Based on the notion that time, space, and number are part of a generalized magnitude system, we assume that the dual-systems approach to temporal cognition also applies to numerical cognition. Referring to theoretical models of the development of numerical concepts, we propose that children's early skills in processing numbers can be described analogously to temporal updating and temporal reasoning.

Hoerl & McCormack discuss the benefits of temporal reasoning mainly with respect to future planning and decision making. I point out that, for humans, the ability to represent particular past times has distinct benefits, which are independent from contributing to future-directed cognition. Hence, the evolution of the temporal reasoning system was not necessarily driven primarily by its benefits for future-directed cognition.

Evidence from our research on young children's temporal understanding supports Hoerl & McCormack's view that young children rely on a temporal updating system to change representations over time. We propose that the shift from temporal updating to temporal reasoning is enabled by children's expanding representations of event sequences, along with developments in language, memory, and other cognitive competencies.

Contrary to Hoerl & McCormack (H&M), we argue that the best account of temporal cognition in humans is one in which a single system becomes capable of representing time. We suggest that H&M's own evidence for dual systems of temporal cognition – simultaneous contradictory beliefs – does not recommend dual systems, and that the single system approach is more plausible.

Hoerl & McCormack (H&M) posit two systems – the temporal updating system and the temporal reasoning system – and suggest that they explain an inherent contradiction in people's naïve theory of time. We suggest there is no contradiction. Something does, however, require explanation: the tension between certain sophisticated beliefs about time, and certain phenomenological states or beliefs about those phenomenological states. The temporal updating mechanism posited by H&M may contribute to this tension.

A central claim by Hoerl & McCormack is that the temporal reasoning system is uniquely human. But why exactly? This commentary evaluates two possible options to justify the thesis that temporal reasoning is uniquely human, one based on considerations regarding agency and the other based on language. The commentary raises problems for both of these options.

This commentary explores how emotion fits in the dual-systems model of temporal cognition proposed by Hoerl & McCormack. The updating system would be affected by emotion via the attentional/arousal effect according to the attentional gate model. The reasoning system would be disrupted by emotion, especially for traumatic events. Time discrepancies described in the dual-systems model are also explained.

We argue that the two temporal cognition systems are conceptually too confined to be helpful in understanding the evolution of temporal cognition. In fact, we doubt there are two systems. In relation to this, we question that the authors did not describe the results of our planning study on ravens correctly, as this is of consequence to their theory.

People can imagine their future selves without taking future-focused action. Identity-based motivation theory explains why. Hoerl & McCormack outline how. Present-focused action prevails because future “me” feels irrelevant to the choices facing current “me” unless future “me” is experienced as occurring now or as linked to current “me” via if-then simulations. This entails reasoning in time and about time.

Hoerl & McCormack claim that animals don't represent time. Because this makes a mystery of established findings in comparative psychology, there had better be some important payoff. The main one they mention is that it explains a clash of intuition about the reality of time's passage. But any theory that recognizes the representational requirements of agency can do likewise.

Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

I offer some clarification concerning the kind of contradiction that Hoerl & McCormack's account could help explain and the scope of the metaphysical intuitions that could be explained by such a theory. I conclude that we need to know more about the sense in which the temporal reasoning system would represent time as a dimension.

Hoerl & McCormack (H&M) discuss the possible function of meta-representations in temporal cognition but ultimately take an agnostic stance. Here we outline the fundamental role that we believe meta-representations play. Because humans know that their representations of future events are just representations, they are in a position to compensate for the shortcomings of their own foresight and to prepare for multiple contingencies.

The model presented by the authors can explain an inherent contradiction in people's naïve theory of time. In this commentary I suggest a way in which another paradox of our phenomenal temporality may be addressed along these lines. In the final section, I also discuss some concerns that may arise about the clear-cut distinction between humans and non-human animals.

Here I consider the possible role of the temporal updating system in the development of the temporal reasoning system. Using evidence from children's acquisition of time words, I argue that abstract temporal concepts are not built from primitive representations of time. Instead, I propose that language and cultural learning provide the primary sources of the temporal reasoning system.

Here we argue how Hoerl & McCormack's dual system proposal may change the current view about the neural correlates underlying temporal information processing. We also consider that the concept of the dual system may help characterize various timing disabilities in neuropsychiatric disorders from the new perspective.

We argue that animals are not cognitively stuck in time. Evidence pertaining to multisensory temporal order perception strongly suggests that animals can represent at least some temporal relations of perceived events.

We focus on three main sets of topics emerging from the commentaries on our target article. First, we discuss several types of animal behavior that commentators cite as evidence against our claim that animals are restricted to temporal updating and cannot engage in temporal reasoning. In doing so, we illustrate further how explanations of behavior in terms of temporal updating work. Second, we respond to commentators’ queries about the developmental process through which children acquire a capacity for temporal reasoning and about the relation between our account and accounts drawing similar distinctions in other domains of cognition. Finally, we address some broader theoretical issues arising from the commentaries, concerning in particular the question as to how our account relates to the phenomenology of experience in time, and the question as to whether our dichotomy between temporal reasoning and temporal updating is exhaustive, or whether there might be other forms of cognition or representation related to time not captured by it.