The thesis of discontinuity between humans and nonhumans requires evidence from formal reasoning tasks that rules out solutions based on associative strategies. However, insightful problem solving can be often credited through talking to humans, but not to nonhumans. We note the paradox of assuming that reasoning is orthogonal to language and enculturation while employing the criterion of using language to compare what humans and nonhumans know.

We examine Carruthers’ proposal that sentences in logical form serve to create flexibility within central system modularity, enabling the combination of information from different modalities. We discuss evidence from aphasia and the neurobiology of input-output systems. This work suggests that there exists considerable capacity for interdomain cognitive processing without language mediation. Other challenges for a logical form account are noted.

High-order constructs such as intelligence result from the interaction of numerous processing systems, one of which is language. However, in determining the role of language in intelligence, attention must be paid to evidence from lesion studies and, in particular, evidence of dissociation of functions where high-order cognition can be demonstrated in face of profound aphasia.

Bloom's book underscores the importance of specifying the role of words and grammar in cognition. We propose that the cognitive power of language lies in the lexicon rather than grammar. We suggest ways in which studies involving children and patients with aphasia can provide insights into the basis of abstract cognition in the domain of number and mathematics.