R2.1. Temporal updating and questions of explanation – the case of foraging behavior

Pan & Carruthers ask how our account would explain the foraging behavior of hummingbirds, which have been shown to be sensitive to the rate at which flowers replenish. As they rightly assume, our account would take it that the birds possess (something like) a timer that gets entrained with the refresh rate of the flower as the bird visits the flower at different intervals after feeding and finds it full again only at some of those intervals. On a temporal updating account, the function of this timer is to make it the case that, at times after feeding that correspond to intervals at which the flower has been found empty, the flower is not represented as full, whereas at times corresponding to intervals at which the flower has been found to be full it is represented as full.

Pan & Carruthers say that they “have no idea how H&M think this is supposed to happen.” We think this might be because they don't distinguish clearly enough between two different types of question. Call the first the mechanism question. In the case of the dog digging for the bone, which we mentioned at the start of this section, the mechanism question is the question answered by saying that it is simply the tendency of beliefs to persist over time that explains why, even after some time has elapsed, the dog still believes that a specific location contains a buried bone. That is to say, how it happens that it has that belief at the relevant time is that it had that belief previously, and that that belief has persisted over time. Similarly, in the case of the hummingbirds, we suggest that the mechanism question is answered simply by saying that particular states of a timer that gets triggered upon feeding from the flower have become associated with a representation of it as empty and others have become associated with a representation of it as full. How this happens is explained by the fact that the two types of representations have become associated with the two sets of states of the timer. As a result, the timer being in the former set of states will cause the bird to represent the flower as empty, and the timer being in the latter set of states will cause it to represent the flower as full.

Contrast the mechanism question with another type of question that can take the form “How does it happen?” Going back to our original example of the dog, one can ask why it actually is that the belief about where the bone is buried persists. Why does the dog not simply lose that belief as soon as the bone is out of sight? We might call this the sensitivity question, as it concerns the fact that the persistence conditions of the belief about the bone are somehow sensitive to the persistence conditions of the bone itself. We are happy to grant that such a question can be raised for the simple temporal updating account of the dog's behavior that we have given. However, the same question also arises for any account that explains the dog's behavior in terms of a belief, on the part of the dog, that it buried the bone in the relevant location in the past. As we said above, such an explanation is not complete unless the dog is credited with the general belief that buried bones tend to stay put, and there is clearly no reason to ascribe such a belief to the dog unless it is somehow sensitive to the persistence conditions of buried bones.

Similarly, if it is the sensitivity question that Pan & Carruthers are after by asking how our account explains the hummingbirds’ behavior, the question is how it happens that the birds’ timer comes to be entrained with the refresh rate of the flower in the first place. This is indeed an important question, because, for example, such entrainment requires the bird revisiting the flower at different intervals after feeding, which it might be thought to have no reason to do because it has emptied the flower of nectar. Just as with the dog, though, it is wrong to think that our account faces this type of sensitivity question, whereas one that ascribes to the bird representations of the time elapsed since its last visit to the flower doesn't. Pan & Carruthers suggest that the birds have a representation with the content “the flower takes between 10 and 20 clicks [of the interval timer] to replenish.” Presumably the idea is that their having this representation, together with a representation of how many clicks ago they visited the flower, is what explains their behavior. But then how does the bird form this representation of how many clicks it takes for the flower to replenish, if not again on the basis of repeated visits to the flower at different intervals after feeding?

Thus, we believe Pan & Carruthers’s impression that our account fails to give an explanation of how it happens (see also Kaufmann & Cahen) may be based on a conflation between two different ways this question may be understood. It is indeed true that the answer to the mechanism question, on its own, does not fully explain animal behavior. Yet it is wrong to think that our account therefore faces an extra explanatory burden, because the sensitivity question, which needs to be answered to provide the full story, is one that alternative accounts of animal behavior face in just the same way.

R2.2. Delay of gratification

Another type of animal behavior that we did not discuss in our target paper is behavior that involves delay of gratification. As Osvath & Kabadayi point out, the study of theirs that we used to illustrate experiments on animal tool saving included two conditions in which, among the items the ravens could choose other than the tool, there was also a food reward, albeit one that was smaller than the one obtainable with the tool. Kabadayi and Osvath (Reference Kabadayi and Osvath2017) argued that the delay after which the birds were given access to the baited apparatus that could be opened with the tool played a significant role in whether they chose the tool or the food reward. The birds were more likely to choose the immediate food reward in a condition in which they had to wait for 15 minutes than one in which they were given immediate access. Osvath & Kabadayi argue that we ignore the role the delay plays in determining the birds’ choice, and hence misdescribe the representations underpinning the birds’ behavior. We note that, unless we have misunderstood their method, their own results do not force the conclusion that the birds are sensitive to the magnitude of temporal delay per se. The authors described the immediate access condition as one in which the reward in the apparatus was “spatiotemporally closer” (Kabadayi & Osvath Reference Kabadayi and Osvath2017, p. 203, emphasis added) – that is, closer in space as well as time – because the birds walked past and saw the apparatus immediately prior to making their selection, whereas in the 15 minute delay condition they had no such prior perceptual access to the apparatus. The confound of spatial and temporal closeness means that it is not possible to be confident that the birds’ behavior was sensitive to the length of the delay.

We will set this point aside because there are numerous other studies that suggest that animals are sensitive to the magnitude of delay periods in delay of gratification procedures (Vanderveldt et al. Reference Vanderveldt, Oliveira and Green2016). Let us assume that Osvath & Kabadayi are right that the specific delay at which the ravens get re-introduced to the apparatus has a systematic effect on their choices. What is at issue is whether this means that the ravens must be representing both the current situation and a different, future, situation in which they will be re-introduced to the apparatus, and weighing up how far in the future that situation will be. Ravens, unlike humans, cannot be simply informed about the distance in the future at which an event will happen. Therefore, any difference in their choosing behavior must be based on their prior experiences, when they were either re-introduced to the apparatus almost immediately or only after a 15 minute delay. These different experiences can have an impact on how the apparatus and its associated reward is represented, and in turn influence tool choice. One straightforward possibility, compatible with the idea that delayed rewards are discounted, is that as a result of their learning experiences the birds place less value on the tool when it only yields a reward after delay. Indeed, our account leaves open the possibility that animals could make flexible trade-offs that adjust to the length of delay until reward. In describing our updating explanation of Clayton and Dickinson's studies of scrub jays’ memory, we suggested that (something akin to) interval timers may determine the representational contents maintained in the updating system, without the birds being able to represent the time of a previous caching event. Similarly, it is possible that representations of reward magnitude are shaped during learning by the operation of some sort of timing mechanism, without assuming that animals can represent the times at which future rewards will occur. Assuming that some type of timing mechanism is involved here is not controversial. Any account of animal sensitivity to delay in temporal discounting studies must appeal to something along these lines. Our argument is that there is no need to assume that animals actually represent future points in time. Rather, such mechanisms could directly affect representations of the magnitude of rewards.

R2.3. Orangutans’ long calls

We believe a third type of animal behavior mentioned in the commentaries, too, can be explained by our account, and this time even without an appeal to timing mechanisms. These are orangutans’ long calls, as discussed by Kaufmann & Cahen (van Schaik et al. Reference van Schaik, Damerius and Isler2013). Van Schaik et al. found that the direction of males’ calls emitted in the evening predicted the main direction in which the animals traveled the next day better than chance. Moreover, other orangutans’ travel direction was influenced by males’ long calls from the previous evening, with females remaining at constant distance from the calling male, whereas other males increased their distance. Kaufmann & Cahen say that “the primary goal of these long calls appears to be to communicate to female orangutans the male's future travel direction” and that the females, as well as other males, “use this information in planning their own travel.” This might make it sound as though the conspecifics can determine the direction of the call and then infer from this that the calling male will be found in a certain area in the future. Yet there is actually no reason for thinking that the conspecifics can determine the direction of the males’ call in the first place. Rather, as van Schaik et al. (Reference van Schaik, Damerius and Isler2013, p. 2) themselves point out, the angular difference between the direction of the call and the line connecting the conspecific to the calling male is likely simply to determine the perceived distance from the calling male, without the conspecifics being able to distinguish between the calling male being far away and calling in their direction or closer but calling in a direction away from them. It is therefore more plausible to think that the representation formed upon hearing the call is simply one of how close the calling male is, which is something that could be done within the temporal updating system. If females simply move toward that perceived location if it appears far away, or subordinates move away from it if it appears near, that will be sufficient to yield the observed effect of females staying within earshot of the calling male and subordinates increasing their distance. Yet this would be behavior simply based on a representation of the calling male's perceived location when the call is heard, rather than a representation of its location at some future time.

Obviously, what also needs to be explained is the fact that the calling males do travel in the direction in which they called, and that the conspecifics adjust their own subsequent movements to the perceived location of the call, even though the call was made the previous evening. Van Schaik et al. (Reference van Schaik, Damerius and Isler2013, p. 8) describe this as being “consistent with the use of some form of episodic memory,” but it is unclear why episodic memory should be required to explain these behaviors. Consider van Schaik et al.’s (2013, p. 9) own remark that “the important point is that a male orangutan is maintaining an internally generated directional choice toward a distant target out of current sensory range, over a prolonged time period, despite meandering routes.” As this makes clear, the crucial explanatory work is being done by the orangutan maintaining this choice over time, that is, forming a representation of a particular distant location as a good location to visit, retaining that representation, and keeping track of its own position relative to that location. We are back to the general type of explanation that we used to account for how the dog, after burying the bone in the garden, can subsequently maintain a representation of its location.

R2.4. Animal behavior in time: Moving the debate forward

We hope that in addressing some of the specific challenges raised by the commentators we have clarified the nature and scope of our account. In each instance, we have suggested that the available evidence does not force the conclusion that animals are capable of temporal reasoning. Of course, our account of these behaviors still leaves a variety of unanswered questions about the precise details of the underpinning mechanisms. However, in our view, mental time travel accounts, when considered properly, also face similar and arguably more difficult questions.

Osvath & Kabadayi’s overall criticism is that we are simply rehashing an outdated claim that animals are stuck in time. However, they do seem to agree with us that what animals do is different from humans. At one point, they also describe their view as one according to which animals might “implicitly represent time, without representing time as such.” Part of our aim was precisely to try to move forward the debate in this area, which has been dogged by the problem that researchers have resorted to concepts and criteria that are difficult to operationalize. We aim to provide a more specific, empirically tractable characterization of one sense in which animals might be stuck in time. We describe this as their being unable to engage in temporal reasoning, but we also give some operational criteria as to when an organism should be described as only capable of temporal updating. We recognize though that our account of animal behavior is likely to remain controversial. In particular, one general question that might be raised about it is whether there could not also be types of temporal cognition that do not fall neatly into the two categories we have described. This is an issue we will return to in section R4.4.Footnote ²

R3.1. Comparison with other domains of cognition

One key issue raised in a number of commentaries concerns the extent to which our account aligns with claims that have been made regarding other domains of cognition, pointing to a more general type of distinction of which the one between temporal reasoning and temporal updating is only one instance. To give examples from the commentaries: Redshaw, Bulley, & Suddendorf link our account with the distinction between skills that do or do not require metarepresentation; Povinelli, Glorioso, Kuznar, & Pavlic identify our account as aligning with a distinction between abilities that do or do not require constructing higher-order analogical-based relations; and DeNigris & Brooks suggest that our distinction is one between symbolic and non-symbolic representational formats, with the developmental transition understood in terms of Karmiloff-Smith's (Reference Karmiloff-Smith1994) notion of representational redescription (see also Hohenberger). A more domain-specific parallel is drawn by Lohse, Sixtus, & Lonnemann, who argue that developmental changes in numerical cognition can be seen as paralleling those we have described in temporal cognition (see also DeNigris & Brooks; Roselli).

We can certainly see the value of considering how our account aligns with more domain-general claims regarding cognitive development. It is also broadly correct to describe the temporal reasoning system as involving a type of higher-order cognition that the updating system does not operate with. However, our account differs from those regarding other domains (such as theory of mind, number, and weight) that the commentators refer to. In those instances, it is typically assumed that infants have some primitive representation of the basic domain, on which the more sophisticated conceptual grasp of the domain builds. For example, in the case of theory of mind, on a number of theoretical approaches, young children are assumed to be operating with some more primitive way of representing the relations between agents and aspects of the world; the developmental achievement is to reach a proper grasp of the nature of the relations in question. The input to the more primitive process is assumed to be perceptually-based in some important sense (such as observation of the interactions between agents and objects), providing an initial “way in” to the domain in question that then provides the foundations for more sophisticated understanding.

By contrast, our view is that the temporal updating system does not provide a similar perceptual “way in” in the case of time, and that the representations of the domain of time with which the temporal reasoning system operates are not simply some sort of more enriched or explicit or redescribed version of representations that the updating system is operating with (see also Tillman). Rather, there is an important sense in which the updating system that very young children possess is not operating with temporal representations at all. Indeed, Oyserman & Dawson describe the updating system as “atemporal.” Similarly, Melnikoff & Bargh comment on our account: “To our knowledge, it is the first dual-systems theory to define its systems in terms of possessing versus lacking a single representational dimension.”

R3.2. Time as a stimulus dimension vs. time as a framework

Hamamouche argues that our account gets the developmental picture completely wrong: in assuming that infants only have the more primitive updating system, we are ignoring evidence that infants are “well-tuned timers” (see also Viera & Margolis for similar points regarding animals). The empirical studies unarguably indicate that very young children possess mechanisms that process temporal duration information. What should be concluded from this? On an alternative developmental picture, one could hold that the representations the updating system deals with are indeed temporal representations of duration, and that the emergence of the reasoning system results from some more explicit or redescribed version of these representations. Such an alternative picture could potentially be seen as aligning with Droit-Volet's description of children as moving from implicit procedural timing to an explicit grasp of the notion of temporal duration (Droit-Volet & Rattat Reference Droit-Volet and Rattat1999). The difficulty with this picture is that it deals only with what we might call time as a stimulus dimension rather than time as a framework (McCormack Reference McCormack, Lerner, Liben and Mueller2015). When time is dealt with as a stimulus dimension, what is processed is the magnitude of stimulus duration; the focus of our paper is with time as a framework in which moments in time have locations relative to each other and relative to the present moment. The latter is what the temporal reasoning system operates with, and our claim is that the updating system does not operate over such a domain because in the updating system other times are not represented at all.

One might argue that it is misleading to describe the temporal updating system as not operating with temporal representations because we are happy to accept that such a system operates with mechanisms that process temporal duration information. Of course, if it is stipulated by definition that the mechanisms that process duration information operate with temporal representations, then, in this sense, the updating system does represent time. However, this only allows for a narrow sense in which duration can be said to be represented. Because the updating system does not represent time as a framework, while duration could be processed as a stimulus property it could not be represented as the amount of time elapsed between two temporal locations (because temporal locations are not represented in the updating system). And this suggests that no proper concept of duration is possible for creatures possessing only the updating system, on the assumption that any conceptual grasp of duration must be grounded in the notion of a period of time between a start point and an end point.

Indeed, these considerations raise the issue of what developmental story should be told about the emergence of the concept of duration (it was this concept that was the focus of Piaget's Reference Piaget and Pomerans1969 work on time). Children do acquire such a concept by the time they are five, as evidenced by their ability to make explicit judgments regarding the lengths of events (Friedman Reference Friedman1990). As yet, we do not know how acquisition of the concept of duration is linked to acquisition of the (other) temporal concepts that the temporal reasoning system operates with (such as concepts of the past and future). We are confident, though, that the reasoning system does not simply deal with representations of time that are somehow more explicit or enriched versions of whatever representations are linked to duration sensitivity in infancy. This is not to say that the temporal reasoning system appears out of the blue. In the target article, we argue that 2- to 3-year-olds may not be full-blown temporal reasoners, but they are not solely reliant on the updating system either. Elsewhere (McCormack Reference McCormack, Lerner, Liben and Mueller2015; McCormack & Hoerl Reference McCormack and Hoerl1999; Reference McCormack and Hoerl2017), we have argued that children of this age have event-based temporal cognition, in which they represent events and event sequences and can think of some events as unalterable (a primitive version of the past tense) and of some as potentially alterable (a primitive version of the future tense). This may be sufficient to underpin some types of future-oriented activity, such as those that involve a sensitivity to the fact that aspects of the environment may change (see Goulding & Friedman). However, children of this age will struggle when they have to reason ahead about the temporal order in which future changes will or should happen (Martin-Ordas Reference Martin-Ordas2018). There are two key limitations at this stage: children do not represent the times of event occurrences separately from the events themselves, and, accordingly, they do not represent the systematic temporal relations between events (i.e., they do not have linear time). Nevertheless, these event representations provide the basis on which children begin to understand time itself (see also Mayhew et al.).

R3.3. Explaining the emergence of temporal reasoning

This still leaves questions about how the temporal reasoning system emerges. A number of the commentators raise the issue of the role of language and enculturation (DeNigris & Brooks; Hohenberger; Mayhew et al.; Tillman); this issue is also raised by some commentators when querying why we believe animals do not engage in temporal reasoning (Gentry & Buckner; Montemayor). The idea that concepts of time are tightly linked to language and/or show substantial cross-cultural differences has a controversial history (Aveni Reference Aveni1990; Gell Reference Gell1992). We have yet to come across convincing evidence that what we have described as the temporal reasoning system could not be assumed to be universal, and in the target article we suggest that culturally specific constructs may be overlaid on its basic functions. This does not mean, though, that we rule out the possibility that the temporal reasoning system emerges through social interaction. On the contrary, we have a great deal of sympathy for such a view. One approach here is to emphasize a specific role for language itself; as DeNigris & Brooks describe, Nelson (Reference Nelson1996) has made a persuasive case for this. In our own writings we have emphasized the role of communication rather than language per se in the acquisition of a linear notion of time. This is because we think that explaining a proper grasp of tense requires making an appeal to distinctive types of shared discourse that allow points in time to be the focus of shared attention with others. This argument is made in detail elsewhere (Hoerl & McCormack Reference Hoerl, McCormack, Eilan, Hoerl, McCormack and Roessler2005), but the general idea is that it is through joint discussion with other people about events at other times that children start to be able to separate out locations in time from the events that occur at those locations and get to grips with the systematic relations between different temporal locations and hence the timeline itself.

Our intuition is that acquisition of temporal concepts is not possible in the absence of such shared discourse about other times, which makes clear, for example, that things in the past were different to how they are right now, or that past events did happen even if they have left no present traces. Indeed, this is part of what motivates us to suspect that animals are not capable of temporal reasoning (in response to Gentry & Buckner; Montemayor; Pan & Carruthers).

R3.4. The self, narratives, and particular times

The picture of the development of the temporal reasoning system that we have just sketched also raises the question of how it links to the developing conception of the self as temporally extended, not least because children's shared discourse about other times typically involves discussions of events in which the child was or will be a participant. We do not have space here to provide a treatment of this issue (see McCormack Reference McCormack, Lerner, Liben and Mueller2015; McCormack & Hoerl Reference McCormack, Hoerl, Moore and Lemmon2001), but in Oyserman & Dawson’s commentary, they suggest that the temporal reasoning system is put to use in motivating action not just through a recognition that one is temporally extended, but through a (more sophisticated) recognition that one's future identity is not yet fully fixed. Specifically, they describe the way in which one's current actions are guided by how one envisages the identity of one's future self, using temporal reasoning to steer an appropriate path toward that preferred self.

This seems plausible, and is in line with the idea that temporal reasoning is closely linked to possession of the narrative form (Campbell Reference Campbell, Pastor and Artieda1996; McCormack Reference McCormack, Lerner, Liben and Mueller2015; McCormack & Hoerl Reference McCormack, Hoerl, Moore and Lemmon2001). In the case of Oyserman & Dawson’s description, the temporal reasoning system serves in a sophisticated way (most likely not present until late childhood/adolescence) to shape the narrative that one wants to have regarding how one's life unfolds. There may, however, be a more developmentally basic link between autobiographical narratives and the temporal reasoning system. Campbell (Reference Campbell, Pastor and Artieda1996) argued that understanding and using autobiographical narratives (which children properly get to grips with much earlier, around 4 or 5) necessitates a grasp of the unique temporal locations of events – the fact that an event occurred at a specific point in one's life has genuine significance in the context of such narratives. It is this way of representing temporal locations – as unique and unrepeated on a timeline – that is embodied in the temporal reasoning system.

Gentry & Buckner suggest that, contrary to our account, animals may, at least in principle, be capable of thinking about locations in time this way. They argue that there appear to be relatively few genuinely distinctive “landmark” events in animals’ lives. Therefore, some animals might be capable of temporal reasoning but their lives may not be populated with sufficiently unique events to construct a structured timeline. While we agree with these commentators that animals have little use for the idea of unrepeated events, it is important to distinguish between an event being unique in the sense of it being unusual (such as moving to a different enclosure) and being unique in the sense of it being represented as happening at a non-recurring time point (an individual occurrence of a repeated event is unique in this sense). Even if an animal did experience a highly salient and rare event, it is difficult to see what use it would make of the fact that this event had occurred at a particular unique time point in its past. Given the nature of animals’ lives, this fact does not seem to have any practical significance at all.

R3.5. Temporal reasoning: What is it for?

If animals have no use for the idea that at a certain event took place at a particular time in the past, what makes it the case that this idea can have significance for humans? Mahr links this question to the normative dimension of human interaction, arguing that the benefits of temporal reasoning do not lie solely in its role in preparing for the future; rather, “in the psychological and social domains, representing particular past events has benefits in which the particularity and pastness of events matter for their own sake.” His suggestion is that grasping the normative dimensions of social interactions (such as one's current obligations) typically hinges on thinking about particular past interactions that explain why the relevant social norm applies. For example, one is entitled to be annoyed if someone fails to keep their promise made yesterday to meet at 5 p.m. today.

One way to think about whether Mahr is right about this claim is to consider whether the temporal updating system could in principle be sufficient for operating according to the relevant social norms. Mahr emphasizes the “particularity” of some instances of events, in the sense that they occur in a specific context. We note, though, that the contextual specificity of the implications of particular event occurrences is not what makes them beyond the scope of the more primitive updating system. Rather, Mahr's interesting claim is that appreciation of the pastness of events per se (which the updating system cannot provide) is necessary in order to fully engage with social norms. The case of promises is a good one to focus on, because of the kind of thinking about time that promising seems to involve. If one properly understands what one is doing in making a promise, one is not just committing oneself to delivering on it; rather, one also simultaneously accepts that at a future point in time, others will be entitled to point back to the current moment in time if the promise is not delivered. We therefore agree with Mahr that something like the temporal reasoning system, and not just the updating system, must be involved in properly operating with these sorts of social obligations.

However, such social obligations are not the only examples where appreciating the pastness of certain events matters: this is also true of certain types of complex emotions. For example, regret involves appreciating that there was a moment in time that has now passed at which future events could have unfolded differently but did not (Hoerl & McCormack Reference Hoerl, McCormack, Michaelian, Klein and Szpunar2016). This brings us to the issue raised by Beck & Rafetseder about the connection between temporal reasoning and counterfactual thought. We agree with their suggestion that developmental research on counterfactual cognition would benefit from a consideration of the “temporal aspects of the demands being made on the child.” In fact, we believe that there is an even tighter link between counterfactual and temporal cognition than their commentary explicitly considers. As we mention above, a key achievement associated with the emergence of the temporal reasoning system is the ability to think about locations in time separately from the events that occur in those locations (event-independent thought about time). Elsewhere, we have argued that engaging in counterfactual thought about events in the past (such as the type of counterfactual thought that underpins regret) involves exactly this sort of event-independent thought about time (McCormack Reference McCormack, Lerner, Liben and Mueller2015; McCormack & Hoerl Reference Hoerl2008; Reference McCormack and Hoerl2017). Put simply, the idea is that it involves representing past times as locations in time at which a variety of different events could have unfolded. More than that, when one is engaging in genuinely counterfactual thought about a specific past event, one grasps the fact that at an earlier point in time, the event that is now in the past was once in the future before it unfolded as it did. This is what is at the heart of the idea that things could have been different. But if this is the right description of counterfactual thought, then it resembles the sort of temporal perspective-taking that we describe in the paper as being a feature of the temporal reasoning system (i.e., that puts to work the fact that at a different point in time, things that are now in the past were once in the future).Footnote ³

R3.6. The origins of temporal reasoning

We have sketched a developmental picture of the emergence of the temporal reasoning system that is distinctive insofar as we have suggested that the temporal reasoning system does not simply operate with representations that are more explicit or enriched than those over which the updating system operates. In this sense, our account contrasts with some accounts of conceptual development in other domains. But if the reasoning system does not straightforwardly emerge from the updating system, what are its developmental origins? Influenced by Katherine Nelson's work, we suspect that the answer to this question will involve considering how children's emerging ability to represent events and event sequences enables them to engage in discourse with others about past and future events, which allows them to grasp the structure and nature of time itself. That is, we believe that the mature temporal concepts employed within the reasoning system are likely to have social origins. Moreover, it is within a broadly social context that the distinctive purposes for which people use the temporal reasoning system seem to be best illustrated, such as in generating and shaping autobiographical narratives, in evaluating past actions by considering alternative choices that one could have made, and in dealing with social norms and obligations. Research on the developmental origins of temporal concepts is sparse, meaning that these suggestions are speculative. We hope that our account at least provides some impetus for addressing what is currently a surprisingly large gap in the literature on cognitive development.

R4.1. Questions of demarcation: Systems and representational formats

Some commentators suggest ways of extending our account of the temporal updating system and the temporal reasoning system that draw on existing ideas about underlying brain processes. Nuyens & Griffiths, in their discussion about the relation between our account and effects of emotion, suggest that the timing mechanisms underpinning some of the workings of the temporal updating system map onto timing processes described in the scalar expectancy theory. Ueda & Hanakawa go further and make suggestions about the neural mechanisms underpinning the two systems, and moreover how these may be impaired in certain clinical populations. We do not wish to make any specific claims about the neural substrates of the two systems, although we acknowledge that some researchers may find this frustrating. Moreover, while we describe our account as a dual systems account, we have sought to make it clear that we understand this label quite broadly. For instance, we are happy to agree with Isham, Ziskin, & Peterson that our account could also be characterized as a dual process account.

Similarly, our account does not seek to distinguish temporal updating from temporal reasoning on the basis that one involves reasoning (and representations that can underpin the relevant reasoning) and the other doesn't. Indeed, we agree with Montemayor that the representations maintained by the temporal updating system could be used to draw inferences (though not necessarily in the particular way he envisages). One basic inference may be illustrated by an example given by De Brigard & O'Neill, who note that rodents can switch to taking a longer path in a maze upon learning that a shorter one that they used to take is closed. On our account, learning that the shorter path is closed causes the rat to update its model of the world so that that path is no longer represented as open, and the rat can then infer which of the remaining paths is now the shortest. We see this as an inference the rat can make on the basis of its present, now updated, representation of its environment alone. De Brigard & O'Neill, by contrast, speak of the animal as being “capable of drawing contrastive inferences between outdated and updated representations.” If this is to mean that the animal still has a representation, now outdated, of the previously shortest path being open, we see no reason for making such an assumption.

Crucially, our account draws a distinction between two cognitive systems for dealing with how things unfold over time based on the content of the representations maintained by those systems. Several commentators, by contrast, suggest variations of or alternatives to our account that involve specific claims about representational formats. Kelly, Prabhakar, & Khemlani (Kelly et al.) suggest that our distinction between temporal updating and temporal reasoning should be seen to map on to two different kinds of iconic representations, which they call “perceptual models” and “event models,” respectively. Similarly, Keven suggests that one should see the temporal updating system as operating with “snapshot-like” representations that he calls event memories, which are based on automatic perceptual processes.

As we are not committed to any specific claim about the representational format of the representations maintained by the temporal updating system, these other accounts may in principle be compatible with ours, but there are also potential pitfalls if questions of content and questions of format are not clearly distinguished from one another. For instance, as Kelly et al. themselves point out, mature thinking about time does not just consist in drawing inferences on the basis of recalled events. It also involves more mundane abilities such as the capacity to simply recount a past sequence of events. It may therefore involve mental states involving quite different representational formats – for example, episodic memories as well as mere beliefs about the time when events happened.

Keven makes a number of claims that we, too, would endorse. For example, he claims that the birds in Clayton and Dickinson's (Reference Clayton and Dickinson1998) study need not be able to remember “the actual experience of caching the food items,” but might instead “remember in the same way I can remember where my keys are without remembering the actual experience of where I put them” (our emphasis). In line with Keven's use of the present tense in drawing this analogy, we similarly believe that the behavior in Clayton and Dickinson's study can be explained by crediting the birds only with a representation that concerns their current environment, though of course one that originates in past experience.

Is there anything more than just a terminological difference between our view and Keven’s? The main reason he seems to prefer to frame his view in terms of the idea of “event memories” is that he thinks that information from past experience is retained in a quasi-perceptual format. As he rightly says, our view is not committed to any specific format in which information is retained by the temporal updating system. We regard this as a further, empirical, issue. But even supposing that the representations that make up the model maintained by the updating system are indeed quasi-perceptual, does it follow that the term “event memories” is an apt one? We believe that questions can be asked about both words in that term. With regard to the word “event,” consider Keven's description of those representations as “snapshots.” Suppose that when I put down my keys, I actually take a photo of them in the location where I put them down, which I then carry around to remind me of their whereabouts. If the only use I subsequently make of this snapshot is to remind me of where my keys are, it seems far from obvious why it should be counted as serving the role of representing an event, rather than simply a state of affairs.

Turning to the word “memory,” Keven exhorts us to “call a memory a memory,” and characterizes our description of the model of the world maintained in mere temporal updating as one made up of representations that are at least “memory-like.” We believe that this terminology, too, is unhelpful, as the term “memory” is first and foremost a name of a capacity, rather than singling out a particular type of representation. Indeed, on our view, when a creature uses the temporal updating system, there is nothing merely “memory-like” about the capacities that allow it to do so. It clearly uses its memory in so far as it acquires, encodes, and stores information. Thus, on that score, we are more than happy to call memory memory. The reasons for describing the creature as having a memory are much less obvious to us.

R4.2. The phenomenology of the present

An existing claim regarding dual systems is that they give rise to what Sloman (Reference Sloman1996) calls “simultaneous contradictory beliefs.” In section 4 of our target paper, we draw on this idea to connect our dual systems approach with a specific aspect of human adults’ everyday picture of time, viz. the fact that it accords a special status to the present moment in time, while also granting that every time has the property of being present when it is that time. Commentators raise a number of questions about this, including: (1) How exactly should this aspect of people's everyday picture of time be characterized (and does it indeed involve a contradiction)? (2) Even if it does involve a contradiction, is this good evidence for the existence of dual systems? (3) How are our claims related to questions about the phenomenology of people's experience of time, which is often held to underpin their everyday picture of time?

The contradiction in people's everyday picture of time, which we suggest might be explained by the existence of the two systems, arises from the idea that time flows or passes. But philosophers have given two somewhat different characterizations of this idea. As pointed out by Miller, Holcombe, & Latham (Miller et al.), as well as Prosser, there are ways of spelling out the idea that time flows that do not obviously involve a contradiction. According to presentism, only present things exist, and what is called the “flow of time” is simply those things changing. On this view, time itself is an abstraction, rather than a dimension of reality, and moments in time are considered logical constructions (Prior Reference Prior, Fraser, Haber and Müller1972; Reference Prior and Copeland1996; for discussion, see Hoerl Reference Hoerl2015). The presentist view of the flow of time does not obviously involve a contradiction. A contradiction only arises on what we might call a moments-based understanding of the flow of time. Contrary to presentism, this understanding operates with a view of time as a dimension made up of different moments of time. According to it, the flow of time is a change over time in which of these moments is present (or, alternatively, a change that consists in events occupying future, present, and past moments in time in succession).

Does humans’ everyday conception of the flow of time correspond more closely to the presentist understanding or to the moments-based understanding of the flow of time? In our target paper, we assumed the latter. In assuming this, we are sympathetic to Prosser’s suggestion that people's everyday picture of time is in fact an amalgam of presentism, on the one hand, and eternalism, on the other – where the latter is the view that reality is extended in time and that all times are equally real. As Prosser suggests, this might be because the temporal updating system embodies something like a presentist view of reality, whereas the temporal reasoning system embodies an eternalist metaphysics.

Even if this suggestion is along the right lines, it only explains one specific ingredient of people's everyday picture of time. It is focused specifically on the privileged status that our everyday picture of time accords the present moment in time, as one ingredient in the idea that time flows or passes. As implied by what we have just said, and as also pointed out by Callender, Kenward & Pilling, and Prosser, another aspect of the idea of time as flowing or passing is that of a constant change of a certain (perhaps hard to define) type – in Callender's words, the idea that “future events draw nearer and past events recede” (emphasis in original). We are not claiming to have given an account of the source of this further idea (for one suggested account, see Hoerl Reference Hoerl2014b). Yet, even if it is thus limited in its scope, our proposed explanation might help address an important question Miller et al. press in their commentary. As they point out, what really needs to be explained is the sense in which it still seems to people that the present has an objectively privileged status, even once they have come to the conclusion that it does not. This seeming, Miller et al. say, is different from belief – it is a matter of phenomenology. But how should we think of the type of phenomenology at issue here?

There are clearly aspects of perceptual phenomenology linked to time, such as the experience of motion (Hayman & Huebner) or sound (Kenward & Pilling). We will discuss these in more detail in the next section. For now, it is enough to note that the present moment in time seeming privileged is not a matter of perceptual phenomenology. It is not something that simply figures in perceptual experience alongside, say, motion or sound.

In drawing on Sloman (Reference Sloman1996) in our target paper, we aimed to show that there is another, distinct kind of phenomenology – one which dual systems can give rise to. While Sloman frames the point in terms of the idea that dual systems can generate “simultaneous contradictory beliefs,” we pointed out that he actually uses the term “belief” in this context in a non-standard way. As Melnikoff & Bargh say in their commentary, contradictory beliefs, as such, might also arise in a single system. What we take Sloman to be arguing, rather, is that the existence of dual systems can explain in particular how situations can arise in which a belief-like state can persist – it seeming as though something is true – even though, at the same time, the content of that belief-like state has been dismissed as untrue by the thinker. This is the result of the more basic system still continuing to deliver its verdict, even though this is not endorsed by the more sophisticated system. This would give us a way of understanding how its seeming that the present moment in time has a privileged status can be an aspect of people's phenomenology, even though it is clearly not a matter of perceptual phenomenology.

R4.3. Temporal updating and perceptual experience

Among the commentaries there are some that do focus specifically on perceptual phenomenology – a topic that we did not touch on in our target article. A common theme is that our account takes insufficient account of the dynamic character of perceptual experiences. For example, Kenward & Pilling mention the ability to perceive sounds and argue that this ability is evidence that perceptual experience “encompasses happening events rather than just a millisecond snapshot” (compare also Roselli). Similarly, Hayman & Huebner write: “If a moving object were experienced only as present, each momentary state would feature a static object, with nothing to bind these states together as an experience of ongoing motion.” And Elliott uses an example from a study with fighting fish conducted by Brecher (Reference Brecher1932) to argue that “events separated by time might, given short intervals between their presentations, be combined to form a meaningful … experiential content.”

How exactly do these claims bear on our account? On our account, the perception of dynamic phenomena plausibly causes a rapid updating of the model of the world maintained by the temporal updating system. For instance, as a creature watches another creature move, new information about the location of the other creature constantly overrides previous information about its location. This is something our account can clearly accommodate. But the commentators seem to think that our account nevertheless seems to leave out something important about the phenomenology of perceptual experience.

We take it that the authors in question think that we face a dilemma. Either we deny that perceptual experience can encompass more than what Kenward & Pilling call a “millisecond snapshot.” But that would be to deny the obvious phenomenological truth that we can perceive such things as sounds and movements. Or we allow that perceptual experience can encompass things that happen over an extended period of time. But then perceptual experience might be sufficient, even in animals, to ground representations of different things happening at different times. As Kenward & Pilling put it, we might be right in claiming that animals are incapable of mental time travel and therefore have no way of representing change over longer periods of time. Yet this does not rule out that they are able to do so within the section of the world they are perceptually conscious of. Thus, contrary to what we say, animals’ model of the world does contain a temporal dimension, it is just that “their representational timeline may be very short” (Kenward & Pilling).

We have no intention of trying to attack the first horn of this dilemma. Nothing we say is meant to imply any claim to the effect that perceptual experience only encompasses a “millisecond snapshot” (cf. Hoerl Reference Hoerl2009; Reference Hoerl2013b). However, things are different with the second horn of the dilemma. Does the fact that perceptual experience encompasses things that in fact happen over a period of time imply that it gives rise to representations of different things happening at different times? We are not convinced it does.

Take, for instance, Elliott’s example of Brecher's fighting fish. Brecher presented the fish with a tachistoscopic display in which an image of a conspecific repeatedly flashed up briefly in succession. He found that at a frequency of around 30 Hz the fish would attempt to attack the image, even though they would not do so at lower frequencies. Arguably, what this means is that only at 30 Hz or higher frequencies did the fish recognize a conspecific in the display, which in turn means that their visual system must be integrating information over a period of time in which what is in fact a succession of images are flashed up in succession. Yet this does not provide a good reason for thinking that the resulting representation is itself one of succession, or some other form of representation in which times or temporal relations figure. Rather, the relevant representation formed is just that of another fish being present.

We can extract from this a general moral that can also be extended to other examples mentioned in the commentaries. Even if it is necessary for an organism to sample information over time to detect a certain feature of its environment, this does not imply that the resulting representation of that feature is one in which temporal properties or relations figure (for a somewhat related argument, see also Prosser Reference Prosser2016, Ch. 6). This might even be applied to Kenward & Pilling’s example of the experience of sound, for instance, which they describe as “inherently a temporal phenomenon.” It is true that sounds themselves are temporal phenomena in that they have an onset, an offset, and a duration. But it is ultimately not clear that this marks any deep difference between the way sounds are related to time and the way, for example, colors are. (On this issue, see also Cohen Reference Cohen2010.) Thus, like the latter, they might simply be represented as qualities instantiated at a time.

The same moral also carries over to other considerations not involving perceptual phenomenology. For instance, Pan & Carruthers argue that foraging animals must have a representation of time because they can compare the rate of reward at the current location with the average rate experienced at other locations and take this into account in calculating whether they should stay where they are or make the effort to move elsewhere. Clearly, as Pan & Carruthers say, “a rate is a measure of quantity per unit of time.” But does that mean that sensitivity to a rate requires an ability to entertain representations in which other times figure?

To adapt an analogy used by Prosser (Reference Prosser2016), think of the dial on a car's speedometer. This acts as a representation of a rate, a rate related to the locations the car occupies at different times, but it does not act as a representation of a succession of events happening at different times. Arguably, people also use it in ways that don't need to involve any reasoning about other times, such as when they simply look at the speedometer, notice that they are breaking the speed limit, and take their foot off the gas. In a similar way, we want to suggest that animals may be sensitive to the rate of reward at different locations, but in a way that does not involve any reasoning about different moments in time.

R4.4. Representing space and representing time

In the preceding section, we mentioned Kenward & Pilling’s suggestion that animals’ model of the world does contain a temporal dimension, but that “their representational timeline may be very short.” The general idea here is that there might be ways of representing time that escape our dichotomy between temporal updating and temporal reasoning. A similar idea can be seen to be at work in some of the commentaries that raise issues regarding the relation between temporal and spatial representation.

On our account, space and time are given very disparate treatment by the temporal updating system, which can represent spatial relationships, but ignores altogether that reality also has a temporal dimension. Callender questions this, and speaks of “how tightly linked [time and space] are in physics, biology, and psychology.” There are clearly a number of ways in which temporal and spatial processing are conceptualized similarly in biology and psychology. Callender mentions the idea that there are “time cells” as well as “place cells” in the brain. Similarly, De Corte & Wasserman draw attention to work that has been trying to establish the existence of “temporal maps” in animals. And Gentry & Buckner ask why mechanisms for spatial representation that have been demonstrated in animals “could not be bootstrapped to represent an additional temporal dimension as well.” To what extent might findings in these areas challenge our view? We will focus in particular on the research on temporal maps.

In a typical backward conditioning study of temporal maps, the animal completes two training phases. In the first, it is repeatedly presented with two different cues (Cue A and Cue B), separated by a time interval. In the second, the animal is presented with a reward, followed soon after by the second cue from the first training phase (Cue B), where the interval between the reward and Cue B is shorter than the interval between Cue A and Cue B in the first training phase. What the research seems to show is that animals integrate the associations between Cue A and Cue B and between the reward and Cue B, including the intervals between them, so that when given Cue A they now expect the reward, despite never having experienced Cue A followed by the reward.

De Corte & Wasserman, who mention this research in their commentary, seem to primarily want to question our characterization of the signature limit that we claim the temporal updating system is subject to. In describing the behavioral implications of a creature operating only with a temporal updating system, we identify as one signature limit of such a system that it cannot deal with situations in which information about changes is received in an order that differs from the one in which these changes happened, and we provide some empirical evidence that children do indeed have problems in situations of this type. We also suggest, though, that even a creature capable only of temporal updating might nevertheless be able to engage in a form of sequential learning, by coming to acquire a routine for updating its model of the world in a particular order.

The type of sequential learning described by De Corte & Wasserman is indeed more complex than anything we describe in the target paper. But does it contradict our characterization of the signature processing limit that the temporal updating system is subject to? Note that, while the animal at first learns about two sequences in isolation from each other, it is still the case that it learns about each of those sequences in the order in which that sequence happens. This is different from the kind of case we had in mind when describing the limitations the temporal updating is subject to. These have to do specifically with the fact that the overall outcome of a sequence of changes can sometimes depend on the order in which those changes happen. Now consider a case in which the animal does not directly witness each of the relevant changes in turn, but receives information about their occurrence in an order that does not correspond to the order in which they actually occurred. The only way it can arrive at a correct representation of the overall outcome is if it can reason about temporal order to infer that overall outcome.

As we read them, De Corte & Wasserman do not necessarily want to deny that the abilities that have led researchers to credit animals with “temporal maps” can be explained without ascribing to them a capacity for temporal reasoning in our sense. The paradigms used in this research are Pavlovian ones, and they are typically interpreted in associationist terms – the idea being that, when an association between two events is being formed, the temporal relationship between them is also encoded as part of the association between them. This can explain why the animal forms certain expectations at certain times.

However, the use of the term “temporal map” might nevertheless prompt a more general query for our approach. We are making two crucial claims about animals: The first is that they cannot engage in temporal reasoning as we describe it, including mental time travel. The second is that the representations they can entertain are ones from which the dimension of time is simply absent. As can be seen in several places in this response, across a number of different commentaries commentators seem prepared to agree with a version of the first claim, but disagree with the second one (see, e.g., Hohenberger; Osvath & Kabadayi; Pan & Carruthers; Roselli). Moreover, the idea that there might be ways of representing things in time that escape our dichotomy of temporal reasoning vs. temporal updating is also a theme in some comments not concerned with animal cognition (see, e.g., Elliott; Hayman & Huebner; Kenward & Pilling; Viera & Margolis). We want to end with some remarks on this general issue, addressing in particular the question as to whether it is correct to think of animals’ temporal maps as closely analogous to the spatial maps commonly ascribed to them in the literature on animal navigation.

A picture of animal cognition on which animals have basic capacities for temporal representation that closely parallel their capacities for spatial representation has been developed by John Campbell (Reference Campbell1994; Reference Campbell, Stöltzner and Stadler2006). On Campbell's account, animals operate with both spatial and temporal frameworks for orienting themselves in their environment, but ones that are crucially different from the kinds of representations of space and time that adult humans can frame. This is because the animal gives causal significance to those frameworks only through its own practical engagement with its environment. In the case of the spatial frameworks used by animals, this implies that, while the animal may be able to represent the direct route from its current location to any other place represented on its cognitive map, “it cannot represent the spatial relations between any two arbitrary places in its environment” (Campbell Reference Campbell, Eilan, McCarthy and Brewer1993, p. 87), irrespective of whether it is located at them. The animal's orientation in time is also limited, according to Campbell, in that it is only an orientation with respect to phase, rather than with respect to particular times. Thus, while an animal with a circadian timer might be said to be able to represent an event as happening at noon, on Campbell's account, “it has no use for the distinction between noon on one day and noon on another” (Campbell Reference Campbell, Pastor and Artieda1996, p. 118). On Campbell's picture, animals do have temporal frameworks, but these are more primitive and do not allow for times to be represented as unique unrepeating locations on a timeline.

We are happy to go along with Campbell's characterization of the spatial representational abilities of animals. Given this, and given that it is possible to construct a structurally parallel model of their temporal representational abilities, which constitutes something like a halfway house between what we describe as temporal updating and temporal reasoning, respectively, what reasons could there be for being skeptical that such a halfway house exists? We note that in the literature mentioned by Gentry & Buckner on ways in which humans recruit spatial representations to think about time, a common claim is that the reverse does not hold – where this is often combined with the claim that time is “abstract” in a way that space is not (Boroditsky Reference Boroditsky2000; Casasanto & Boroditsky Reference Casasanto and Boroditsky2008). We think this might point to an important distinction in how talk about temporal maps and spatial maps in animals should be understood.

In the case of spatial maps, there is good reason to think that possession of such a map by an animal involves the ability to represent places in its environment, because the animal uses the map for navigation, that is for actively moving from one place to another. This provides for a concrete sense in which the animal can give significance to the fact that there are places other than the one at which it is located. Yet there is no analogue to this in the case of time. Even if we ascribe to the animal a temporal map such as the ones posited in the literature on backward conditioning, there is nothing the animal can or needs to do to exploit the information encoded in the map other than form the right representations (i.e., first of Cue A, then of the reward, and then of Cue B) at the appropriate moments. But if all an animal can do is generate the right representations at the right moments, then it is not clear that it is useful to describe it as possessing a map of time in the way the term “map” is usually understood, that is, as something that gives the topography of a domain. As we have argued, it could generate the appropriate representation at any given moment without representing other moments in time at all. Thinking of the issue in this way gives the term “mental time travel” its proper import: What is significant about the term is the idea of mentally navigating the temporal domain, that is, making use of a mental map of the structure of relations between points in time. What we are seeking to do is reframe the debate over whether animals can engage in mental time travel as a debate about whether they possess maps of time in this sense.