Core Imagination

3.1 The Problem of Missing Environmental Inputs

If we want to vindicate the role of imagination in modal knowledge acquisition, then we have to show that we imagine possible situations and that we don’t imagine impossible situations. To a large extent, the constraints to imagination guarantee that we imagine possible situations and that we don’t imagine impossible situations (but, as we argue in Section 5.2, contextual beliefs have a role too). This is perhaps the standard view of philosophers and psychologists alike (e.g., Nichols 2006; Kind 2016; Kind & Kung 2016; Langland-Hassan 2016; Williamson 2016b; Lane et al. 2016; Balcerak Jackson 2018; Harris 2021). The role of constraints in the cognitive science of imagination is just an instance of the more general role of constraints in cognitive science at large.

The traditional picture has it that cognitive science concerns the constraints that govern transitions between mental representations (e.g., Chomsky 1980; Marr 1982). Constraints are what ensure that, given particular inputs, a narrow set of outputs are available. In the case of visual perception, constraints determine that, given a retinal representation of patterns of the light, there are just a few admissible transitions to representations of higher-level properties of the visual scene (edges, depth, etc.). Since the constraints to visual perception are able to track law-like connections between the presence of certain patterns of retinal stimulation and the presence of certain higher-level properties, visual perception outputs an accurate enough representation of the visual scene (at least in normal conditions).

But what are the origins of these constraints? In the case of visual perception, it isn’t difficult to give a rough sketch. Retinal inputs provide the visual system with feedback about its model of the connections between retinal inputs and higher-level properties. In contrast, it is often thought that the search for the origins of imaginative constraints faces a problem of missing environmental inputs. For instance, since visual imagination doesn’t involve retinal stimulation, it might seem that we must give a very different account of the origins of the constraints to visual imagination. These sorts of worries seem to have motivated some philosophers to think that, in contrast with visual perception, we choose the constraints to imagination ourselves (Wittgenstein 1967; Sartre 1972). However, this leads those philosophers to conclude that imagination is of little epistemic relevance (Balcerak Jackson 2018).

The issue is this. If we choose the constraints ourselves, knowledge through imagination is akin to financial gain through handing oneself a dollar (Langland-Hassan 2016). Suppose that, when you are using your imagination to make modal judgements, you chose to impose the constraint that people don’t walk through walls. If you then infer that people can’t walk through walls from the fact that you never imagine people walking through walls, it seems that your imagination didn’t give you any interesting new modal knowledge. Although the constraint you impose is non-modal (that people don’t walk through walls), your choice to impose it seems to draw upon your knowledge that people can’t walk through walls. The natural upshot is that if imagination has a role in modal knowledge acquisition, it must operate under unchosen constraints. The next section discusses mental simulation as a plausible source of unchosen constraints.

3.2 The Recreativist Solution

According to the recreative view of imagination, imagination involves the mental simulation of other cognitive processes (Currie & Ravenscroft 2002; Goldman 2006). But what is mental simulation? For our purposes, some mental process M* is a (mental) simulation of another mental process M just in case M* is distinct from M, but nonetheless resembles M in some important respects (Goldman 2006). An important aspect of resemblance between the offline process (which simulates) and the online process (which is the target of simulation) is resemblance of functional profile. Mental simulation is important because it allows you to make use of the constraints of online processes without the need for the environment to provide the inputs that trigger them. This comes out clearest with propositional imagination or “offline belief”. As the name suggests, offline belief simulates (online) belief. And due to this, offline belief inherits some of the functional features of (online) belief. For instance, if you believe that if it rains it pours, and you believe that it rains, then you believe that it pours. The same goes for offline belief. If you offline believe that if it rains it pours, and you offline believe that it rains, then you offline believe that it pours.

The crucial point is that if some online process is subject to constraints, then the offline process that simulates that online process inherits those constraints. The origins of the constraints to some offline process are no more mysterious than the origin of the constraints to the online process it simulates (and mental simulation itself).⁷ Epistemic use of imagination is more like cashing a check than handing yourself a dollar.

3.3 Core Imagination

The recreative solution doesn’t in itself tell us which online processes imagination recreates. It therefore doesn’t in itself elucidate the nature of the constraints that imagination inherits from the processes it recreates. We adopt a pluralistic outlook that recognises that imagination involves the recreation of lots of different online processes and therefore inherits lots of different sort of constraints. We suggest that philosophers and cognitive scientists adopt a divide-and-conquer approach to the issue, investigating interestingly related clusters of imaginative constraints. This already happens, at least in broad outline. Some philosophers investigate recreation of perceptual processes (e.g., Balcerak Jackson 2018; Gregory 2020), others investigate recreation of more cognitive processes (e.g., Currie & Ravenscroft 2002; Nichols 2006; Williamson 2007, 2016a), and yet others focus on the simulation of sensorimotor loops (e.g., Jones & Wilkinson 2020; Rucińska & Gallagher 2021; Jones & Schoonen 2024).

Our implementation of the recreative solution says that there is a sort of offline process, which we baptise ‘core imagination’, that recreates core cognition. Let us emphasise at the outset that our endorsement of the existence of core imagination doesn’t involve commitment to a sui generis sort of imagination. The suggestion is rather that we are able to simulate (some) cognitive processes and that we therefore can and often do simulate core cognition. For us, ‘core imagination’ just refers to mental simulation of core cognition. Core imagination is just one (integral) part of the whole that is imagination. Importantly, there is reason to expect at the outset that exploration of this proposal is of interest given that core cognition sits at the intersection of perception and cognition. Given that core imagination inherits the perceptual-cum-cognitive nature of core cognition, it is of interest to those that investigate those imaginative processes that recreate perception and those that investigate imaginative processes that recreate cognition. We now turn to exposition of our positive view.

To motivate the view that core cognitive constraints constrain online thought, consider two classic experiments. In an experimental set-up in which a car rolls down a ramp and passes behind an occluder, Baillargeon (1986) has shown that infants (6- and 8-month olds) expect objects not to pass through each other (see also Baillargeon et al. 1985). In the test stage, there were two conditions. In the expectation-consistent condition, infants saw the occluder raise to reveal a block that stood behind the tracks (i.e., without blocking the path of the car). In the expectation-inconsistent condition, infants saw the occluder raise to reveal a block that stood on the tracks (i.e., blocking the path of the car). If children expect objects not to pass through each other, then the expectation-inconsistent condition in which it seems that the car teleports through the block ought to surprise them. This is what Baillargeon (1986) found.

In another classic experiment, Spelke et al. (1995) showed that infants expect that objects don’t teleport. Infants were shown an initial discontinuous event in which there are two occluders with a gap in the middle. An object a passes behind the left occluder and then an object b with the same appearance exits the right occluder without any object appearing in the gap (it is ambiguous whether a = b). At the test stage, infants were shown two events in which the occluders were no longer present. In the one-object event, one object enters the scene left and exits right. In the two-object event, one object enters left and stops at the previous location of the left occluder and a distinct but similar object starts at the previous location of the right occluder and exits the scene right. If infants expect objects not to teleport, then their interpretation of the initial event is more similar to the two-object test event than the one-object test event. Hence, if infants expect that objects don’t teleport, then the one-object event ought to cause dis-habituation. This is what Spelke et al. (1995) found.

Taken together, these two experiments (and others like them) support the view that the principles of object perception constrain infants’ expectations about objects. Despite the emphasis of the role of core cognition in infant development, it is important to note that core cognition operates throughout the lifespan (Spelke 2000, 1253; Spelke & Kinzler 2007, 90; Carey 2009, 69-87; Rips 2017, 160).⁸ Core cognitive constraints—like SOLID and NO-TELE—are constraints to online cognition.

We now want to put forth the hypothesis that core cognitive constraints are constraints to imagination (or “offline cognition”). In particular, principles of object perception like SOLID and NO-TELE constrain imagination. To motivate this claim, we offer an illustrative example. Suppose that you have a flight from Amsterdam to Dresden. Your plan was to get to the airport in your car. But at the last minute you lock your keys in your car. You want to know whether it is possible that you still make your flight. You use your imagination to acquire this knowledge. You imagine various situations. You imagine hailing a taxi, getting a train, cycling, and so on. But you don’t imagine your keys teleporting into your pocket. And you don’t imagine reaching through your car door in order to unlock the car from the inside. Nor do you ever imagine teleporting into your car or to your destination. Left to its own devices, your imagination just doesn’t represent situations like that. Our suggestion is that imagination doesn’t represent situations like that because it inherits core cognitive constraints.

But how do core cognitive constraints block the imagination of situations that violate those constraints? Just like in online thought, the principles of object perception generate (offline) expectations about entities that we categorise under object in imagination. For instance, since in imagination you categorise the keys under object, you expect in imagination that the keys don’t teleport and that the keys don’t pass through other objects. By default, our imaginative episodes don’t develop in ways that violate those (offline) expectations (Williamson 2007, 2016a). If we suppose that imagination has its traditional role in modal judgement and knowledge acquisition (judge p possible if you imagine p), then our proposal predicts that adults don’t judge violations of core constraints possible. We further embrace the more ambitious claim that an adult judges p impossible if they don’t imagine p by default.

4.1 Descriptive Undergeneration

The descriptive objection claims that we make incorrect predictions about non-expert adults’ modal judgements. It says that there are some situations, like phase objects, that (i) are core inconsistent and yet (ii) non-expert adults judge those situations possible. In response, we grant (i). The whole point of imagination constrained by core cognition is to take advantage of core constraints to block the imagination of situations that violate those constraints. But what we want to emphasise is that (ii) is an empirical claim and recent psychological literature about modal judgement suggests that it is false.

Psychologists use the technical term ‘impossible event’ to pick out events that violate core cognitive constraints rather than laws of nature or metaphysical principles—it therefore departs from standard usage of that term in the philosophical literature. For example, Shtulman & Carey (2007, 1017) chose their “impossible events” to “violate physical laws known at least implicitly by most children (see Spelke 1990)”. Here Shtulman and Carey refer to Spelke’s (1990) prominent work ‘Principles of object perception’, in which she argues that the principles of core object cognition constrain adults’ expectations. This highlights that an event is an “impossible event” in Shtulman and Carey’s sense if it violates core object constraints. In the mouths of psychologists, utterance of ‘adults judge “impossible events” impossible’ means that adults judge events that violate core constraints impossible.

We can now ask whether, given some event that psychologists deem an “impossible event”, children and adults judge that event impossible. If so, then our main predication that adults judge events that violate the core constraints impossible is borne out and the descriptive objection fails. Again and again developmental studies have found that children of at least four years are able to distinguish normal possible events from impossible events (see Shtulman & Carey 2007, 1020; Shtulman & Phillips 2018, 162; and the references therein). Given some normal possible event, like cleaning a closet, children judge that this event “could happen in real life”. But given some impossible event, like walking through a wall, children judge that this event “couldn’t happen in real life” (examples from Shtulman & Carey 2007). Of course, adults are able to make the same distinctions. Given some event that violates core constraints, adults are highly reliable in their judgements that these events are impossible—and this result persists across studies from different labs and experimental paradigms. The result persists even if adults are given time to reflect (Phillips & Cushman 2017). In fact, adults often cite (simplifications of) core constraints to justify their modal judgements. For instance, adults that judge it impossible to walk through a wall give justifications like “walls are solid”.

The descriptive objection claims that our account makes incorrect predictions about non-expert adults’ modal judgements. It says that there are some situations that (i) are core inconsistent and yet (ii) non-expert adults judge those situations possible. But we’ve just seen that (ii) is false. It is taken as an unsurprising result in modal psychology that children and adults judge events that violate core constraints impossible. So, the descriptive objection fails.

4.2 Normative Undergeneration

The normative version of the undergeneration objection says that core constraints permit fewer possibilities than there are. To answer that objection, we show that in the quotidian sense of ‘possible’ relevant in everyday life, violations of core constraints are impossible. That is, we delineate the target of our epistemology: non-expert adults’ knowledge of everyday modal claims. These include claims such as ‘The couch could fit into the room’ and ‘We could make that deadline’. In particular, we argue that non-expert adults use modal statements to communicate propositions with more substantive restrictions than some epistemologists of modality seem to realise.

Logicians and philosophers have known for some time that modal expressions are similar (if not identical) to quantifier expressions (Copeland 2002). But linguists made it clear that natural language modal expressions, like natural language quantifier expressions, often come with implicit domain restrictions (Kratzer 1977, 1981, 2012). To illustrate the point, we start with a brief discussion of implicit quantifier domain restriction.

Implicit quantifier domain restriction is everywhere (Westerståhl 1984; Von Fintel 1994; Marti 2003; Kratzer 2021). Consider a commonplace example like (1).

Imagine (1) spoken from Father to Mother at their children’s bedtime. The surface form of (1) doesn’t settle the restriction to the domain of ‘everyone’. An alien might think that Father intends to communicate that everyone in the universe is asleep. But Mother knows that what Father communicates receives a more perspicuous expression in the surface form of (2).

The restriction to ‘everyone’ in (2) is quite explicit. The restriction is to children of Father and Mother. The point is that the explicit restrictions to ‘everyone’ in (2) are implicit in (1). To see this, consider that it is no objection to the proposition that (1) communicates (in the relevant context) that the kids next door are still awake.

Implicit modal domain restriction is unavoidable.¹⁰ To illustrate this, consider everyday examples like (3).

Imagine (3) as spoken from Father to Mother in IKEA. The surface form of (3) doesn’t reveal any restriction to the domain of ‘can’ (an existential quantifier that ranges over the set of possible worlds). The proverbial Martian (or a philosopher) might think that Father intends to communicate that there is no possible situation whatsoever in which the sofa fits into the living room. But Mother knows that what Father communicates receives a more perspicuous expression in (4).

The restriction to (4) is quite explicit. The restriction is to situations that have a match of circumstances and that align with our priorities to a reasonable extent (Kratzer 1981; Portner 2009). The point we want to make is that the explicit restrictions to the domain of ‘can’ in (4) are implicit in (3). To see this, consider that it is no objection to the proposition that (3) communicates (in the relevant context) that Father and Mother might demolish several walls in their house to fit the sofa.¹¹

Despite the fact that modals with implicit domain restrictions are widespread in natural language usage, epistemologists of modality often restrict themselves to investigation of our knowledge of modalities that have very few, if any, substantive restrictions. In particular, they focus upon knowledge of metaphysical modal statements. However, while it is appropriate to explore our acquisition of metaphysical modal knowledge, philosophers ought to avoid a stance that ignores other types of modal knowledge that are of more use in everyday life to non-philosophers.¹² From this everyday perspective, metaphysical modal knowledge is just a marginal type of modal knowledge. Just as epistemologists of visual perception don’t restrict themselves to long-distance sight, epistemologists of modality shouldn’t restrict themselves to the acquisition of metaphysical modal knowledge.

Nichols (2006, 245) suggests that epistemologists of modality ought to pay more attention to our knowledge of nomological possibilities (i.e., that which is possible in view of the laws of nature) since these are the sort of modals relevant to decision and action. We think that this is a step in the right direction. But most of the modal statements relevant to everyday decision and action are far more restricted than nomological modals (Strohminger & Yli-Vakkuri 2018a, 1157). For instance, quantum possibilities with low objective probabilities (e.g., phase objects) aren’t relevant to everyday decision and action. To see this, consider (3) again. Suppose Mother responds with (5).

As a response to (3), (5) sounds terrible to us. It isn’t just that Mother expects too much of Father (i.e., expects him to instantiate events with very low objective probabilities); it is that (5) just isn’t responsive to the proposition that Father communicates with (3). The proposition that (3) communicates in IKEA just quantifies over possibilities that are normal in some sense of that difficult term (Knobe & Szabó 2013; Yalcin 2016; Phillips & Bloom 2017; Phillips & Knobe 2018; Aimar 2019). It is no response to (3) then to point out that there are abnormal possibilities in which the sofa fits.

Notice that (5), as a response to (3), is comparable to (6) as a response to (1).

The right response to those that insist upon surface forms and ignore propositions communicated is to point out their mistakes. Father didn’t communicate that the kids next door were asleep. Father just communicated a true claim about his own children. If you think that (6) isn’t an appropriate response to (1), then we think that you ought to adopt the same attitude to (5) and (3) since there is no relevant difference between them.

To summarise, non-expert adults use modal statements to communicate modal propositions whose restrictions are more substantive than the laws of nature. It seems, rather, that non-expert adults use modal statements to quantify over situations that are normal—i.e., quotidian possibilities. We admit that it is somewhat unclear what the right analysis of “normal” is. But that is everyone’s problem. Our response to the normative undergeneration objection is just that situations that violate core constraints are in fact quotidian impossibilities. We know them when we see them and phase objects are not quotidian possibilities. Plausible theories of the nature of quotidian modalities must capture this intuition.

5.1 Peripheral Constraints

Here is an instance of the overgeneration objection. The imagination relevant to modal knowledge acquisition shouldn’t allow transition from a state i₁ that depicts that x is a human to a state i₂ that depicts that x is an African bullfrog. Presumably humans can’t become African bullfrogs. But core cognitive constraints probably don’t block transitions of that sort. Hence, core constraints overgenerate possibilities.

This is no genuine objection to our proposal. This is because it is no part of our positive proposal that core constraints exhaust the constraints to imagination. We admit that there are further important “peripheral” constraints to imagination.

• (Peripheral) Some constraint to imagination is peripheral just in case it is not a member of the deductive closure of the set of core constraints.

In the African bullfrog example, there is probably some more general peripheral constraint at work that rules out that a member of a species S becomes a member of another species S′ (cf. Gelman 2003 and the references therein). But since it is hopeless to give an informative discussion of every constraint to imagination in a single paper, it is a methodological mistake to expect us to further explore that issue here. We admit that if imagination has a role in modal knowledge acquisition, some peripheral constraints must block that transition. But our thesis is that core constraints are an important proper subset of the constraints to imagination and that is enough to generate the substantive philosophical problems that we have sought to address in this paper (especially Section 4).¹⁴

For purposes of illustration, we draw analogies with another science which concerns the generative strength of cognitive constraints: generative linguistics. Generative linguists attempt to state principles that have the right strength in that those principles permit grammatical sentences and rule out relevant ungrammatical strings. The linguist doesn’t give a grammar of an entire language. Rather, the linguist provides a “fragment” of the grammar that rules out some ungrammatical strings. For instance, a linguist might state some principles that govern question-formation. Those principles rule out those ungrammatical strings that violate principles of question-formation. But of course, these principles won’t rule out unrelated ungrammatical strings like ‘runs smokes’. We would not say that the linguist’s proposal overgenerates sentences because it doesn’t rule out ‘runs smokes’. Clearly the linguist is just giving a fragment of the complete grammar and expects that some other “peripheral” principle of the complete grammar will rule out ‘runs smokes’. The linguist indulges in the theoretical hopes of an optimistic scientist engaging in normal science. We intend our proposals in that spirit.

5.2 Contextual Beliefs

Here is another instance of the overgeneration objection. Suppose that Thomas is trying to get to the airport. His car broke down. He can’t get to the airport in a Ferrari because his wife doesn’t have one. But core constraints don’t block Thomas’s imagination that his wife turns up in a Ferrari to take him to the airport. Hence, core constraints overgenerate possibilities.

This is no genuine objection to our proposal. There is no reasonable requirement that core constraints or peripheral constraints block the imagination of situations that are impossible for highly contextual reasons. To illustrate, it is no constraint to imagination that Thomas’s wife doesn’t have a Ferrari. Suppose that a few years later, Thomas learns that his wife got herself a Ferrari. Next time he gets stuck in the airport he can imagine that he gets to the airport in a Ferrari. Genuine constraints to imagination don’t change from context to context. Instead, contextual beliefs have a role in blocking imagination of some impossible situations.

Contextual beliefs are beliefs about contextually relevant matters. In Thomas’s case, he wants to know whether it is possible in view of his circumstances that he can get to the airport in a Ferrari. His beliefs about whether his wife has a Ferrari are therefore the contextual beliefs in that situation. In his original conundrum, he believes that his wife doesn’t have a Ferrari. In conjunction with other contextual beliefs and imaginative constraints, this belief blocks his imagination that he gets to the airport in a Ferrari. But after he learns that his wife bought a Ferrari, his contextual beliefs and imaginative constraints permit imagination that he gets to the airport in a Ferrari.

This is just the ubiquitous phenomenon of variation within constraints. Whenever there is variation within constraints, plausible proposals about the constraints ought not rule out any of the permissible variation. The constraints block whatever is impermissible in any context. The variation within constraints is explained by input from the variable ambient environment. For instance, that cognitive device that infants utilise in their acquisition of competence with the grammar of their ambient language must include principles that rule out sentences or structures that are ungrammatical in every possible human language. However, it ought not include principles that rule out strings that are ungrammatical in some languages but grammatical in others. It shouldn’t include principles that block permissible variation. Permissible variation is instead explained as a result of the setting of parameters—i.e., the interaction between the subject and its variable context (cf. Chomsky 1981).