1.1. Temporal updating

A creature capable of what we call temporal updating maintains a representation of how things are in its environment, which can be conceived of as map-like in so far as it contains information about locations, but which can also contain information about the existence of objects, and features of those objects, while leaving the location of those objects underdetermined. As things change over time, the creature will receive new information, and this information may contradict an aspect of its existing representation. But all the creature does in response to receiving such information, using the updating system, is change the relevant aspect of its representation of the environment. That is to say, crucial to the temporal updating system is that it deals with changing input by changing representations, rather than by representing change. If a change happens, it simply records the new, changed state of affairs, rather than also representing that things were previously different from how they are now. Thus, the temporal updating system operates with a model of the world that concerns the world only ever as it is at present. Other times, and how things are at other times, are not represented in the model at all.

We should stress that when we say that the model of the world used in temporal updating is a model that concerns the world only as it is at present, this is compatible with it being based on information the creature has gathered over time. It can therefore also include information about features of the world that are currently outside the creature's sensory scope, but which the creature has learned about – that is, about features of locations it does not currently occupy, or about the existence of certain objects. There is even a sense in which this provides for a primitive way of representing goal states: The creature can think of certain items represented as existing in its environment as desirable, and of certain locations in that environment as good locations for doing certain things, and it can respond to these opportunities its environment might afford. This would allow it to act in ways that de facto prepare it for future encounters with those items or locations, even though other times are not represented in its model of the world as such.

In order for the temporal updating system to work, the creature's model of the world has to maintain information over time and also update as new information is received. This updating will result in changes to the creature's world model; these include changes about, for example, what objects are at which locations, but also about what is or is not desirable or what the right thing to do is at certain places. Thus, some updating will happen as a result of changes that occur in the creature's environment, independent of the creature itself, but some will happen because of changes in the creature's motivational state (we discuss an example of the latter in sect. 2.3). Certain parameters will govern these maintenance and updating processes, and we assume that these parameters will vary considerably in a context- or task-dependent way. For example, some types of information may be maintained for only very short periods of time and quickly lost or updated, consistent with the idea of the contents of a working memory store changing dynamically, whereas others might be maintained for lengthy periods and be resistant to change. The types of mechanisms involved in making updates to the creature's model of the world in response to changes purely extrinsic to the creature are also likely to be quite different from those involved when the changes are changes in the animals’ motivational state. What these mechanisms are, though, and what parameters govern their operations are empirical questions, and none of the arguments given below require making any particular assumptions about them, other than the basic assumption that information about objects and locations can be maintained even when they do not remain within sensory range.

1.2. Temporal updating and behavior

What follows is a description of some of the behaviors that we believe the temporal updating system can support. In each instance, we also specify what we take to be the related limitation, that is, what a creature cannot do if it is operating only with a temporal updating system.

1. (i) Single-trial learning. A creature capable only of temporal updating can acquire new information about the world from even a single learning episode and change its model of the world accordingly. This information can be of a variety of types, combined in various ways (e.g., information about the spatial location and nature of an object), and it can be held in memory without the creature continuously making use of it (e.g., it might only do so at a later occasion after being cued). Limitation. Making use of information acquired in the past, even if it stems from just one learning episode, is separate from and does not require representing that information as stemming from the past, which is something a creature capable only of temporal updating cannot do.

2. (ii) Elapsed-time sensitivity. A creature capable only of temporal updating can nevertheless be sensitive to how much time has elapsed since a certain event happened. Aspects of its model of the world might have a “shelf life.” That is, after incorporating a new piece of information of a certain type into its representation of the world (e.g., where some food is located), it might then only store that information for a certain amount of time and as a result its representation will change yet again at a later point in time. This could be governed systematically by an interval timer. Once a certain amount of time has elapsed on such a timer, the creature would no longer operate with a model of the world that includes the relevant piece of information (see sect. 2.1 for more detail). Limitation. There is no sense in which the creature needs to be representing how long ago it obtained the relevant piece of information, the representation of which is governed by a timer. This piece of information simply is or is not included in the creature's model of the world as a function of how long ago it was obtained.

3. (iii) Sequential learning. The type of sensitivity to elapsed time we have just characterized involves a process governing what happens to elements of a creature's model of the world over time, without temporal relations being represented within the model itself. Similar processes might also explain certain basic forms of sequential learning. A creature might become sensitive to the temporal order in which certain kinds of sequences unfold by acquiring a routine for updating its model of the world in that order, rather than that order being represented in the model itself. Limitation. A signature limit of the temporal updating system is that the correct functioning of the system depends on the creature receiving information about changes in its environment in the same order in which those changes happen; it will produce errors in situations in which these two orders come apart.

4. (iv) Anticipation. We can distinguish at least two ways in which such a creature might produce behaviors that serve to prepare for future states of affairs. First, the creature may possess some sort of temporal sensitivity whereby it behaves in a certain way when a phase timing system is in a certain state (e.g., turning up at a certain location at a certain time of the day), thus enabling it to behave in a way that yields future benefits. Second, as we said, such a creature may have a primitive way of representing goal states, by representing items existing in its environment as desirable, or locations in that environment as good locations to do certain things. This may cause it to act in ways that are optimal given certain possibilities its environment may afford (discussed further in sect. 2.2). Limitation. If they are not immediately accessible, the items represented as desirable (or the locations represented as good locations to do certain things) will de facto, at best, be encountered by the creature at some point in the future. However, the creature can represent these items (and locations), and respond to their presence in its environment, without having the means to represent its potential encounters with them as events occurring at a separate, future point in time.

1.3. Temporal reasoning

The key difference between a creature capable only of temporal updating and one that is able to engage in what we call temporal reasoning is that the latter operates with a model of the world that includes a temporal dimension. That is to say, the model contains addresses for different points in time, and can therefore contain information not just concerning the world as it is at present, but also information about states of affairs different from those existing in the present, which existed in the past or will exist in the future. Here we summarize what we take to be the most fundamental kinds of representational resources this involves.

1. (i) Representing particular times: A creature capable of temporal reasoning can represent events as happening at particular times, each of which only comes round once. Creatures not capable of temporal reasoning, by contrast, while capable of becoming sensitive to repeated temporal patterns in their environment (e.g., processes that display a circadian rhythm), will not distinguish between individual instantiations of these patterns as distinct unique occurrences (Campbell Reference Campbell, Pastor and Artieda1996).

2. (ii) Representing temporal order. Because a creature capable of temporal reasoning can represent the temporal order relations between events happening at different times, it can use information about this order to arrive at a correct model of the world. It is not restricted to arriving at a correct model of the world only if it receives information about changes in its environment in the same order in which those changes occur.

3. (iii) Tense. A creature engaging in temporal reasoning is also capable of using the system of particular times as a framework for orienting itself in, by using tense, that is, locating events in the past, present, or future. By contrast, the representations entertained by a creature capable only of temporal updating are tenseless, or untensed. Its model of the world concerns the world as it is at present, not because items in it are represented as present, but simply because it is the model entertained at present.

Having briefly outlined some of the key features of both the temporal updating system and of temporal reasoning, we will turn to considering ways in which the distinction between these two systems might be relevant to the interpretation of existing empirical research. Before doing so, we add two brief clarificatory comments.

First, we assume the existence of particular timing mechanisms, which can explain how even a creature capable only of temporal updating might nevertheless display forms of behavior that are sensitive to elapsed time. Timing mechanisms of some sort are widely assumed to be available even to basic creatures (e.g., insects, Bradshaw & Holzapfel Reference Bradshaw and Holzapfel2010); we remain neutral on their nature (see Grondin Reference Grondin2010). Clearly, there are important further questions about the precise ways in which these mechanisms operate, and the limitations they are subject to. It is important to note, however, that our suggestion is not that there is one form of cognition – temporal updating – that relies on the existence of mechanisms of this type, and another one – temporal reasoning – that does not. Mechanisms keeping track of time can obviously also be involved in contexts in which individuals make explicit judgments, for instance, about how long ago a certain event occurred (Friedman Reference Friedman, Hoerl and McCormack2001). The issue at stake concerns the function the relevant mechanisms play as part of the two systems: In one case, they simply govern the updating and maintenance of elements of the creature's model of its present environment; in the other, they ground a representation of a temporal interval extending into the past (see sect. 2.1).

Second, as we characterize it, the difference between temporal updating and temporal reasoning is fundamentally concerned with what a creature can represent – that is, whether or not its model of the world contains a temporal dimension. In characterizing the distinction in this way, we have assumed that not all of the ways in which a creature might be sensitive to aspects of its environment involve that creature actually representing those aspects. That is, we are operating with a notion of representation that distinguishes representing an aspect of the world from simply being sensitive to it (see also Peacocke Reference Peacocke and Phillips2017). This has to be distinguished from a broader notion of representation such as that involved when lower-level brain mechanisms are described as operating on “representations” (e.g., one might describe the early visual system as “representing” the differences between the two retinal images, but this is clearly not part of what is visually represented in the viewer's perception). There has been considerable debate on how exactly to characterize the relevant difference between these different notions of representation (for some influential early discussions, see Dennett Reference Dennett1969; Stich Reference Stich1978). For present purposes, we want to emphasize that the distinction we are drawing between merely being sensitive to temporal features of the world and representing time is not just a terminological one. If a creature can do the former but not the latter, this has concrete behavioral implications. For example, as we have explained, the correct functioning of the temporal updating system is dependent on the creature receiving information about changes in its environment in the order in which these changes happen. This is a signature limit of the temporal updating system that the temporal reasoning system is not subject to (see sect. 3.1 for further discussion).

2.1. “What-when-where” memory

The most influential paradigm that has been taken to measure MTT to the past in animals is that of Clayton and Dickinson (Reference Clayton and Dickinson1998). These researchers aimed to demonstrate that scrub jays can remember three key pieces of information about past events: what happened, where it happened, and when it happened. For present purposes, it is the last of these pieces of information that is crucial. Representing that something happened at a particular point in the past is an instance of temporal reasoning. We therefore need to ask whether these studies provide good evidence that animals can do so.

In the original study, what was taken as evidence that birds can remember “when” information was the fact that whether or not they returned to a cache site was appropriately delay-dependent. As shown in Figure 1, birds that learned that worms degraded over a period of 124 hours did not return to a cache of worms if given access to it after a 124-hour delay, but instead returned to a cache of non-degrading peanuts. By contrast, if the delay was just 4 hours, birds returned to the cache of worms (their preferred foodstuff) rather than the peanuts (see also Clayton et al. Reference Clayton, Yu and Dickinson2003b). To think that this study measures MTT is to think that the birds can remember the event of caching the worms, and how long ago this caching event occurred (Salwiczek et al. Reference Salwiczek, Watanabe and Clayton2010). Our claim is that there is no need to make such an assumption in order to explain the birds’ behavior. It could be that the birds have some form of interval timing mechanism that governs how long the representation of edible worms remains a part of their model of the world (McCormack Reference McCormack, Hoerl and McCormack2001). Such a timer would begin to operate at the time of caching, and if the worms are then found to be rotten upon retrieval after a given interval (as in the learning phase of this study), the timer will subsequently ensure that a caching site is no longer represented as containing edible worms once that interval has elapsed (see Figure 1). In that way, we need not assume that the birds can remember the caching event itself; they simply do or do not continue to represent the hidden worms as a function of the state of their internal timer. Notably, this is quite different from assuming gradual forgetting of the locations of cached foodstuffs, although one could potentially describe it as a form of interval-timer controlled forgetting. Characterized in this way, what is distinctive about this type of forgetting is that it is appropriately flexible to the interval in question.

Figure 1. Illustration of test trials in Clayton and Dickinson's (Reference Clayton and Dickinson1998) study. In (a) 124-hour trials, scrub jays cached worms in Tray 1 and peanuts 120 hours later in Tray 2. After another 4 hours, they were allowed search in both trays. In (b) 4-hour trials, the birds initially cached peanuts in one tray and then cached worms in another tray after a 120-hour delay; 4 hours later they were allowed to search in both trays. Worms are the birds’ preferred food, but birds in the Degrade condition of the study received a series of pre-training trials in which they learned that worms had degraded after a 124-hour period. These birds preferentially searched for peanuts in 124-hour trials and worms in 4-hour trials. The figure contrasts the type of representation assumed to underpin the birds’ preferences according to an MTT account with that which is assumed by the temporal updating account. On the former account, the representations have tensed content that leads birds to infer that the worms are not edible. On the latter account, it is assumed that whether the birds’ model of the world continues to include a representation of edible worms in Tray 1 is governed by an interval timer.

There are obviously further questions to be asked as to how exactly such an interval timing mechanism, which is triggered by the initial caching event, might function. Studies of interval timing in animals typically use considerably shorter intervals. Indeed, Buhusi and Meck (Reference Buhusi and Meck2005) define interval timing as covering the range from under a second to 24 hours. However, there is no reason in principle to assume that animals do not have timing mechanisms that would allow them to be sensitive to the length of a 124-hour period (or even longer). Certainly, we are not committed to the idea that such a mechanism need be a dedicated internal clock; for example, a mechanism that keeps track of how many (fractions of) circadian cycles have passed would also be sufficient. Moreover, it is not just our account that needs to postulate the existence of such a mechanism that keeps track of time. Any account that holds that the birds actually remember the caching event and how long ago it occurred must also assume the existence of a mechanism that allows them to make an accurate judgment about the distance in the past at which that event occurred.

Clayton et al. (Reference Clayton, Yu and Dickinson2003b) explicitly consider, and do not reject, the possibility that the scrub jays’ search behavior in their task could be governed by some interval timing mechanism, even in the case of somewhat more complex experimental designs. However, they do not seem to believe that this has a bearing on whether the task can be taken to measure MTT to the past. Our argument is that such a mechanism would allow animals to show the appropriate level of temporal sensitivity in the absence of any capacity to represent past events, by facilitating temporal updating in a way that is delay-sensitive. The crucial point is that in order for the timing mechanism to fulfill its purpose, it is enough for it to govern what happens to elements of the animal's model of its current environment; we need not postulate any ability to represent other times within this model (see also Hoerl Reference Hoerl2008).

2.2. “Mental time travel to the future”

We now turn to considering whether a temporal updating account can also explain animal behavior in studies purporting to measure MTT to the future. Two types of tasks have been used in this area: tasks involving tool saving (inspired by Tulving's Reference Tulving, Terrace and Metcalfe2005 original “Spoon test”; Dufour & Sterck Reference Dufour and Sterck2008; Mulcahy & Call Reference Mulcahy and Call2006; Osvath & Osvath Reference Osvath and Osvath2008) and tasks involving animals caching food that they do not currently desire eating (Correia et al. Reference Correia, Dickinson and Clayton2007; Cheke & Clayton Reference Cheke and Clayton2012). We will consider each in turn.

2.2.1. Tool-saving tasks

A study by Kabadayi and Osvath (Reference Kabadayi and Osvath2017) can serve to illustrate the general structure of the tool-saving tasks. In this study, ravens first learned that a certain tool – a stone – could open an apparatus containing a food reward (see Figure 2). The following day, they were re-introduced to the baited apparatus, but now the tool to open it was not available, and the apparatus was removed after a while. One hour later, and at a different location, the ravens were offered a forced choice selection between the functional tool and three non-functional distractors. Fifteen minutes after that, they were re-introduced to the apparatus. Kabadayi and Osvath found that the ravens selected the functional tool on the first test trial of this kind, and that they did so also on the majority of further trials, on which they had to make their selection 15 minutes before being given access to the apparatus.

Figure 2. Illustration of the tool-saving procedure in Kabadyi and Osvath's (Reference Kabadayi and Osvath2017) study, in which ravens preferentially select a stone that can be used to operate an apparatus to release food (Only part of the study carried out by Kabadyi and Osvath is described here). The figure contrasts the type of representation assumed to underpin the ravens’ performance according to an MTT account with that which is assumed by the temporal updating account. On an MTT account, birds infer the need for the tool by representing a future event in which they will re-encounter the apparatus. On a temporal updating account, the birds’ behavior is governed by a representation that includes information about objects outside of their current sensory scope (the apparatus) but does not include tensed content.

Does success in this tool-saving task require temporal reasoning, or can it be achieved using only the more basic temporal updating system? As we said before, an animal capable only of temporal updating maintains a model of the world only as it is at present. However, we allowed that this model could include items that the animal currently has no perceptual access to. Even if the ravens are capable only of temporal updating, the apparatus is still likely to figure in their model of the world when they are presented with the tool and the distractors, since they have learned about its existence. Upon being re-introduced to the tool, the birds might therefore realize that this gives them the potential opportunity to open the apparatus, and this might be enough to motivate them to select the tool. That is to say, they select the tool because they want to open the apparatus, which they think of as part of their current environment.

Kabadayi and Osvath (Reference Kabadayi and Osvath2017) say that their study “suggests that ravens make decisions for futures outside their current sensory contexts” (p. 203). It is important, however, to distinguish between at least two ways in which this claim might be interpreted. As indicated, we agree that the birds’ behavior takes account of an object not currently within their sensory scope. As it is not within their current sensory scope, it is also true that they will therefore have access to that object only after a delay (if at all). Nevertheless, it does not follow from this that, in acting on the basis of their representation of this object and its properties, the ravens must also be representing their future encounter with that object as such, as happening at a separate point in time distinct from the present. It is true that the experiments in question de facto involve a delay between the time when the tool is selected and the time when it can be used. But it is far from obvious that this delay plays any role in the reasoning that leads the birds to choose the tool. (It is interesting to note, in this context, that the birds chose the functional tool already on the first test trial, before they had any opportunity to learn that they would be re-introduced to the apparatus a set delay after tool choice.)

Part of what might motivate the idea that tool-saving behavior demonstrates temporal reasoning capacities is that it seems to require some form of grasp of potential opportunities the environment might afford. But there is a more demanding and a less demanding way of understanding what the latter involves. In a different context Osvath and Osvath (Reference Osvath and Osvath2008, p. 662) describe planning in humans as involving “a capacity to construct mental experiences of potential events, something that could be expressed as a projection of the self into possible future events.” To think of the ravens as engaging in planning in this sense would be to ascribe to them a capacity to represent modalities themselves – the ability to represent the future time of being confronted with the apparatus as a point in time distinct from the present at which two possible states of affairs could obtain – the animal having the functional tool or not having it – depending on what the animal does now. What we are arguing is that success in tool-saving tasks does not necessarily require a grasp of possibility in this sense (for a study suggesting that non-human primates are in fact unable to represent such dual possibilities, see Redshaw & Suddendorf Reference Redshaw and Suddendorf2016). It requires a grasp of possibility only in the more basic sense of requiring a grasp of the apparatus as an object that is potentially accessible, even though it is not within the animal's sensory scope. Such a grasp can be grounded in a representation simply of how the world actually is now (e.g., “there is a baited apparatus that can be opened with this tool”), albeit one that might leave some aspects of states of affairs in that world underdetermined. More specifically, it can be grounded in a representation of the form we take to be involved in the temporal updating system – a representation on which the object is represented as existing somewhere in the birds’ current spatial environment, and in this sense as potentially accessible. Together with the motivational state of desiring the contents of the apparatus, this seems sufficient to explain why the birds choose the tool.

2.2.2. Caching tasks

To illustrate the second type of task that has been taken as evidence of future MTT in animals, we will describe the study by Cheke and Clayton (Reference Cheke and Clayton2012). This study, depicted in Figure 3, relies on the fact that the birds show specific satiety effects; that is, if they are sated on one food type, they prefer to eat a different food (note the specific set of foods used varied between birds; we illustrate one example set, and also only part of the overall study). This study started with a baseline caching trial in which birds were pre-fed with their maintenance diet that did not include peanuts or raisins, and then given the opportunity to cache each of the latter two food types freely in two trays. This was followed, after a delay, by a first retrieval stage in which they were pre-fed raisins and subsequently given access to Tray 1 only. After a further delay there was a second retrieval stage in which they were pre-fed peanuts and subsequently given access to Tray 2 only. In the test trials, which occurred some time after these retrieval stages, birds were pre-fed peanuts and then again allowed to cache both raisins and peanuts freely in the two trays. Of interest was whether the birds would cache the two foodstuffs in a manner that corresponded to which food they would prefer to retrieve from which tray, given their specific satiety at retrieval from the relevant tray. Would they cache peanuts in Tray 1, because they will be sated on raisins when Tray 1 becomes available, and would they cache raisins in Tray 2, because they will be sated on peanuts when Tray 2 becomes available? In fact, three out of four birds showed this pattern.

Figure 3. Illustration of the procedure in Cheke and Clayton's (Reference Cheke and Clayton2012) study for one pair of food types (peanuts and raisins). Boxes represent trays made available as caching locations; discs represent containers with food – black for peanuts, white for raisins. In the initial phase of the study (left-hand side of the figure), the birds were allowed to freely cache peanuts and raisins in two trays. In this initial phase, birds had not been pre-fed either food type. After a delay, they were pre-fed raisins and then allowed to retrieve from Tray 1. The pre-feeding of raisins meant that they no longer desired the raisins in the tray, preferring the peanuts. After a second delay, they were pre-fed peanuts and allowed to retrieve from Tray 2. The pre-feeding of peanuts meant that they no longer desired the peanuts in the tray, preferring the raisins. In the subsequent test trial (right-hand side of the figure), the birds were first pre-fed peanuts and were then again allowed to freely cache raisins and peanuts in both trays. The birds now preferred to cache peanuts in Tray 1 and raisins in Tray 2. On an MTT account, the birds infer that they should cache peanuts in Tray 1 on the basis of a representation of a future event in which they will find peanuts but not raisins desirable. On a temporal updating account, it is assumed that the birds update their model of the world, learning during the two retrieval stages that Tray 1 is a good place to cache peanuts and Tray 2 is a good place to cache raisins.

Cheke and Clayton's (Reference Cheke and Clayton2012) discussion frames this finding in terms of the idea that animals can “act for a future need that is different from their current one” (p. 171), or “overcome their current desire to anticipate … future needs” (p. 171), implying that it demonstrates MTT capacities. As we will argue, though, this is a somewhat misleading characterization, and an explanation of the birds’ behavior purely in terms of temporal updating is readily available. According to this alternative explanation, birds will, under normal circumstances, represent both caching trays as equally good locations for caching food. This is what happens in the baseline caching trials, in which they cache foods in equal amounts in both trays. The birds are then given the opportunity, in the two retrieval stages, to retrieve food from Tray 1 only when pre-fed raisins and from Tray 2 only when pre-fed peanuts. In response to this, we suggest, they update their model of the world, such that now Tray 1 is represented as a good location for peanuts but not raisins, whereas Tray 2 is represented as a good location for raisins but not peanuts. This change in their model of the world explains why they subsequently differentially cache each foodstuff in a different location.

One might object that this explanation leaves out the significance of the fact that the birds are pre-fed peanuts at the start of the test trial and are thus, when subsequently allowed to cache, already sated on this food. Despite this satiation, they nevertheless cache peanuts in Tray 1. This seems to be what is behind Cheke and Clayton's (Reference Cheke and Clayton2012) claims about the birds overcoming their current desires in favor of future ones, which suggest an argument along the following lines: The birds are currently sated on peanuts. Yet, they cache peanuts in the tray that will become available after they have been pre-fed raisins. Thus, they must be able to realize that, at that future time, they will desire to eat peanuts, rather than raisins, and this is what motivates them to cache peanuts in that tray, even though they do not desire peanuts at present (see Figure 3). As characterized, this argument rests on the assumption that an animal restricted to thinking only about how things are at present is thereby also restricted to acting only based on its present appetitive desires. Note that, in the case of food-caching birds in particular, there is no reason for making such an assumption. As Cheke and Clayton (Reference Cheke and Clayton2012) note, there is separate evidence that the motivational systems for eating and caching operate semi-independently from one another. Furthermore, they also describe a separate experiment, consisting only of the equivalent of the test trial in the study described above, which shows that, while specific satiety reduces the motivation to cache the pre-fed food type, it does not eliminate it.

Thus, insofar as Cheke and Clayton's (Reference Cheke and Clayton2012) study can be described as one in which the birds “overcome” a current desire in favor of one that will serve their future needs, the issue at stake cannot be that the motivation to cache the pre-fed food clashes with a current lack of motivation to eat that food, brought about by specific satiety. Rather, the only sense in which the birds can be said to “overcome” an existing motivation is that, by default, if pre-fed one food type, they have a motivation to cache less of that food type, and this changes into a motivation to selectively cache the pre-fed food type in a particular tray once they learn that that food type is desirable at retrieval from the relevant tray (see also Cheke & Clayton Reference Cheke and Clayton2012, p. 174). This is entirely compatible with an account on which the relevant retrieval trials simply cause the bird to update its representation of which tray is a good location for caching which food.

2.3. Past and future thinking and animals: Concluding remarks

Comparison across Figures 1–3 should make one aspect of our account clear. In each instance, the representation that we are assuming underpins the birds’ behavior, must necessarily also be part of what is represented according to an MTT account (i.e., that Tray 1 does not contain edible worms, that the stone should be chosen because it operates the apparatus, that Tray 1 is a good place to cache peanuts). Because of this, the representations we are positing cannot be considered to be implausibly ad hoc. Other questions one might raise with respect to our account also arise in the same way for accounts that postulate MTT abilities in animals. Thus, we have already noted that an MTT based interpretation of Clayton and Dickinson's (Reference Clayton and Dickinson1998) study also has to assume the existence of some sort of mechanism that keeps track of time, which underpins animals’ putative ability to remember “when” information. Similarly, in connection with our interpretation of Kabadayi and Osvath's (Reference Kabadayi and Osvath2017) study, questions might be asked about the conditions under which animals continue to represent an object as part of their current environment, even if it is outside their sensory range, and the conditions under which they stop doing so. Identifying these conditions is an empirical matter, and it is highly likely that the conditions vary by context and across species. But note that an explanation of the birds’ behavior that ascribes to them an ability to imagine future events raises exactly parallel questions as to the conditions under which the animal does or does not assume the future event will occur.

The key point that the plausibility of our account hinges on is whether we are correct about the general means by which the birds arrive at the representations that underpin their behavior, that is, purely as a result of the operation of the temporal updating system. And, as should be clear, there are real constraints on what is available to such a system: Only a model concerning the world as it is at present is maintained, tensed content is absent from that model, and the correct functioning of the system depends on information about changes in the environment being received in the same order in which those changes happen. These constraints mean that, in explaining animal behavior, our account only allows for a distinctively narrow set of options. The alternative MTT account assumes that the birds arrive at these (very same) representations necessary to guide behavior as a result of first remembering a past or imagining a future event. Note, though, (and this is not always made clear) that MTT alone does not deliver these representations: that is, to guide behavior, remembering the event of caching worms has to be combined with other information about how long it takes worms to degrade and how much time has actually elapsed, and then an inference has to be reached about the contents of Tray 1. Thus, the plausibility of that account hinges not only on whether animals can be thought to engage in MTT, but on whether they can be thought to use the information it delivers alongside any other information that is required to yield a conclusion as to what needs to be done right now.

Before leaving the issue of animal cognition, we want to briefly consider two recent theoretical accounts that have also attempted to provide an alternative explanation of animals’ performance in these sorts of tasks. Redshaw (Reference Redshaw2014) has argued that animals may have “uncontextualized” representations of events, by which he means representations that fail to locate these events in any specific temporal context (in his view, such contextualizing would require metarepresentational abilities). And in articulating his own dual systems theory, Keven (Reference Keven2016) has argued that animals (and young children) do not possess episodic memory but may possess event memories that are “perceptually-based [and] snapshot-like.” Unlike episodic memories, he believes these event memories are not organized into narratives with temporal-causal structure. Both accounts therefore share the idea that animals have some type of free-floating representations of past (or future) events. Furthermore, although the two authors do not make this explicit in their discussions, their accounts are both compatible with one idea we are pressing, namely that there is no reason to believe that animals are capable of thinking about particular, unique, times. Nevertheless, the account we have put forward differs fundamentally from their accounts. The temporal updating system simply maintains a model of the world that records information about the environment and is updated in response to new information. Situations that obtained or will obtain at other times do not feature in such a model, even in an uncontextualized way. One way to put this is to say that on Redshaw's (Reference Redshaw2014) and Keven's (Reference Keven2016) accounts, animals are not truly cognitively stuck in time: they can mentally meander through time even if they have no idea where in time their meandering takes them. By contrast, on our account, animals really are cognitively stuck in time: they cannot think about other times at all.

Yet, while our account is thus more radical than those offered by Redshaw (Reference Redshaw2014) and Keven (Reference Keven2016), it can actually be seen to construe animals’ behavior as more purposive than their accounts do. Note that, precisely because of their supposedly uncontextualized nature, it is ultimately not clear how exactly event memories of the type envisaged by Redshaw and Keven are supposed to explain the types of animal behaviors we have described – a point Redshaw himself seems to acknowledge in the context of discussing tool-saving behaviors in animals, which he characterizes simply as cases in which an uncontextualized representation of using the tool in question induces a bias to select it again. That is, it is not clear how uncontextualized representations of how things were or will be at unspecified other times can systematically and appropriately guide present action (e.g., how can they generate the types of representations described at the beginning of this section, such as “Tray 1 does not contain edible worms”?). By contrast, even though on our account animals are not capable of representing situations obtaining at other times at all, the model of the current world they operate with can clearly give them good reasons to act in certain ways. For instance, we assumed that the ravens in Kabadayi and Osvath's (Reference Kabadayi and Osvath2017) study choose the functional tool because it allows them to open the apparatus containing the food reward, which they represent as an item existing in their environment.

3.1. Temporal updating versus reasoning about temporal order

Even infants can be sensitive to and learn about event order. Numerous studies of deferred imitation in infants have conclusively established that, at least by the second year of life, they can observe a short sequence of actions and reproduce those actions in the correct order even after a delay (e.g., Bauer & Mandler Reference Bauer and Mandler1989; Bauer et al. Reference Bauer, Wenner, Dropik and Wewerka2000). Preschool children also rapidly acquire a repertoire of what have been described as “scripts” for routines (Nelson Reference Nelson1996).

These studies of infants and pre-schoolers suggest that children are very good at remembering and reproducing actions in the correct order. This basic ability in itself, however, is something that can fall within the scope of the temporal updating system rather than the temporal reasoning system. A key limitation of the temporal updating system that might be used to show whether children do indeed rely on it in learning about sequences is that the correct functioning of the system depends on it receiving information about events in the same order in which those events occur. We have described this as a signature limit of temporal updating, which contrasts sharply with a much more sophisticated way in which adult humans can deal with change over time, by engaging in genuine temporal reasoning about what happens when.

Although relatively few studies have examined temporal reasoning skills in young children, the evidence suggests that they struggle in situations in which the order in which they find out about successive changes may not reflect the order in which they happen – that is, in situations in which they cannot rely purely on temporal updating. In one study carried out by McCormack and Hoerl (Reference McCormack and Hoerl2005), children learned that pressing (e.g.) a red button caused a marble to be released into a window of a box, and that pressing a blue button caused a toy car to be released. There was only ever one object in the window of the box at a time, so if the red button was pressed to yield a marble, on pressing the blue button the marble dropped away and was replaced by a car. Children also learned about two dolls that always acted in a particular order. The window of the box was then covered over, and two types of tasks were carried out. In one version of the task, children watched as one doll pressed the red button and then the other doll pressed the blue button. Under this condition, when asked which object was in the window of the box, even 3-year-olds were able to answer correctly. This task can be solved by temporal updating: children can sequentially update their model of what is in the box window: initially representing it as empty, then as containing a marble, and then as containing a car. However, in another version of the task, the dolls pressed their buttons behind a screen, out of sight of the children, and the dolls were then left beside the buttons they had pressed. Temporal updating could not be used to pass this version of the task, which required that the children infer the window's contents by reasoning about the order in which the dolls had pressed their buttons, and even 4-year-olds struggled to do this (see also McCormack & Hoerl Reference McCormack and Hoerl2007). Similar results were found in an earlier study by Povinelli et al. (Reference Povinelli, Landry, Theall, Clark and Castille1999), which used video clips to decouple the order in which children found out about two events from the order in which they actually happened.

Other studies have indicated that children of this age also have difficulties appropriately reasoning about temporal order relations in planning tasks, such as in circumstances where they have to think ahead about the order in which events are going to unfold in the future (Lohse et al. Reference Lohse, Kalitschke, Ruthmann and Rakoczy2015; McColgan & McCormack Reference McColgan and McCormack2008; relatedly see also Kaller et al. Reference Kaller, Rahm, Spreer, Mader and Unterrainer2008; Tecwyn et al. Reference Tecwyn, Thorpe and Chappell2014). Martin-Ordas (Reference Martin-Ordas2018) asked children to select one of three objects to bring back to two rooms they had visited earlier. The correct answer was to choose the key needed to open a marble box containing marbles to use on a marble run. Although 3- and 4-year-olds correctly selected the key, they were unable to judge which room they should then visit first – the room with the marble box or the marble run room. It was not until children were 5 that they could reason appropriately about the order in which these future visits needed to happen.

The claim that children below 5 years find it difficult to reason about before-and-after relations in time might sound surprising given that children actually acquire the verbal terms “before” and “after” at an earlier age (Busby-Grant & Suddendorf Reference Busby-Grant and Suddendorf2011). There is, however, evidence regarding children's competence in using and interpreting those terms that is in line with what our account would predict. Specifically, they have difficulty correctly interpreting these terms when the order in which events are mentioned in a sentence does not match their order in the world (e.g., “Anna took off her coat after she took off her hat.” Blything & Cain Reference Blything and Cain2016; Blything et al. Reference Blything, Davies and Cain2015), suggesting they use an order-of-mention strategy to interpret them. While there are a variety of interpretations of this finding (Blything et al. Reference Blything, Davies and Cain2015; Pyykkönen & Järvikivi Reference Pyykkönen and Järvikivi2012), one possibility is that this reflects pre-schoolers’ difficulties with temporal reasoning and their tendency to use the temporal updating system.

Taken together, the findings we have discussed here suggest that while even infants can learn about and be sensitive to event order, difficulties in reasoning about temporal order persist into the preschool years, with the findings from some studies suggesting that the errors children make may be due to falling back on the temporal updating system. By the time children are 5, existing evidence suggests that they have consolidated some important new temporal reasoning skills.

3.2. Thinking about other times

As with animals, there is considerable debate over how infants’ and preschoolers’ memory abilities should be characterized (e.g., Bauer Reference Bauer2007; Fivush Reference Fivush2011; Howe & Courage Reference Howe and Courage1997). There have been attempts with various degrees of success to use a supposed “what-when-where” paradigm analogous to that used with animals (Burns et al. Reference Burns, Russell and Russell2015; Martin-Ordas et al. Reference Martin-Ordas, Atance and Caza2017; Russell et al. Reference Russell, Cheke, Clayton and Meltzoff2011). Notably, even relatively older children struggle with tasks analogous to that of Clayton and Dickinson (Reference Clayton and Dickinson1998) that require sensitivity to how long ago an item was hidden, which by our account of animal performance in such tasks is unsurprising because children would have no need in everyday life to have their search behavior governed by sensitive interval timing mechanisms. Performance in the tasks more typically used to measure infant memory (Bauer et al. Reference Bauer, Wenner, Dropik and Wewerka2000; Rovee-Collier Reference Rovee-Collier1999) can be straightforwardly accounted for in terms of the temporal updating system. However, it is less straightforward to explain pre-schoolers’ verbal descriptions of non-current events merely in terms of the idea of temporal updating. Existing studies suggest that children who are 2–3 years old can talk about both past and future events, albeit often providing limited and fragmented information (Hayne et al. Reference Hayne, Gross, McNamee, Fitzgibbon and Tustin2011; Peterson Reference Peterson2002; Weist & Zevenbergen Reference Weist and Zevenbergen2008). It is widely accepted that children of this age can refer to things that are outside their current sensory scope (Sachs Reference Sachs and Nelson1983), which is something that the temporal updating system could handle if these things are still part of their model of the world as it is now. However, children do not just refer to things outside their current sensory scope, they often use tense to describe non-current events, and we have assumed that the temporal updating system does not operate with tensed representations. Given that 2-3-year-olds can refer to events in the distant past and in the future, and 3-year-olds also use temporal adverbs (Weist & Buczowska Reference Weist and Buczowska1987; Weist & Zevenbergen Reference Weist and Zevenbergen2008), it might seem paradoxical to argue that they cannot think about the past or future.

We accept that children of this age do not rely only on the basic temporal updating system. However, we want to argue that they are at an intermediate stage at which they nevertheless do not yet possess genuine temporal reasoning abilities, and, in that sense, do not have proper concepts of the past or future. To make this argument it is necessary to consider more carefully the nature of the domain over which the temporal reasoning system operates. Temporal reasoning operates over the domain of times, with times arranged in a linear array such that each time occupies a unique unrepeated location in the array. Reasoning about such a domain involves a grasp of two distinctive types of systematicity that obtain within it. First, systematic before-and-after relations exist between points in that array because of its linearity – that is, for a sequence of times A, B, and C, if A happens before B and B happens before C, A must also happen before C. Second, which times are in the past, present, and future changes systematically with the progression of time: for the sequence of times just mentioned, if A is now present, then both B and C are in the future. But when B will be present, A will be past and C future, and when C will be present, both A and B will be past.

There is no reason to believe that young pre-schoolers can reason about the domain of time in this way. While they may talk about events that are in the past or the future, there is no reason to believe that they have a sense of where in the past or future those events are located, or a grasp of the systematic temporal relations that obtain between these events. In Tillman et al.’s (2017) recent study, 3-year-olds were unable to make judgments about the relative order of a set of past and future events (their previous and next birthdays, breakfast this morning, and dinner this evening). Indeed, 3-year-olds in this study were unable to reliably judge the deictic status of these events (nor the deictic meaning of time words such as “yesterday”). Similarly, Busby-Grant and Suddendorf (Reference Busby-Grant and Suddendorf2009) found that children of this age could not discriminate the relative distances in the future of even very widely separated events (e.g., going home from day care versus next Christmas).

Important improvements in children's ability to think about the temporal locations of events occur between 3 and 5 years. There is evidence that by the time children are 4, they can begin to make some discriminations about the relative recency of unrelated events in the past (Friedman Reference Friedman1991; Friedman et al. Reference Friedman, Gardner and Zubin1995; Friedman & Kemp Reference Friedman and Kemp1998; McCormack & Hanley Reference McCormack and Hanley2011; though see Pathman et al. Reference Pathman, Larkina, Burch and Bauer2013). However, even 4-year-olds struggle to order the times of events in the future (Friedman Reference Friedman2000; McCormack & Hanley Reference McCormack and Hanley2011), or to judge the remoteness of past and future events (Busby-Grant & Suddendorf Reference Busby-Grant and Suddendorf2009; Tillman et al. Reference Tillman, Marghetis, Barner and Srinivasan2017). Moreover, a number of studies have shown that they tend to confuse near past and near future times (Friedman Reference Friedman and Kail2003; Friedman & Kemp Reference Friedman and Kemp1998). Indeed, the ability to order events in time continues to improve substantially over the next few years (Hudson & Mayhew Reference Hudson and Mayhew2011; Pathman et al. Reference Pathman, Larkina, Burch and Bauer2013; Tillman et al. Reference Tillman, Marghetis, Barner and Srinivasan2017).

We have suggested that reasoning over the domain of times involves not just understanding the relations that obtain between points in time but also understanding that which points in time are in the past, present, or future changes systematically with the progression of time. Extremely few studies have addressed children's ability to engage in the kind of temporal perspective taking that grasping this requires, but those that have indicate that children below 4 do not have this ability (Cromer Reference Cromer1971; Harner Reference Harner1980; Reference Harner and Friedman1982). In Cromer's task, children had to consider the deictic status of an event from a point in time that was not the present. For example, children were told a story about a girl who visited a farm where a number of things happened, including her seeing birds, and who then returned from the farm. Children had to judge (e.g.) at what stage in the story the girl could refer to seeing the birds in the past tense. It was not until children were 4–5 years old that they were able to answer these types of questions correctly.

Coupled with the findings discussed in the last subsection, the evidence weighs heavily in favor of the idea of an important transition in the period from 3-5 years in children's ability to engage in temporal reasoning. During this period, children acquire mature concepts of time and start to be able to reason about the domain of linearly ordered times. This leaves the question, though, of how we want to characterize temporal cognition in the early preschool years, if we want to argue that children of this age cannot properly think about the past and future. We suggest that at this age children are able to make some sort of discrimination between situations that have obtained and situations that are yet to come. One way to put this is to say that they may retain models of the world that have been superseded (i.e., of past states of affairs), or models of the world as it has yet to be (i.e., of future states of affairs). As demonstrated by generally accurate use of past and future tense, they can usually appropriately discriminate between these models, in a way that corresponds to which of these two types they belong to. Nevertheless, we do not believe that children of this age are treating some models as descriptions of situations located at specific past times and others as descriptions of situations located at specific future times. Rather, we believe that children of this age may simply make a categorical distinction that marks a difference between these two types of situations; specifically, we believe that children discriminate between situations that are no longer alterable and situations that are still potentially alterable (see McCormack Reference McCormack, Lerner, Liben and Mueller2015; McCormack & Hoerl Reference McCormack and Hoerl2017, for considerably more detail on this proposal and our developmental model). However, this is different from having one unified model of the world within which time itself is represented. Having such a unified model goes beyond just representing certain sets of states of affairs and being able to discriminate between them. It involves representing time as one of the dimensions along which reality is extended, and as a linear dimension along which these sets of states of affairs can therefore be organized, so that they can all be captured in one set of systematic temporal relations in which they stand to each other. Temporal reasoning, in other words, operates with a four-dimensional picture of reality, on which everything that happens can be described by giving its location and the time at which it happens. It is the discovery of time as this fourth dimension that is the crucial step in the transition to a temporal reasoning system.

Space precludes us from commenting more than very briefly here on further developmental questions regarding cognitive prerequisites for the development of temporal reasoning – in particular regarding claims that have been made to the effect that temporal reasoning requires language (Bennett Reference Bennett1964), or that it requires a capacity for metarepresentation (Redshaw Reference Redshaw2014). With regard to the role of language, we believe it is plausible (although we will not develop the argument here) that acquisition of the basic temporal concepts discussed here requires language, perhaps because it is only through discussing non-current events with others that children begin to grasp how such events are temporally organized (Hoerl & McCormack Reference Hoerl, McCormack, Eilan, Hoerl, McCormack and Roessler2005; Welch-Ross Reference Welch-Ross, Moore and Lemmon2001). This does not mean, though, that children learning different languages or growing up in different cultures acquire different concepts of time. We assume that our description of the temporal reasoning system captures basic and universal features of human thinking about time, and this includes a notion of time as linear. Although cultures may differ in the extent to which they emphasize cyclical or repeating patterns in time, we follow Gell (Reference Gell1992) in assuming that linearity is a universally basic feature (McCormack Reference McCormack, Lerner, Liben and Mueller2015, McCormack & Hoerl Reference McCormack and Hoerl2017). The features of the temporal reasoning system that we have highlighted will of course be overlaid by further culturally specific constructs, such as different ways of metaphorically mapping time onto space or of measuring time using a calendar system. These culturally specific aspects of development have a protracted developmental time course (Friedman Reference Friedman and Kail2003; McCormack Reference McCormack, Lerner, Liben and Mueller2015).

With regard to the issue of metarepresentation, we note an interesting structural parallel between the account we have proposed of the development of temporal reasoning capacities and Perner's (Reference Perner1991) influential account of the development of metarepresentation. On Perner's account, children move from having only one model of the world through an intermediate phase of being able to switch between different models, before finally being able to conceive of them as different representations of the same reality. On our account of the emergence of temporal reasoning, children are initially capable only of temporal updating, and thus operate with a tenseless model of the world. They then begin to be able to maintain models describing non-current states of the world but they do not represent these as states organized along a single temporal dimension, and therefore do not grasp the systematic temporal relations between them. In acquiring genuine temporal reasoning, a unified model emerges that allows children to represent how these states are temporally organized and interrelated.

Although the structural parallel is interesting, we note, however, that there is an important difference between Perner's (Reference Perner1991) description of the emergence of metarepresentation and our description of the emergence of temporal reasoning, in that the accounts differ in terms of the type of systematic relations between models that children need to learn to grasp. Perner's claim is that children need to grasp how different models of the world are related to the actual world – specifically, that they are representations of reality – and it is through this that children understand how the models relate to each other, as different possible ways of representing the very same world. That is, grasping the type of systematic relations that Perner is interested in is a consequence of understanding the representational nature of mental states. In our account, children must grasp the systematic temporal relations between different models of non-current states of the world by realizing they are located at points on the same timeline. It cannot be straightforwardly assumed that grasping this type of relation necessarily requires grasping the representational nature of mental states, although we recognize that there is a more detailed developmental story to be told about how this new ability comes about, further discussion of which we provide elsewhere (Hoerl & McCormack Reference Hoerl, McCormack, Eilan, Hoerl, McCormack and Roessler2005; McCormack Reference McCormack, Lerner, Liben and Mueller2015; McCormack & Hoerl Reference McCormack and Hoerl1999; Reference McCormack, Hoerl, Moore and Lemmon2001; Reference McCormack and Hoerl2017).

3.3. Animal cognition revisited: Lessons from developmental studies?

Before turning to adult human cognition, we want to briefly consider whether the findings of developmental studies might help illuminate what types of animal research would be capable of providing a test of the hypothesis that animals rely only on the temporal updating system. Developmental studies have looked in detail at children's ability to represent and reason about event order information, and two types of findings are of note. First, developmentalists have devised studies that provide children with information about changes that have happened in a sequence, but do not provide this information in the order in which the changes themselves unfolded (both by showing mis-ordered videoclips that children need to mentally re-order [Povinelli et al. Reference Povinelli, Landry, Theall, Clark and Castille1999] and by requiring children to infer the sequence from two pieces of information that are presented simultaneously [McCormack & Hoerl Reference McCormack and Hoerl2005; Reference McCormack and Hoerl2007]). The temporal updating system as we have described it can only provide an accurate model of how the world is now if changes are encountered in the sequence in which they actually occur, so reliance on that system would result in task failure. Second, we also note that some developmental planning tasks require that children do more than simply select a tool that is functional for obtaining a reward that exists somewhere in their current environment. In McColgan and McCormack's (Reference McColgan and McCormack2008) study, children must bear in mind the order in which events are going to unfold in the future and appropriately place an object so that it will be encountered later at the right point in a sequence of future events; in the study of Martin-Ordas (Reference Martin-Ordas2018), children must think ahead about the order in which they need to visit two rooms so that they are appropriately prepared when they later encounter the reward apparatus. We anticipate that it might be possible to devise animal versions of both these types of studies, and such studies would prove particularly illuminating in testing our hypothesis about limitations in animal cognition.