Phillips et al. make a strong case that knowledge representations should play a larger role in cognitive science. Their arguments are reinforced by comparable efforts to place moral knowledge, rather than moral beliefs, at the heart of a naturalistic moral psychology. Conscience, Kant's synthetic a priori, and knowledge attributions in the law all point in a similar direction.

I add support to Phillips et al.'s thesis that representations of knowledge are more basic than representations of belief through a historical account of the development of philosophical theories of knowledge and belief. On the basis of Aristotle's criticisms of his Presocratic predecessors, I argue that Western philosophy developed theories of knowledge long before it developed theories of belief.

Because knowledge entails true belief, it can be hard to explain why a given action is naturally seen as driven by one of these states as opposed to the other. A simpler and more radical characterization of knowledge helps to solve this problem while also shedding some light on what is special about social learning.

Phillips et al. argue that our capacity for representing knowledge is more basic than our capacity for representing belief. But they remain neutral on the further claim that our “belief capacity” depends on our “knowledge capacity.” I consider how this further claim might help to explain some of the generalizations the authors catalog, and explore one way of understanding it.

Phillips et al. argue that understanding what others know is central to social cognition across species and that this understanding underlies human-unique accumulation and transmission of cultural knowledge. Knowledge representations can't be both what we have in common with our evolutionary ancestors and what sets us apart from them. Belief representations are necessary for human-unique social learning.

Knowledge and belief attribution are discussed in the context of episodic and semantic memory theory and research, with reference to patient-lesion and developmental studies under naturalistic conditions. Consideration of how episodic and semantic memory relate to each other and intersect in the real world, including how they fail, can illuminate the approach to studying how people represent others' minds.

The ability to reason about ignorance is an important and often overlooked representational capacity. Phillips and colleagues assume that knowledge representations are inevitably accompanied by ignorance representations. We argue that this is not necessarily the case, as agents who can reason about knowledge often fail on ignorance tasks, suggesting that ignorance should be studied as a separate representational capacity.

I accept the main thesis of the article according to which representation of knowledge is more basic than representation of belief. But I question the authors’ contention that humans' unique capacity to represent belief does not underwrite the capacity for the accumulation of cultural knowledge.

Comparing knowledge with belief can go wrong in two dimensions: If the authors employ a wider notion of knowledge, then they do not compare like with like because they assume a narrow notion of belief. If they employ only a narrow notion of knowledge, then their claim is not supported by the evidence. Finally, we sketch a superior teleological view.

Phillips et al. present a number of arguments for the premise that knowledge is more basic than belief. Although their arguments are coherent and sound, they do not directly address numerous cases in which belief appears to be a developmental precursor to knowledge. I describe several examples, not necessarily as a direct challenge, but rather to better understand their framework.

The central claim in the target article is that representations of knowledge are more basic than representations of beliefs. However, the authors are blending together two distinct concepts of knowledge: “awareness” and “propositional knowledge.” Distinguishing these two concepts of knowledge clarifies how the developmental and comparative data fit within the philosophical literature.

Phillips et al. conclude that current evidence supports knowledge-, but not belief-reasoning as being automatic. We suggest four reasons why this is an oversimplified answer to a question that might not have a clear-cut answer: (1) knowledge and beliefs can be incompletely equated to perceptual states, (2) sensitivity to mental states does not necessitate representation, (3) automaticity is not a single categorical feature, and (4) how we represent others' minds is dependent on social context.

More basic than the authors' distinction between knowing and believing is a distinction between knowledge-by-acquaintance (I know John Smith) and propositional knowledge/belief (I know/believe that John Smith lives in Durham). This distinction provides a better account of both the comparative and developmental data.

Phillips et al. make a compelling case for a reversal in the current paradigm in “other minds” research by considering the representation of other people's knowledge more basic than the attribution of belief. Unfortunately, they only discuss primates. In this commentary, I argue that the representation of others' knowledge is an evolutionary ancient trait, first appearing during the Cambrian explosion.

Phillips and colleagues convincingly argue that knowledge attribution is a faster, more automatic form of mindreading than belief attribution. However, they do not explain what it is about knowledge attribution that lends it this cognitive advantage. I suggest an explanation of the knowledge-attribution advantage that would also help to distinguish it from belief-based and minimalist alternatives.

Whereas Phillips and colleagues argue that knowledge representations are more basic than belief representations, we argue that an accurate analysis of what is fundamental to theory of mind may depend crucially on the context in which mental-state reasoning occurs. Specifically, we call for increased study of the developmental trajectory of mental-state reasoning within socially evaluative contexts.

This response argues that when you represent others as knowing something, you represent their mind as being related to the actual world. This feature of knowledge explains the limits of knowledge attribution, how knowledge differs from belief, and why knowledge underwrites learning from others. We hope this vision for how knowledge works spurs a new era in theory of mind research.

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g., 7), but also non-natural rational numbers (e.g., 3.5). It does not represent irrational numbers (e.g., √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.

To support the claim that the approximate number system (ANS) represents rational numbers, Clarke and Beck (C&B) argue that number perception is abstract and characterized by a second-order character. However, converging evidence from visual illusions and psychophysics suggests that perceived number is not abstract, but rather, is perceptually interdependent with other magnitudes. Moreover, number, as a concept, is second-order, but number, as a percept, is not.

Clarke and Beck propose that the approximate number system (ANS) represents rational numbers. The evidence cited supports only the view that it represents ratios (and positive integers). Rational numbers are extensive magnitudes (i.e., sizes), whereas ratios are intensities. It is also argued that WHAT a system represents and HOW it does so are not as independent of one another as the authors assume.