One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To do this, (...) I summarize Clark’s notion of a difference maker in explaining complex causation that criss-crosses between mind and world and apply it to Menary’s Open MIND. MIND Group, Frankfurt, 2015a) discussion of mathematical cognition as a case of enculturation. I argue that while Menary’s views on enculturation can help explain what makes the difference between numerate and anumerate cultures, it cannot help specify what makes the difference between numerate and anumerate individuals. I argue that features of enculturation do not provide an account of innovation capable of explaining how individuals manage to improve and modify the practices of their cultural niche. This is because Menary’s construal of the role of enculturation in the development of mathematical cognition focuses mostly on the inheritance and transmission of practices, not on their origins, which involve individual-level understanding, rather than population-level practices and pressures. The upshot is that culture provides the necessary background conditions against which individuals can innovate. This role is crucial in the development of numerical abilities—crucial, but explanatorily limited. (shrink)

We examine the question of which aspects of language are uniquely human and uniquely linguistic in light of recent suggestions by Hauser, Chomsky, and Fitch that the only such aspect is syntactic recursion, the rest of language being either specific to humans but not to language (e.g. words and concepts) or not specific to humans (e.g. speech perception). We find the hypothesis problematic. It ignores the many aspects of grammar that are not recursive, such as phonology, morphology, case, agreement, and (...) many properties of words. It is inconsistent with the anatomy and neural control of the human vocal tract. And it is weakened by experiments suggesting that speech perception cannot be reduced to primate audition, that word learning cannot be reduced to fact learning, and that at least one gene involved in speech and language was evolutionarily selected in the human lineage but is not specific to recursion. The recursion-only claim, we suggest, is motivated by Chomsky’s recent approach to syntax, the Minimalist Program, which de-emphasizes the same aspects of language. The approach, however, is sufficiently problematic that it cannot be used to support claims about evolution. We contest related arguments that language is not an adaptation, namely that it is “perfect,” non-redundant, unusable in any partial form, and badly designed for.. (shrink)

That words express a conceptual content is uncontroversial. This does not entail that their content should break down neatly into a grammatical part, relevant for language and to be analyzed in linguistic terms, and a conceptual part, relevant for cognition and to be analyzed in psychological terms. Various types of empirical evidence are reviewed, showing that the conceptual content of words cannot be isolated from their linguistic properties, because it is affected and shaped by them. The view of words as (...) labels or containers for a non-linguistic conceptual content stems from a naive disregard of the complex and structured nature of lexical knowledge. On the contrary, knowledge of language is shown not just to organize and categorize conceptual content in a way not reducible to non-linguistic cognition, but also to affect its scope, as the range of verbalized concepts is both limited by abstract templates and expanded by productive word formation. This suggests that lexical knowledge is a distinctively linguistic dimension of conceptualization, and that words do not so much label or package concepts, as provide an inner form for conceptual knowledge. (shrink)

Frege proved an important result, concerning the relation of arithmetic to second-order logic, that bears on several issues in linguistics. Frege’s Theorem illustrates the logic of relations like PRECEDES(x, y) and TALLER(x, y), while raising doubts about the idea that we understand sentences like ‘Carl is taller than Al’ in terms of abstracta like heights and numbers. Abstract paraphrase can be useful—as when we say that Carl’s height exceeds Al’s—without reflecting semantic structure. Related points apply to causal relations, and even (...) grammatical relations like DOMINATES(x, y). Perhaps surprisingly, Frege provides the resources needed to recursively characterize labelled expressions without characterizing them as sets. His theorem may also bear on questions about the meaning and acquisition of number words. (shrink)