and developed in the discourse to which the participants are jointly attending. Language has multiple special features; but I suggest that the openness of linguistic communication should be seen as a special case of the more general phenomenon of the openness of joint attention.
* * * * * * * * * *
Appendix: Reflexivity, Self-Involving Situations and Self-Referential States
This Appendix discusses the relation between the above treatment of full attention and two other approaches found in the extensive but scattered literature to other issues about mutual psychological properties. The first of these other approaches makes use respectively of self-involving situations; and it plunges us into metaphysical issues.
Self-Involving Situations: It can be tempting to elucidate the openness of full joint attention in terms of self-involving situations thus: when x and y are engaged in full joint attention to o, there is a situation S such that:
(si) S is a situation in which x and y are attending to o;
(sii) S is a situation in which x and y’s awareness that they are both attending to o is open-ended;
(siii) S is a situation in which x and y are perceptually aware of S.
Such a situation S is not merely self-involving. It is more specifically what we can call psychologically self-involving, in the sense that it involves a psychological relation to itself. Self-involving situations have been invoked by several writers, in a range of disciplines from psychology, philosophy and linguistics, to account either for mutual knowledge, or of weaker versions of mutual mental states. One of the most vigorous, and formally creative, proponents of this style of approach, Jon Barwise, went so far as to write that “Shared understanding in all its various guises (mutual belief, common knowledge, public information) rests on circular, or at least non-wellfounded situations. In as much as there are assumptions of such shared understanding throughout game theory, law, communication theory, and the like, we are constantly caught in non-wellfounded situations”.
Psychologically self-involving situations also have the power to give rise to iterations of attitudes. Once again, for the sake of illustration we start with a state other than awareness, to make the formal structures clear. Suppose we have a person - John - and a situation S which consists in the holding of (sa) and (sb):
(sb) John knows that S exists.
Let us write S ╞ A for ‘A holds in situation S’ (as in ‘A is a fact of situation S’ in the way this is used in the situation-theory of Barwise and Perry). Suppose also that we have the following Principle K holding of John’s knowledge:
(Principle K) If John knows that S exists and S ╞ A, then John knows that A.
From (Principle K), (sa) and (sb), it follows that
(1) John knows that p.
(2) S ╞ John knows that p.
So from (Principle K), (sb) and (2), we have
(3) John knows that John knows that p.
(4) S ╞ John knows that John knows that p.
And so forth, for arbitrarily many iterations of ‘John knows that’ applied to p. All of these follow from the Principle and the individuation of the psychologically self-involving situation S. The individuation of S together with the Principle are jointly clearly stronger than any finite list of iterations of ‘John knows that’ applied to p. No finite set of such iterations, however long, has the same implications as the self-involving situation S when combined with the Principle. So arbitrary iterations can be obtained from a psychologically self-involving situation, in the presence of a suitable principle governing the psychological relation in question.
Now we can return to full joint attention and its situation-theoretic characterization in conditions (si) – (siii). Actual perceivers are not like ideal knowers. Consider the principle
If x perceives situation S, and S ╞ A, then x perceives that A.
We cannot expect such a principle to hold without restriction. When S is psychologically self-involving, as in our characterization of full joint attention, this principle would imply the existence of arbitrarily high iterations of ‘perceives that’ in x’s perceptual states. Since these states - unlike beliefs conceived as inexplicit in Schiffer’s - are not dispositional, this principle would imply the existence of actual occurrent perceptual states that full joint attenders do not in fact enjoy. Ordinary perceivers go only so far in extracting what it is in principle possible to extract from a perceptually self-involving situation. So the clauses (si) – (siii) do not commit us to saying that x and y actually have arbitrarily complex perceptual states with contents like ‘He perceives that I perceive that he perceives….’. When x is perceptually aware of the state S described in clauses (si) – (siii), x’s perceptual system has the information to compute correctly from states it is already in to new contents, such as ‘y is aware of a state in which I’m aware of a state in which he’s attending to o’. But it does not follow from the fact that x has the information to compute, subpersonally, to this content, that he actually carries out the computation. On all of these most recent points, the advocate of self-involving situations for characterizing full joint attention can say much the same as I said in the main text, in defending the treatment in terms of mental states and events that are self-referential.
Are self-involving situations metaphysically legitimate? The intuition that the involve an unacceptable regress of individuation has various sources. Anyone who has been brought up on the iterative hierarchy as the intended model of ZF set theory will have been trained to find self-involving situations suspect. If we want a rational articulation of the suspicion, it is likely to be formulated intuitively as the idea that the world itself must be well-founded. On this view, self-involving situations need not be ruled out; but they are legitimate only if their existence can be explained in terms of situations, states of affairs or other entities that are well-founded. We can this ‘insistence on objective well-foundedness’. Proponents of non-well-founded situations have developed illuminating formal theories of what they would have to be like, and what is involved in commitment to them. Peter Aczel’s non-well-founded set theory is a particularly elegant exposition of these commitments. Aczel shows that existence of non-well-founded sets is implied by nothing more than the axiom that every graph has a unique decoration. Valuable as this formal development is, I do not think that by itself it can answer the doubts of someone who insists on objective well-foundedness. The simplest case of a one-element graph which generates a set which is a member of itself seems to involve something which is individuated in terms of itself (see Aczel, p.XXX). This will concentrate, rather than answer, the doubts of those who insist on objective well-foundedness.
This Appendix is no place for a full-dress discussion of whether the world must be objectively well-founded. But I do have one positive proposal to make, a proposal which explains why attempts to characterize mutual mental states in terms of self-involving situations are found attractive, and even legitimizes some of them, while not contradicting any principle to that the world must be objectively well-founded. Let us first distinguish between eliminable and ineliminable self-involving situations. An eliminable self-involving situation is one whose existence can be fully explained in terms of situations or other entities that are not self-involving. The person who insists that reality must be objectively well-founded should not have any quarrel with the existence of eliminable self-involving situations. Now the positive proposal I offer is that some self-involving situations consist in the occurrence of self-referential mental states or events. The self-involving situations can, in these cases, be obtained from self-referential mental states by what we can call ‘an inside-out transformation’. Suppose the person x is as follows:
x is aware that p; and
x is aware that this whole awareness exists.
I suggest that we can, with preservation of truth, transform this into the following statement about a self-involving situation:
There is a situation S which is constituted by the facts that
x is aware that p, and
x is aware that S exists.
Self-involving situations descriptions of which are attainable by such transformations are in the nature of the case eliminable in the above sense, and are consistent with reality being objectively well-founded. I suggest this is the source of the attractiveness of using self-involving situations to characterize full joint attention, and other phenomena of mutuality. The explanation in terms of this inside-out transformation, if correct, also implies that the legitimacy of self-involving situations in the description of these psychological phenomena does not by itself legitimize self-involving situations that are not reachable by use of inside-out transformations. Whether self-involving situations not so reachable are metaphysically legitimate remains open. Nothing here excludes the hypothesis that the world must be objectively well-founded.
Fixed-Point Characterizations: A principle which characterizes a notion informatively in terms of itself is what logicians call a ‘fixed-point principle’. One approach developed by some theorists of mutual notions is to try to use fixed-point principles to individuate those very notions themselves. In the case of mutual knowledge, for instance, we can say that x and y mutually know that p iff
x and y know that p, and
x and y know that it is mutual knowledge that p.
In his paper ‘Three Views’, Jon Barwise noted that this fixed-point characterization will not be equivalent to the characterization in terms of repeated finite iterations of knowledge when x and y have limited logical abilities (p.378). Joint attention under the approach I have been suggesting also supports a fixed-point principle. x and y are jointly attending to o iff:
x and y are attending to o;
x and y are aware this attention is open-ended; and
x and y are each aware that they are jointly attending to o.
The above discussion shows that we do not require ineliminable self-involving situations to explain how it can be that a particular fixed-point principle holds. Fixed-point characterizations, taken in themselves, are of course not well-founded; but in all the cases discussed here, the fixed-point characterizations of mutual psychological states that are true hold in virtue of psychological states and events that are well-founded.
 I am grateful to Naomi Eilan for encouraging me to write up in more systematic form remarks I made about the relations between joint attention and common knowledge in the general discussion session at the 1999 Warwick Conference on Joint Attention. (This is also known as calling my bluff.) I have been greatly helped by the challenge of responding to Stephen Schiffer’s incisive critical comments on an earlier draft, and by Gilbert Harman’s guidance on the massive existing literature on common knowledge.
 This proposal is made in John Campbell’s paper [ref] in this volume; and in Chapter 8, ‘Joint Attention’, of his Reference and Consciousness (Oxford: Oxford University Press, 2002).
 This means that if co-attention is construed in the weaker, first way there will be a gap in Campbell’s argument that perception of co-attention provides a basis for mutual knowledge.
 D. Lewis, Convention: A Philosophical Study (Cambridge, Mass.: Harvard University Press, 1969), esp. Ch. II, Section 1; and S. Schiffer, Meaning (Oxford: Oxford University Press, 1988 reprinting), esp. Ch. II, Section 2.
 See C. Peacocke, A Study of Concepts (Cambridge, Mass.: MIT Press, 1992), Chapter 3.
 Such states have been used by Gilbert Harman in the characterization of mutual knowledge. He observes: ‘A group of people have mutual knowledge of p if each knows p AND WE KNOW THIS, where ‘THIS’ refers to the whole fact known.’ See his review of Jonathan Bennett’s Linguistic Behavior, in Language 53 (1977) 417-24, at p.422. Harman also makes use of self-referential intentions to analogous iterative effect in his review of Schiffer’s Meaning, in the Journal of Philosophy 71 (1974) 224-229.
 J. Barwise, ‘Three Views of Common Knowledge’, in Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge ed. M. Vardi (Los Altos, Ca.: Morgan Kaufmann, 1988)
 This summarizes his formulation on pp.34-5.
 Schiffer himself slips into the very natural, and in my view true, description of one person as seeing that the other sees something to be the case (p.31).
 Knowledge and Its Limits (Oxford: Oxford University Press, 2000), pp.34-41.
 ‘Exploration of the Autistic Child’s Theory of Mind: Knowledge, Belief and Communication’, Child Development 60 (1989) 689-700: see in particular their discussion of knowledge-formation tasks.
 ‘Sexual Perversion’, Journal of Philosophy 66 (1969) 5-17.
 There is significant and illuminating use of self-involving situations in H. Clark and C. Marshall, ‘Definite reference and mutual knowledge’, in Elements of Discourse Understanding, ed. A. Joshi, B. Webber and I. Sag (Cambridge: Cambridge University Press, 1981); J. Barwise, ‘Three Views of Common Knowledge’, op. cit.; and D. Sperber and D. Wilson, Relevance (Oxford: Blackwell, second edition 1995), at p.42.
 J. Barwise, The Situation in Logic: CSLI Lecture Notes 17 (Stanford, Ca.: CSLI, 1996), p.198.
J. Barwise and J. Perry, Situations and Attitudes (Cambridge, Mass.: MIT Press, 1983); J. Barwise, The Situation in Logic.
 Non-Well-Founded Sets, CSLI Lecture Notes 14 (Stanford, Ca.: CSLI, 1988).