Imagination constrained, imagination constructed

ABSTRACT

A number of authors have asked what it takes for a course of mental imagery to be epistemically or practically useful. This paper addresses a prior question, namely, the difference between courses of imagination that are realistic and those that are fantastic. One approach, suggested by recent literature concerning the utility of imagery, holds that a course of imagination represents realistically if and only if the course of events represented conforms to certain accepted constraints. Against this it will be argued that the constraints cannot be both permissive enough and restrictive enough. An alternative approach adds as a necessary condition that realistic courses of imagination are constructed in accordance with certain procedures on the basis of remembered perceptions.

KEYWORDS:

• Mental imagery
• imagination
• perception
• representation
• similarity

1. Using imagination

We often use our visual imaginations to guide our actions. An experienced builder of bird houses can knock out a pretty good bird house without having to measure all the pieces, just by visualizing the pieces she needs and cutting them to size accordingly. If I come to a puddle on the trail and it is not too broad, I can imagine jumping over it. If I need to fill six glasses with lemonade, I try to make enough lemonade in the pitcher so that I can imagine filling all six glasses with the contents. A person playing pool imagines striking the cue ball with the cue in such a way that the cue ball will strike the target ball in such a way that the target ball will roll into a pocket, and he then tries to act as he had imagined.

In order to use our visual imaginations to solve problems in these ways, it is important that we be able to distinguish between courses of imagination representing what will work and courses of imagination representing courses of action that will not work. If the bird house builder imagines a roof that is too small for the rest of the bird house, she needs to be able to detect that fact. If I make only enough lemonade for six glasses, but I imagine filling ten glasses with it, then I need to be able to tell that what I am imagining is mistaken.

This paper will be concerned with drawing the distinction illustrated in these examples. But before I can specify my aims more precisely, I need to say that the kind of imagination I will be concerned with is exclusively the use of mental imagery. What I call a course of imagination is a series of mental images. A course of imagination may include the imagery of sensory modalities other than vision, but the examples in this paper will mostly be confined to visual imagery. I will assume that it is clear enough what ‘mental imagery’ means, even though it is a nontrivial philosophical task to define it. Roughly, mental imagery consists of endogenously generated representations having the same representational format as perceptions. There is also imagination in a broader sense, consisting wholly or in part of discursive, proposition-bearing thoughts, but that is just not the kind of imagination I am concerned with.

In light of the examples above, one might reasonably ask: What is the difference between courses of imagination that are useful and those that are not? A number of recent authors, some of whose views I will review, have posed this question, but I think there is another question that we need to answer first. Whether a course of imagination is useful will depend on what we want to do with it. If I imagine a workable procedure for replacing a flat bicycle tire, that will not be of any help when I want to replace the tumbler belt in an electric clothes dryer. But I might recognize that I have imagined a workable procedure for changing a flat bicycle tire, even if I have no flat tires. More generally, a course of imagination may realistically represent a course of events but be useless because one will not find oneself in a position where such a course of events might be initiated.

So the question we need to ask is not, ‘What is the distinction between useful courses of imagination and useless ones?’, but rather, ‘What is the distinction between courses of imagination that are realistic and those that are fantastic?’ In these terms, imagining filling six glasses with the lemonade in the pitcher might be realistic, while imagining filling ten is fantastic. This will be a different distinction than the distinction between useful and useless courses of imagination, because there will be realistic courses of imagination that we have no use for. If I imagine a sheep being shorn by a shepherd, then that may be realistic. If I imagine a sheep being shorn by another sheep, then that is fantastic. But I have no use for either of those courses of imagination, since I am not in the business of shearing sheep. There might even be courses of imagination that we regard as realistic and distinguish from fantastic variants, although the distinction could not be put to use in any human activity. A geologist might distinguish between imagining molten lava flowing down a mountain in a realistic way and imagining its flowing down in a fantastic way, while the prudential relevance of both of these imaginings may be only that they represent the lava flowing down in some way.

Still, we may assume that the useful courses of imagination will be confined to those that are realistic. So an account of the distinction between realistic and fantastic courses of imagination, while of interest for its own sake, will also be a contribution to an account of the distinction between useful and useless courses of imagination. Occasionally we may find it useful to entertain a fantastic course of imagination, for instance, when we are trying to imagine a story line for a science fiction movie. I will assume that these odd cases can be sequestered by means of a good definition of basic practical uses. But I will not try to give the definition here. Moreover, we should not expect the distinction between realistic and fantastic to be perfectly sharp; the boundary between the two will be in many ways vague. Imagining that the pitcher of lemonade will fill seven or eight glasses might lie in the vague borderline between realistically imagining that it will fill six glasses and fantastically imagining that it will fill ten.

Finally I can state my objective: It is to criticize one kind of account of the realistic/fantastic distinction and to contrast it with another kind. The account of realism that I want to criticize claims, roughly, that the realistic courses of imagination are those that conform to certain constraints. No one who has said this has worked the theory out in any detail, but so many people have endorsed the vague idea in some way that it will be worthwhile to try to formulate it in a sympathetic manner and then explain why it does not work. My criticism will be basically that the constraints cannot be both permissive enough to allow the realistic imagining of non-closed systems and restrictive enough to rule out every fantastic eventuality. The alternative I want to propose in place of the constraints theory holds that realistic courses of imagination must be constructed in accordance with certain constructive procedures on the basis of perceptual experiences that we have actually had. Some candidate constructive procedures will be described, but this part of the paper will remain programmatic, since the purpose of this paper is to criticize the account based on constraints and promote as a promising alternative the account based on constructive procedures.

2. What some people have said

Quite a number of recent authors have been concerned with the question of how mental imagery can be useful for epistemic and practical purposes. Many of them have answered that the useful courses if imagination are those that conform to some kind of constraints.

For instance, Amy Kind (2018) asks how we can put our power to create mental images to use in justifying beliefs. Her answer is that we can do that insofar as our imaginings are constrained by our beliefs. Kind’s aim is to explain how acts of imagining can produce beliefs in such a way that those beliefs are justified. While her examples (drawn from stories about Nikola Tesla and Temple Grandin) illustrate practical problem-solving by means of mental imagery, she takes the product of this problem-solving to be justified belief. The reason the mental imagery can generate justified beliefs is that mental imagery is itself constrained by beliefs.

I have various beliefs about the world – about what color the shoes are, about what sorts of things have scared my children in the past, about the typical volume of students’ voices in the hallway, and about my colleague’s mental states. These beliefs about the world infuse my imaginings. In doing so, they act as constraints on my imagination, just as pre-programmed variables set constraints on computer simulations. (Kind 2018, 243)

Kind leaves a lot of questions open, in particular, how beliefs can interact with mental imagery in such a way that the product of the imagery is justified belief.¹

Like Kind, Joshua Myers (2021a, 2021b) is concerned with the use of mental imagery in forming justified beliefs, although he allows that imagination may have non-cognitive uses as well, for instance, in pretense (2021a, section 2). An act of imagination may convey justification to a belief that it generates. But it does that, he says, only if it is constrained by what what he calls constrainers (2021a, section 4). Myers says that constrainers may be many kinds of mental states, such as perceptions, beliefs, memories, intentions and regularities ‘encoded’ in the ‘perceptual system’ (for example, regularities about how towers of blocks fall) (2021b, 105). But in his examples, the constrainers that constrain how a course of imagination unfolds are supposed to be beliefs. (He does not say what the contents of the pertinent beliefs might be but only what they must be about.) Moreover, Myers needs the constrainers in his account of justification through imagination to be beliefs, because acts of imagination can bestow justifications on beliefs only if the acts of imagination are themselves justified, and the only kind of justification for imaginings that he countenances is that which they inherit from the justified beliefs that constrain them (2021a, section 5).

In contrast to Kind and Myers, Peter Langland-Hassan (2016) does not confine the utility of imagination that concerns him to learning facts about the world but includes practical utility as another kind of utility that imagination might have. He describes imagination has having a ‘capacity to guide action and rational inference’ (2016, 62). Langland-Hassan is concerned with both propositional imagining and episodes of forming mental imagery in my sense, which he calls sensory imagining, but I will confine my attention to what he says about the latter. Langland-Hassan dubs the kind of sensory imagining that he deems most useful for practical and epistemic purposes guiding chosen imaginings (Langland-Hassan 2016, 63). An episode of guiding chosen imagining begins with an intention to imagine something. It may be a deliberate intention or it may be a mere intention in action, such as the intention to choose one drinking glass rather than another from the cabinet (Langland-Hassan 2016, 62). Once we have formed an initial image in accordance with our intention, a sequence of imaginative states ensues, which form the imaginative episode (Langland-Hassan 2016, 64). The sequence of imaginative states develops from the initial image in accordance with what Langland-Hassan calls lateral constraints (Langland-Hassan 2016, 69–71). It continues in this way, that is, until a further intention intervenes that modifies or redirects the imaginative episode by adding imagistic content that does not just follow from the imaginative states that came before in accordance with the lateral constraints (Langland-Hassan 2016, 63, 75). Intentions set the task, and imagination, in conformity to constraints, generates the solution.²

Langland-Hassan does not want to say that what he calls lateral constraints are propositions believed. But he does describe them as ‘stored generalizations about the behavior of different kinds of objects in different settings’ and he posits a set of algorithms that ‘allow’ conformity to such generalizations (Langland-Hassan 2016, 71). He writes, ‘It is normally thought that imagination is a cognitive faculty with its own internal logic or principles of operation that determine how imaginings unfold across time’ (Langland-Hassan 2016, 67). He emphasizes that the constraints describe events in the world, such as the behavior of a basketball rolling off a table; they do not describe the sequence of ‘appearances’ of things in our imagination (Langland-Hassan 2016, 71). The picture we get from Langland-Hassan, then, is that the lateral constraints are generalizations about how things happen that we are somehow wired to respect in the sense that when we are trying to imagine in a way that is useful for practical and epistemic purposes what we imagine at each stage in an imaginative episode will follow from what we imagined coming before in conformity to those generalizations. I do not think he would deny that some of these generalizations might also be believed.

None of these authors proposes a definition of an epistemically or practically useful course of imagination. But they and others clearly have some hunch in common, so that it would useful to try to formulate on their behalf a general account and see whether it survives scrutiny. If not, then of course one might blame the extrapolation rather than anything these authors actually say. But even in that case, the exercise, if the result is negative, will highlight the fact that it is really not clear how the hunch is supposed to be developed with precision, and we might get the sense that these authors are going down a wrong path.³

Towards extracting a general account from the views of these authors (which I will do in section 4), I think it is important to revise the question somewhat, as I indicated in the introduction. We need to formulate it not as a question about the distinction between useful and useless courses of imagination but as a question about the distinction between realistic and fantastic courses of imagination. Compare the question, ‘What makes an assertion useful?’ Here it would seem clear that we would want to separate out the question, ‘What makes an assertion justified?’ Having answered that, we could then address the questions, ‘When is a justified assertion useful?’ and ‘How can an unjustified assertion sometimes be useful despite its being unjustified?’ My reformulation of the question about courses of imagination is similar in spirit, although I do not want to attribute to realistic courses of imagination the property of being justified. We want first to identify a characteristic of courses of imagination that the useful courses of imagination must normally possess, and then we might go on to address the question of what makes a course of imagination possessing this characteristic useful in a given setting. The pertinent characteristic is what I am calling realism. It might sometimes be hard to hold the distinction between realism and utility in mind, because the use for imagination that some authors have envisioned is its use in justifying beliefs. Even then, however, we can distinguish between the realism of a course of imagination and its utility in justifying beliefs. Having said what I think realism is and what it is not, I will not then go on to address the further question of usefulness. I do not see any reason to think that Langland-Hassan, Kind or Myers would object to this strategy.

3. What the realistic/fantastic distinction is not

The examples in the first section show well enough, I hope, that we do draw a distinction between realistic and fantastic courses of imagination. I do not know of any way to define it apart from the sorts of theories that I will consider in this paper. As we have seen, we cannot maintain, as a pretheoretical way of drawing the distinction, that the realistic courses of imagination are those that we are prepared to rely on and the fantastic those that are not prepared to rely on.

The distinction between realistic and fantastic courses of imagination that I intend to account for is a subjective distinction, between what is realistic for the agent and what is fantastic for the agent. What is realistic for an agent is not necessarily what would be realistic for others, better instructed by experience. I presume, however, that what makes a course of imagination realistic is not simply that the agent judges it to be. Rather, a course of imagination that is realistic for an agent is one that has those properties that ought to lead the agent to deem it realistic. An account of the distinction between realistic and fantastic courses of imagination must identify the properties of a course of imagination that make it realistic for the agent. Inasmuch as Langland-Hassan, Kind and Myers all hold that the constraints on useful imagining are mental states of the imaginer, they should agree that the realistic/fantastic distinction should be relativized to agents in this way.

Not only is it not the case that the realistic/fantastic distinction is constituted by the judgments of the imagining agent, but also it is not the case that agents who make use of the distinction have to be aware of it as such. To the extent that agents are able to confine the courses of imagination that they put to use to those that are realistic, they will have to be sensitive to the distinction. That means that they are reliably able to filter out and not rely on those courses of imagination that are fantastic. But they can do this without in any sense metacognitively conceiving of some courses of imagination as realistic and others as fantastic. How we should say they are able to do this will depend on what we, as theorists, take the distinction to consist in, which is the topic of this paper.

There are areas of human experience that the distinction between realistic and fantastic to be defined here does not pertain to. In particular, we may distinguish between realistic and fantastic interactions with other thinking beings. I might imagine a conversation and take it to be unrealistic that the person I am representing would ever say such a thing. I do not propose to account for the distinction as it pertains to this area of human experience. The distinction at issue in this paper concerns imagining the motions and interactions of bodies, including living bodies. I acknowledge that it might not always be easy to segregate the two areas of experience.

I acknowledged at the start that, in addition to the kind of imagining exclusively by means of mental imagery that is exclusively my subject, there is also a kind of mixed-mode imagining, in which one imagines a sequence of events and accompanies these imaginings with proposition-bearing thoughts about the imagined objects and events.⁴ For instance, I can imagine a child taking a sip of what looks like coffee and then grimacing and I can think, ‘She doesn’t like the taste’. Among such mixed-mode imaginings we might also distinguish between those that are realistic and those that are fantastic, and some of the fantastic ones might be realistic with respect to the purely imagistic component. But this is another aspect of the realistic/fantastic distinction that I will simply set aside for present purposes.

A course of imagination might be realistic and yet represent a highly improbable course of events. Suppose the pool player imagines the cue ball striking the four ball, the four ball striking the nine ball, the nine ball striking the twelve ball and the twelve ball going into a pocket. The probability of such an event, described as I just described it, relative to the class of attempts to drive the twelve ball into a pocket, might be quite low, and yet the course of imagining might be realistic, provided the velocities and angles are realistic. For every course of imagination of any complex event, if we describe it in enough detail, then the probability of an event so described, relative to any general reference class, will be very low. So the distinction between probable (or not improbable) and improbable event types is incomparable to the distinction between realistic and fantastic courses of imagination that is my topic.

My question about the distinction between realistic and fantastic courses of imagination is also not the same as the metaphysical question about what possible worlds there are. Again, the former question concerns a subjective distinction, but an answer to the question ‘What is metaphysically possible?’, if answerable at all, ought to be the same for everyone. My question is also not the same as the question what a person regards as metaphysically possible. My question is specifically about a distinction in mental imagery. There are certainly questions about metaphysical possibility that cannot be answered by means of mental imagery (such as whether Richard Nixon might have had different parents).

There is perhaps a connection between my question and the metaphysical question, inasmuch as if a course of imagination is realistic for an agent, then the agent must not regard that course of imagination as representing a metaphysical impossibility. But an agent’s not regarding a course of imagination as representing an impossibility is not sufficient to ensure that it is realistic for the agent. There is a possible world in which a sheep shears another sheep, I might suppose, but if I imagine that, then what I imagine is not realistic. There is a possible world in which a dog communicates in English, but if I imagine that, then what I imagine is not realistic. Though some authors have wanted to approach the metaphysical question via the consideration of what we can imagine (e.g. Gregory 2020), my question is not that one.

In my own positive account, I will assume that perceptions, including remembered perceptions, are internal representations that stand in a relation of representation to external states of affairs and consequently may be accurate or inaccurate. I will also assume that perceptual and imagistic representations do not classify objects into kinds; consequently, they do not have propositional content.⁵ Mental images represent in the same way as perceptions, except that they need not be grounded in things that exist, so that they may not in any clear sense be assessable for accuracy. How to make sense of the idea that a representation represents something that does not exist is another philosophical problem in its own right, but not one that I will take up here. The authors I criticize may not all share my assumption that the contents of perceptual and imagistic representations are not propositions, but my criticisms will not turn on this question. Since perceptions and images, according to me, do not have propositional content, descriptions, in words, of what they represent must not be understood as expressing the propositional contents of these perceptions and images.

It would be a mistake to turn my question about the distinction between realistic and fantastic into a question about the meaning of a modal operator, whether it be ‘possibly’ or some other. Because, as I assume, images do not have propositional content, my question cannot be translated into a question about the meaning of an operator under which that propositional content may be embedded.

4. The constraints theory, generally formulated

The constraints theory holds, roughly, that the realistic courses of imagining are distinguished from the fantastic through their conformity to certain constraints. In order to formulate the constraints theory more precisely, there are basically two questions that need to be addressed. First, what is the nature of the constraints and conformity to the constraints? And, second, what is the relation between the constraints and realistic courses of imagination?

We have already seen that Kind (2018) thinks of the constraints as beliefs. Myers lists several kinds of mental states as potential ‘constrainers’ (2021b, 105), but in his examples, the constrainers are beliefs, and the constrainers that he appeals to in his account of justification through imagination apparently have to be beliefs. Langland-Hassan explicitly endorses a more liberal conception of his lateral constraints, such that the constraints may ensure conformity to generalizations without these generalizations being the objects of belief (2016, 71).

For all of these authors, the constraints on useful courses of imagination are supposed to describe conditions on events that we might imagine. The constraints are mental states, but they do not directly represent the mental images or the course of imagination. They constrain our imagination in the sense that the events we imagine must conform to them. What violates a constraint is, in the first instance, a course of events such as might be imagined, but we can also say that in a secondary sense a course of imagination violates a constraint if the course of events imagined violates it.

Quite apart from what these authors say, there is considerable leeway in how the constraints in the constraints theory might be conceived. We could think of the constraints as propositions that the imagining agent believes. These beliefs could be beliefs of which we sometimes are aware, or they could be beliefs that are always unconscious. Or we could think of the constraints as architectural constraints written into the mind’s operating system, i.e. as methods of computation.⁶ These architectural constraints could be in part intrinsic to the inherited structure of any human being that matures in a biologically normal way in a biologically normal environment. But presumably, this structure would be largely a product of learning, shaped by the particular events to which the person happens to be exposed. Such architectural constraints might still be thought of as representing the nonmental world, inasmuch as there may be generalizations about the world such that a course of imagination conforms to the constraints if and only if the events represented conform to these generalizations. However, since what is constrained is only the imagination and not the nonmental world, we do not have to suppose that the constraints accurately represent what happens in the nonmental world.

What it might mean to say that a course of imagination conforms to a constraint will depend on what kind of content an imagistic representation is supposed to have. If the content of imagistic representations is exclusively propositional content, then perhaps we can understand conformity as instantiation, defined as a relation between propositions. If we do not think that imagistic representations have propositional content, because, for instance, we think that images represent more in the manner of pictures or maps and that pictures and maps do not have propositional contents, then we can suppose that a course of imagination conforms to a constraint inasmuch as images elicit conceptual representations and these elicited conceptual representations have propositional contents that instantiate the general conditions of the constraints, so that the constraints indirectly constrain what can be imagined.

If there are many different constraints that a course of imagination has to conform to, then it might be a problem to explain what in the mind ensures that a course of imagination satisfies them all. A proponent of the constraints theory can get around this by supposing that the mind employs some kind of heuristic to ensure satisfaction of the constraints that are most relevant to the course of imagination at issue. Call the constraints identified by the heuristic the critical constraints for a given course of imagination. The constraints theorist can then draw a distinction (which I have so far not drawn) between a course of imagination’s being realistic for an agent and its being regarded as realistic by the agent. While a course of imagination really is realistic for the imagining agent if and only if it conforms to all of the constraints, the agent will regard a course of imagination as realistic if and only if it conforms to the critical constraints for that course of imagination. However, in what follows I will not attend to this distinction.

As for the relation between realistic courses of imaginations and the constraints, we can distinguish between two basic approaches. According to what I will call the determinative constraints theory, the constraints must entirely dictate the development over time of a realistic course of imagination. For any stage in a realistic course of imagination, the next stage is a determinate function of the constraints and the content of the imagining at the earlier stage. According to I will call the nondeterminative constraints theory, the constraints are merely necessary conditions that a course of imagination must satisfy in order to count as realistic and any course of imagination that satisfies all of the constraints thereby qualifies as realistic. On this account, different courses of imagination may share a single starting point but develop in different ways and yet still both count as realistic, provided they both conform to all of the constraints.

Between these two extremes we might identify a kind of constraints theory that specifies where the constraints must completely determine the course of a realistic course of imagination and where the constraints merely provide individually necessary but jointly sufficient conditions. Perhaps Langland-Hassan could be interpreted as taking such an approach. In what he calls guiding chosen imaginings, a realistic course of imagination not interrupted by any new intentions must strictly proceed in accordance with the constraints. The changes in what is imagined brought about by a new intention need not follow by constraints from what is imagined to come before. However, the changes brought about by new intentions must conform to certain constraints considered as necessary conditions, since otherwise what is intended might introduce an element of the fantastic into the course of imagination.

Against some versions of the constraints theory one could make the following objection: It puts the mental imagery out of business. For instance, if we said that the constraints always take the form of propositions believed, then one could make the following objection: Wherever it appears to us, introspectively, that we are using mental imagery to solve a problem, that appearance is an illusion. Really, we are simply drawing conclusions from the constraints, and the mental imagery provides only an expendable illustration of some of the intermediate conclusions. To the extent that Kind and Myers take the constraints to be beliefs, this objection would seem to bear on their views. Myers acknowledges the objection and rejects it (2021a, section 3; 2021b, 113–117). However, I will not develop this objection any further, because it is clear enough that some other conceptions of the constraints, in particular Langland-Hassan’s, can evade it, even if Myers’s does not. As I explained, we could suppose that the constraints are innate or acquired principles of computation or, more generally, transformations, and that the transformations operate on mental imagery. The constraints might govern transformations of mental images and still, as required, express generalizations about the motions and interactions of nonmental objects.⁷ On this account, realistic courses of imagination might be all and only those that conform to the constraints, and still the mental imagery would play an essential role as that on which the constraints operate.

5. Against the determinative constraints theory

The creation of a realistic course of imagination, as conceived of by the determinative constraints theory, may be illustrated with my example of the pool player. The pool player begins by perceiving a pool table with pool balls on it in a certain configuration and by intending to imagine striking the cue ball with the cue in a certain direction. From there, the determinative constraints take over and dictate the motions of the balls that will be imagined until the balls are imagined coming to rest. At that point, the pool player can continue the imaginative episode by intending to imagine striking the cue ball, in its newly imagined position, among the other balls in their newly imagined positions, from a certain angle. Again, the subsequent imaginative episode is dictated by the determinative constraints. And so on. The realistic courses of imagination will be just those that follow in this way from an initiating intention in accordance with determinative constraints.

The problem with the determinative constraints theory is that it applies only to imaginings of closed systems. By a closed system I mean a system in which the only active forces are those that arise from the objects represented in the system at the start. Not every closed system in this sense will be a closed system as a physicist would define closed systems, since I do not stipulate that all of the energy exhibited by events in the system must derive from elsewhere in the system. (In a closed system in my sense, an animal might spontaneously start to move, although we do not account for the energy that it uses in doing so.) In a closed system in my sense, some objects present at the start can give rise to what is effectively a new object (as the birdhouse builder can build a birdhouse). But in a closed system no object not present at the start and not created within the system can initiate a series of events, because that initiation will require a force that does not arise from the objects that are present at the start.

The example of the pool table is suitable for illustrating the determinative constraints theory, because in this case, we can almost suppose that each subsequent imaginative state follows from the previous imaginative state with the same inexorability as each subsequent state of motion of the pool balls follows from the one before, provided nothing is imagined to intervene in the represented sequence of events. But only if we are imagining a closed system of this kind, in which the only active forces are those that arise from the objects represented in the system at the start, will there be constraints that dictate what must happen next. Even the physical laws of motion dictate what will happen next only on the assumption that the system they are applied to is closed (in the even stronger sense from physics). The law of gravity does not tell us that a dropped object falls to the earth, because nothing prevents another object from catching it before it hits the ground. (The law of gravity is an equation that describes one force, among others.) I do not contend that there are determinative constraints for every closed system in my sense, but only that there are none for systems that are not closed.

There are at least two problems for the assumption that the constraints determine what we must imagine given what we have imagined to begin with. The first problem is that even when what we imagine is a closed system, most of us do not know any set of constraints that completely determine how we should imagine the system developing. We do not know such constraints explicitly, and we do not know them in the sense that we are disposed to imagine in conformity to them. The objection is not that the constraints we follow need not express genuine laws of nature – the truth of the constraints as laws of nature is not required by the determinative constraints theory. The objection is that we do not even know of any constraints that determine what we should imagine. For some closed systems there might actually be laws of physics that determine what will happen next, but even then most of us do not in any sense know what they are.

The second problem is that it is just not true that our realistic imaginings are confined to imaginings of closed systems. If I am learning to drive, I can realistically imagine driving continuously until I come to a red stop light, but I can also realistically imagine suddenly stopping to avoid an oblivious pedestrian who has stepped into the road. Imagining the interference of objects from outside the system might be one of the best ways we have to prepare ourselves for what might happen. The default in our perceptual experiences is certainly not that no events due to objects from outside the system that we are observing intervene. Apart from very rare, tightly controlled scenarios, outside events intervene in the course of events we perceive almost incessantly. We can expect that our realistic imaginative episodes will resemble our perceptual experiences in this respect. Our imaginative episodes will be very frequently punctuated by imagined events from outside the system that we are imagining, and the intervening events that we imagine will not follow by constraints from the events that we imagined coming before.⁸

As I said in the previous section, one might wish to modify the determinative constraints theory by allowing that the imagining of an event from outside an imagined closed system is the product of a special intention to modify the course of imagination, subject to nondeterminative constraints, and one might propose this as a solution that Langland-Hassan might wish to adopt. But I think Langland-Hassan would not endorse this answer, and the answer is only as good as the nondeterminative constraints theory to be considered in the next section.

If we acknowledge that our realistic courses of imagination are frequently punctuated by imagined events that do not strictly follow by the constraints from what we imagined before, and suppose that all of these undetermined imaginings require a new intention, then the result will approximate the conception of imagination that Langland-Hassan calls Only Top Down, which says that a course of imagination is entirely dictated by the thinker’s intentions. He rightly rejects this on the grounds that it leaves the imagistic representations little real work to do (Langland-Hassan 2016, 66–67). Intentions merely set the task that is supposed to be solved by letting imagination run in conformity to the constraints. Moreover, the imaginings that Langland-Hassan calls misguiding chosen (Langland-Hassan 2016, 79) share the element of guidance by intentions but not the conformity to lateral constraints, and they are not supposed to be useful. Rather, it is supposed to be conformity to the lateral constraints that bestows on the course of our imaginings the potential to be practically or epistemically useful.

In any case, the proposed modification will be only as good as the nondeterminative constraints theory in the next section. When we intend to imagine intervening events from outside an imagined closed system, the intervening events that we imagine may be either realistic or fantastic. An oblivious pedestrian stepping into the road is quite realistic. But if I imagine that Superman steps into the road and carries my car over the traffic jam in the intersection, then that is fantastic. So if we wanted to accommodate non-closed systems by appeal to intentions to imagine intervening events from outside the closed system imagined, then we will need there to be nondeterminative constraints sufficient to distinguish the realistic interventions that we might intend to imagine from the fantastic interventions that we might intend to imagine.

6. Constraints without determination

Let us turn then to the second conception of the constraints theory, the nondeterminative constraints theory. According to this, the constraints are individually necessary and jointly sufficient, but courses of imagination that share a common starting point may develop in various ways while satisfying all of the constraints. The basic problem is that once we open the door to alternative developments within the confines of the constraints, it is hard to see how we can close the door to developments that are fantastic. In criticizing this theory, I will assume that if there really are the sorts of constraints that the nondeterminative theory needs, then in principle we could comprehensively write them out. My challenge will be a challenge to the contention that we can do that.

To get a sense for the problem, consider a yellow leaf blown from the branch of a tree by a soft breeze on an autumn day. It wafts gently to and fro as it sinks to the ground, and we can imagine many different irregular trajectories all of which would count as realistic. But we can also imagine trajectories that would count as fantastic. Imagine the leaf defying the lift of the air beneath it and shooting speedily to the ground. Or the leaf suddenly goes into a rapid spin or shoots rapidly from side to side, or remains for several minutes suspended in exactly the same spot in space. Or imagine a goat wandering around in its pen. We can realistically imagine it turning left, turning right, climbing up on its rock, tugging on a bush, making bleating sounds. But we do not realistically imagine it jumping up and doing a double flip in the air or imagine it roaring like a lion.

It is hard to see how we could write the constraints so that all and only those motions that are realistic for us would satisfy the constraints. One strategy would be to write constraints that tell us what is not allowed: no shooting to the ground for the leaf, no roaring like a lion for the goat. But this seems to require an endless list. For any finite list of odd behaviors that are forbidden, there will be still other odd behaviors that we need to forbid as well. It will turn out that we forgot to mention that the leaf will not suddenly disintegrate into a puff of dust. Or we forgot to mention that the goat will not within 30 seconds grow hair down to the ground.

The other strategy would be to write constraints that tell us positively what is allowed. The constraints will be of the form: Under conditions C, all and only motions/behaviors of kind K will be realistic. We do not have to think of such constraints as determinative. Kind K may include many different kinds of motions/behaviors for a given starting state. Even so, this option still presumes that conditions C define a closed system in the sense I have defined in the previous section. If the conditions C do not define a closed system, then there will not be any kind K such that only events of kind K are allowed. But first, as we observed in the critique of the determinative constraints theory, it is not correct that our realistic imaginings are confined to imaginings of closed systems. It is not correct, for instance, that every realistic course of my imagining me driving represents me as continuing to drive until I reach a stop sign. It is not correct that a course of imagining the goat in its yard will be realistic only if it represents the goat as walking along a path in its yard. I can imagine that somebody opens the gate and lets the goat out.

And second, even if we confine ourselves to closed systems, in the sense that we imagine no new forces introduced by objects from outside of the system we imagined at the start, we still come back to the question of how to rule out all of the odd things we can imagine happening but which must not happen if what we imagine is to count as realistic. The leaf must not turn into a frisbee. The goat must not start to play chess. Since the constraints are not now supposed to be determinative, we cannot simply suppose that the imagined system runs its course determined by the constraints applied what we imagined at the start. I see no alternative to falling back on the strategy of listing the things that must not happen. But we cannot expect any such list to be comprehensive.

Thus I take myself to have provided a difficult challenge to the claim that realistic courses of imagination are exactly those that conform to a set of constraints. Still, I grant that failure to conform to some constraint might disqualify a course of imagination from realism. It might contravene some architectural constraint on processing, innate or acquired, or it might violate a general belief. I can imagine a tall brick being moved behind an rectangular board, and then imagine the board being lowered in the direction of the brick all the way to the floor. This course of imagination might contravene a basic disposition to expect object permanency.⁹ Perhaps nothing would prevent me from imagining myself building some bird-like wings and then using them to fly other than my belief, based on a failed experiment, that they would not work. But since any elaborate course of imagination will represent an event that is unlikely to happen just as it is imagined (see section 3 above), we should stipulate that the beliefs and architectural constraints that may rule a course of imagination fantastic are exclusively those that are possessed already prior to the occurrence of the course of imagination in question, not merely beliefs to the effect that nothing quite like that (the event precisely as imagined) will happen.

7. Realism in construction

A plausible alternative to the constraints theory would be to say that realistic courses of imagination must be constructed from present and remembered perceptions by means of admissible constructive procedures. By construction here I mean the application of additive and transformative procedures defined over perceptual and imagistic representations. For example, if I imagine two people in a room together whom I have only perceived separately, that is a kind of additive constructive procedure. Or if I imagine a small rug stretched to cover the length of a hallway, that is a kind of transformative constructive procedure.

Although a course of mental imagery may present itself to us as continuous, we can usefully think of it as consisting of a sequence of frames. We can think of these frames as analogous to the frames in an old-fashioned motion picture on film. There will be certain structural constraints that each frame has to meet in order to represent a geometrically realistic scene. Moreover, as noted at the end of the previous section, when we have antecedent general constraints that we expect our perceptions to conform to, we may impose those as conditions on realistic courses of imagination as well.

Leaving open for the moment the nature of the representation of geometrical structure and the content of the constructive procedures, we can propose the following general definition of a realistic course of imagination: A course of imagination is realistic for agent S at time t if and only if (1) it conforms to all general constraints that S possesses prior to t, (2) each frame in it is for S at t a realistic representation of spatial configuration, and (3) it can be constructed by S at t in accordance with admissible constructive procedures. A course of imagination is fantastic if and only if it is not realistic. This is what I will call the constructive theory. In the remainder, I will specify the constructive theory still further by explaining in a general way how realism in the representation of spatial configuration can be defined and by proposing some candidates for admissible constructive procedures.¹⁰

Admissible constructive procedures, as I will explain them, are an altogether different kind of thing than the constraints posited by the constraints theory. The constraints of the constraints theory are constraints on the contents of our imaginings. As we have seen (sections 2 and 4), they are supposed to be facts about the world that our imaginings have to respect. The admissible constructive procedures, in contrast, will be rules of permission defined on perceptual and imagistic mental representations as such.

I should stress also (though this implies no contrast with the constraints theory) that admissible constructive procedures will not be criteria by which the mind reflects on its own contents and judges a course of imagination to be realistic. Rather, when a course of imagination is constructed in the admissible way (and the other two conditions in the definition above are satisfied), it thereby counts as realistic for the agent. Admissibly constructed courses of imagination get dropped, so to speak, into the realism box.

7.1. Realistic representation of spatial configuration

A condition on a course of imagination being realistic is that each frame in the sequence be a realistic representation of spatial configuration. In some respects our perceptions of spatial configuration may be systematically inaccurate. For instance, we may systematically underestimate the distance of things from ourselves, so that lines that appear to extend from our bodies in parallel actually diverge (Hatfield 2016). Nonetheless I will suppose that there is a way of representing spatial configurations in perception that the mind, so to speak, settles for as accurate. Thus the frames in a course of mental imagery that realistically represent spatial configuration may be defined as those that are formed in the way that perceptions are formed when they are formed in the way that the mind settles for as accurate (except that nothing is actually perceived).

The case in which a representation is fantastic will be the case in which the representations of spatial relations fail to resolve, so that agent does not settle for its perceptual representations being accurate. For instance, when we look at the perceptually descending staircase depicted in M. C. Escher’s lithograph ‘Klimmen en dalen’ (1960), the image fails to resolve in that we cannot consistently represent the stairs on opposite segments of the staircase in relations of higher and lower. When we look at the Penrose triangle, the image fails to resolve in that we cannot consistently represent a given surface as nearer or farther than another given surface.

In section 3, I said that a realistic course of imagination is not just what the agent judges to be a realistic course of imagination but rather one that has those properties that ought to lead the agent to deem it realistic. So in particular, to say that an agent settles for a perceptual representation of spatial configuration as accurate is not to say that the agent upon reflection judges it to be accurate. (Agents do not often reflect on their perceptual representations at all.) To explain the realism of representations of spatial configuration more precisely we would need to define the relation between a perceptual representation and an external scenario that holds when the representation is one that an agent, in the intended sense, settles for as accurate.

To do that, we would need to do at least the following two things. First, we would need to identify the entities that may be the basic elements of spatial configuration represented in perception. These might include edges and surfaces, but perhaps also major axes, spatial orientations and whole objects.¹¹ Second, we would need to define in a precise way the relation that holds between a structure of parts in a perception and a structure of parts in the external world when the agent settles for the perception as an accurate representation of the external structure. In my opinion, that relation can be defined as a homomorphic mapping of perceptual parts into external parts, relative to a mapping of relations between internal parts into relations between external parts (Gauker 2020). But a further development of this conception of the perceptual representation of spatial configuration is beyond the scope of this paper.

7.2. Admissible constructive procedures

Among courses of imagination that realistically represent spatial configurations, some will represent the motions of, and interactions between objects realistically, and others will represent them fantastically. An important difference will be in part that the former are grounded in past experience in the right way. Realistic courses of imagination are not confined to memories of actually perceived events. But remembered perceptions can serve as models for constructing a course of imagination that, by virtue of its being so modeled, is realistic. There are at least two sorts of admissible constructive procedures by means of which remembered perceptions may be transformed into realistic courses of imagination. I call these transformations cut-and-paste and morphing.

Cut-and-paste is an operation, or a collection of a number of distinct operations, in which the mind takes remembered perceptions or courses of imagination already qualified as realistic and seamlessly recomposes their component parts. In one such operation, the mind takes a remembered sequence of perceptions or an admissibly constructed sequence of mental images A-B-C, cuts it into two sequences, A-B and B-C (with a common member B), and takes another remembered sequence of perceptions or admissibly constructed sequence of mental images D-B-E, cuts it into two sequences, D-B and B-E, and then pastes sequence A-B to sequence B-E to form the sequence A-B-E, which has never been experienced as a perception. To ensure a realistic transition, it is important that the last member of the first pasted-in sequence be identical to the first member of the second paste-in sequence (and that it occur in the new sequence without repetition). If the last member of the first sequence is not also the first member of the second sequence, then nothing prevents the transition from the end of the first sequence to the beginning of the second sequence from being completely fantastic.

An example of this kind of cut-and-paste operation would be the following: I have observed the center fielder (in a game of American baseball) throw the ball to the third baseman (A), who in turn threw the ball to the second baseman (B), who in turn threw it to the first baseman (C). I have also observed the left fielder throw the ball to the third baseman (D), who in turn threw it to the second baseman (B), who in turn threw it to the catcher (E). Accordingly, I can join in imagination the first two segments of the first of these remembered perceptions (A-B) to the second two segments of the second of these remembered perceptions (B-E), to form a course of imagination in which the center fielder throws to the third baseman, the third baseman throws to the second baseman, and the second baseman throws to the catcher (A-B-E). The segment of this course of imagination that is common to the two remembered perceptions is the image of the third basemen throwing the ball to the second baseman (B).

Another kind of cut-and-paste operation allows the construction of a representation of two simultaneous sequences of events from two prior representations of independent sequences of events. Sequences of events will be independent in the requisite sense if they do not involve different parts of one individual body and the bodies in the sequences do not come into contact. So if I realistically imagine a cat walking down the sidewalk from left to right and realistically imagine a dog walking along the sidewalk from right to left, then I can realistically imagine the cat and the dog passing each other on the sidewalk, provided each keeps to its side of the sidewalk and they do not collide.

A background assumption for my presentation of a second admissible constructive procedure, morphing, is that perceptions and imagistic mental representations, apart from representing spatial configurations of particulars and surfaces, represent also the locations of things in a many-dimensional space of objective qualities. The dimensions of the quality space are dimensions of variation that we are perceptually sensitive to, such as hue, length, weight, perhaps fierceness, perhaps jerkiness of motion, etc. (There might be thousands of dimensions.) The representations of location in objective quality space can be modeled as marks in a perceptual similarity space. A mark need not have a value on every dimension. Although I call it a perceptual similarity space, endogenously generated imagistic representations may have locations in this perceptual similarity space as well. Since a perception is also a representation of a spatial configuration of parts, both the whole and each of the parts may have their own locations in perceptual similarity space. Questions that I will not take up here are: how to define the mapping from points in perceptual similarity space into points in objective quality space, and how, in terms of that mapping, to define the accuracy of perceptions in representing locations in objective quality space.

As an individual perception may be conceived as a having a location in a perceptual similarity space, so too a sequence of perceptions may be conceived as a sequence of marks in perceptual similarity space. Call a smooth curve drawn through such a sequence of marks a trajectory through perceptual similarity space. An individual mark in perceptual similarity space may be translated across perceptual similarity space by adding or subtracting a certain amount to its locations on each of a number of dimensions. A uniform translation of a trajectory through perceptual similarity space is a curve through perceptual similarity space that results from translating each point on the trajectory in the same way, that is, by, for each dimension, adding to or subtracting from that mark the same amount that is added to or subtracted from the other marks on that dimension. Morphing a sequence of remembered perceptions means forming a series of mental images that lie on a uniform translation of a trajectory through remembered perceptions. (Morphing need not involve imagining a process of one thing being transformed into another thing.)

Examples of morphing in this sense would include: Imagining a piece of driftwood floating down the river and then morphing the images into a course of imagination representing a raft floating down the river. Perceiving someone making a funny face and then imagining someone else making that funny face. (This example assumes that there are dimensions of perceptual similarity space suitable to representing the similarities and differences among faces.) Perceiving someone making a dress out of cloth and imagining someone making a dress out of plastic. (One component of the perception, namely, the perception of the cloth, is morphed, while the perception of the other component, the sewing, is simply duplicated in imagination.) Perceiving someone run around the edge of the football field at a certain pace and then imagining someone running around the edge of the football field at a faster pace.

As the example of running should indicate, there have to be certain limits on the extent of acceptable morphing. In my imagination I can morph an image of a runner running fast into an image of a runner running ten times as fast, but the result will be fantastic. Sometimes these limits might be imposed by judgments. I happen to know that no one can run a mile in less than a minute. But there might be some innate disposition to confine our morphing within limits, and that disposition might be fine-tuned through learning. I acknowledged in section 3 above that the distinction between realistic and fantastic courses of imagination is liable to be somewhat vague. The limits on morphing may be one source of vagueness.

The reason morphing is defined as a uniform translation of a trajectory through similarity space is that nonuniform translations are liable to produce monsters. If I observe a terrier jump through a hoop and morph my memory of that into the image of a spaniel jumping through a hoop, then what I imagine has to look like a spaniel both before the jump and after. If I observe a toy robot that walks across a table top, I can imagine a bigger toy robot that moves across the table top. But in doing so I have to grow all the parts uniformly in my imagination. If I grow the torso to a much greater extent than the legs, then the legs might not realistically support the torso. For purposes of disqualifying monsters from realism, it will be important to specify the dimensions of similarity space correctly. If we countenance gerrymandered dimensions, then even a uniform translation across similarity space may produce monsters.

My hypothesis is that whatever course of imagination cannot be constructed from one or more of the admissible constructive procedures is not realistic, that is, is fantastic. Whatever the admissible constructive procedures might prove to be, this hypothesis entails significant limitations that might be questioned. Having perceived someone playing a guitar with his hands and having perceived someone playing a bass drum with his foot, it should not follow that I can realistically imagine someone playing a guitar while at the same time playing a bass drum. I first have to actually perceive something like that. But this same limitation will spare us some embarrassing errors. Having seen a watchmaker construct a tiny watch and having seen the watchmaker ride a bus over bumpy terrain, I should not regard as realistic a course of imagination in which the watchmaker makes the watch while riding the bus.

8. Strategies for addressing counterexamples

It will be reasonable to test this account of realism in imagination against possible counterexamples. I cannot answer in advance all of the purported counterexamples that readers might come up with, but I can identify the strategies that are available for addressing them.

Regarding purported cases of overgeneration (fantastic courses of imagination that my account purportedly qualifies as realistic), I would ask readers to consider the following questions: Does your imagined counterexample not violate some antecedent constraint that informs your expectations about what you will see? Have you in real life really had the experiences that are supposed to form the basis for your cutting-and-pasting and morphing? Are there no transitions in the imagined sequence that are not based on any actual observations? Have you taken your morphing too far (translated it too far across the relevant dimensions of perceptual similarity space)?

Regarding purported cases of undergeneration (realistic courses of imagination that my account rules fantastic), I would ask readers to consider the following questions: Why do you think that what you are imagining is realistic if you have never seen anything like that? If you think that there are some general principles that vouch for the realism of what you have imagined, are those principles not based on past experiences that could form the inputs to a construction of what you have imagined on the basis of morphing and cut-and-paste? And of course another response to purported cases of undergeneration will be just to concede that they are counterexamples and then to try to accommodate them by identifying additional admissible constructive procedures that would generate them from present and remembered perceptions. I am certainly open to finding some more.

9. Conclusion

The paper began by posing a question posed by others, namely, how imagining by means of mental imagery can be useful. I proposed, however, to shift away from that question to an underlying question, namely, what the difference is between realistic and fantastic courses of imagination. A number of authors hold that the realistic (or, in their terms, useful) courses of imagination are those that conform to certain constraints. The constraints theory was criticized on the grounds that there is no way to tailor the constraints so that they are both permissive enough and restrictive enough. Finally, an alternative account of the realistic/fantastic distinction was introduced dubbed the constructive theory. This theory acknowledges that conformity to antecedent beliefs is a necessary condition on the realism of a course of imagination but requires in addition that realistic courses of imagination be constructed on the basis of remembered perceptions in accordance with certain procedures. Two candidate admissible procedures were identified, called cut-and-paste and morphing.

Acknowledgments

I thank Peter-Langland-Hassan and also Bence Nanay’s group at the Center for Philosophical Psychology at the University of Antwerp, especially Kevin Lande, Beate Krickel, Geraldo Viera and Magdalini Koukou, for feedback on an earlier version. I also thank an anonymous referee for this journal, whose comments resulted in significant improvements.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by a grant from the Austrian Science Fund (the FWF) for Project I-3517-G24, The Puzzle of Imagistic Cognition.

Notes

1 In an earlier paper, Kind (2016) does not commit to the constraints being beliefs. What she says is that world has to be imagined not necessarily as it is but ‘as it is in all relevant respects’ (2016, 153). This appears to be a standard different from conformity to beliefs.

2 One might have expected that Langland-Hassan would present his theory again in his 2020 book (Langland-Hassan 2020). While the book continues the theme that mental imagery is more or less powerless without the addition of propositional attitudes, he does not in fact develop or reiterate the material in his 2016 paper.

3 For other contributions to the topic of useful imagination, see Williamson (2007, ch. 5), van Leeuwen (2013), Dorsch (2016), Balcerak Jackson (2018), Williams (2021) and Stuart (2021). Like Kind and Myers, Dorsch is concerned with the place of imagination in epistemology; he holds that those beliefs may count as knowledge because ‘we make sure that they are formed in a reliable manner, namely in strict conformity to the truth-preserving constraints that we have imposed ourselves on our imaginative project’ (2016, 99). Williamson (2007) is concerned with the evaluation of counterfactual conditionals and supposes that our endorsement of a counterfactual conditional is underlain by acts of imagination that accord with an intuitive physics, but he does not explain what kind of knowledge he takes intuitive physics to be. Stuart (2021) distinguishes between two kinds of imaginative process, unconscious and automatic versus conscious and controlled, and describes both as constrained in various ways. In passing he compares the constraints to inference rules, but otherwise does not attempt to explain what they are. Williams (2021) criticizes Langland-Hassan’s theory and offers as an alternative a conception of imagistic cognition grounded in what he calls generative models (see note 8 below). Balcerak Jackson comes somewhat closer to my own proposal in describing some episodes of imagination as ‘recreating’ perceptual experience (2018, 221), but she does not explain how imaginings can diverge from perceptual experience while remaining realistic. Van Leeuwen says that ‘constructive imagination uses beliefs by default to infer new imaginings from imaginings that have already occurred’ (2013, 226). Van Leeuwen describes the processes of forming mental images as ‘constructive’, as I will do, and he allows that in using our imaginations to generate fictions our imaginations may contravene our beliefs, but it is not clear whether he countenances a category of realistic imaginings the construction of which is not entirely guided by beliefs.

4 Such imaginings have been thematized by several authors, for instance, Kung (2010) and Langland-Hassan (2015).

5 The assumption that perceptions are representations is widely, if not universally, shared. The claim that the contents of perceptions are not propositional is controversial, but I have defended it in several publications (Gauker 2011, Gauker 2012, Gauker 2017), and it should be familiar as well from other authors; see Brewer (2006), Crane (2009) and Echeverri (2017).

6 Kind and Kung introduce the term ‘architectural constraint’ in describing constraints on imagination, but they apply the term much more broadly than here and even Kant is described as positing architectural constraints on imagination (2016, 21–22).

7 Kind and Kung’s appeal to architectural constraints might be considered a nod in this direction (2016, 21–22), and Myers hints at this too, in writing of encoded regularities and subdoxastic representations of mechanical laws (2021b, 105, 114).

8 As noted above, in note 3, Williams (2021) offers an answer to our question about imagery that appeals to the theory of generative models. The theory of generative models deals exclusively with predictions within tightly closed systems, such as towers of blocks that may or may not fall over when nudged (Battaglia et al. 2013). More generally, research on folk physics (e.g. Kubricht, et al. 2017) appears to be confined to the study of tightly closed systems.

9 I am alluding of course to a long and robust tradition of research on young children’s expectations regarding the motion and permanency of objects (e.g. Spelke 1990, Baillargeon, et al. 1995).

10 In a recent paper (Gauker 2020), I have tried to define these procedures in terms of a more precisely developed account of perceptual representation.

11 For a philosophical defense of the thesis the perceptual representations may be conceived as having parts, see Lande (2020). Perceptual parsing of the objects of perception is the subject of much research in the psychology of perception (e.g. Singh 2015).