While Spelke provides powerful support for concept nativism, her focus on understanding concept nativism through six innate core knowledge systems is too confining. There is also no reason to suppose that the curse of a compositional mind constitutes a principled reason for positing less innate structure in explaining the origins of concepts. Any solution to such problems must take into account poverty of the stimulus considerations, which argue for postulating more innate structure, not less.

I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific structure and consequently that there is no domain-general alternative to an innate domain-specific small number system.

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.

Where do human numerical abilities come from? Leibovich et al. argue against nativist views of numerical development noting limitations in newborns' vision and limitations regarding newborns' ability to individuate objects. I argue that these considerations do not undermine competing nativist views and that Leibovich et al.'s model itself presupposes that infant learners have numerical representations.

Smaldino's proposed extension of the theory of cultural evolution embraces emergent group-level traits. We argue, instead, that group-level traits reduce to the traits of individuals, particularly when it comes to the question of how group-level traits are inherited or transmitted, and that this metaphysical fact is integral to the theory of cultural evolution.

Carey rightly rejects the building blocks model of concept acquisition on the grounds that new primitive concepts can be learned via the process of bootstrapping. But new primitives can be learned by other acquisition processes that do not involve bootstrapping, and bootstrapping itself is not a unitary process. Nonetheless, the processes associated with bootstrapping provide important insights into conceptual change.

Concepts are mental symbols that have semantic structure and processing structure. This approach (1) allows for different disciplines to converge on a common subject matter; (2) it promotes theoretical unification; and (3) it accommodates the varied processes that preoccupy Machery. It also avoids problems that go with his eliminativism, including the explanation of how fundamentally different types of concepts can be co-referential.