Developing earlier studies of the system of numbers in Mundurucu, this paper argues that the Mundurucu numeral system is far more complex than usually assumed. The Mundurucu numeral system provides indirect but insightful arguments for a modular approach to numbers and numerals. It is argued that distinct components must be distinguished, such as a system of representation of numbers in the format of internal magnitudes, a system of representation for individuals and sets, and one-to-one correspondences between the numerosity expressed by (...) the number and its metrics. It is shown that while many-number systems involve a compositionality of units, sets and sets composed of units, few-number languages, such as Mundurucu, do not have access to sets composed of units in the usual way. The nonconfigurational character of the Mundurucu language, which is related to a property for which we coin the term 'low compositionality power', accounts for this and explains the curious fact that Mundurucus make use of marked one-to-one correspondence strategies in order to overcome the limitations of the core system at the perceptual/motor interface of the language faculty. We develop an analysis of a particular construction, parallel numbers, which has not been studied before, elucidating the whole system. This analysis, we argue, sheds new light on classical philosophical, psychological and linguistic debates about numbers and numerals and their relation to language, and more particularly, sheds light on few-number languages. (shrink)

Thomas Reid, the Scottish natural and moral philosopher, was one of the founding members of the Aberdeen Philosophical Society and a significant figure in the Scottish Enlightenment. Reid believed that common sense should form the foundation of all philosophical inquiry. He criticised the sceptical philosophy propagated by his fellow Scot David Hume and the Anglo-Irish bishop George Berkeley, who asserted that the external world did not exist outside the human mind. Reid was also critical of the theory of ideas propagated (...) by Locke and Descartes, arguing that it was incompatible with physical and experiential facts. For Reid, our senses demonstrate that the external world must exist, and this work is organised in chapters examining each of the senses in turn. The book, based on his lectures, was first published in 1764 when Reid was a regent professor at King's College, Aberdeen, and was reissued in 1818. (shrink)

Pedagogy is a pillar of human culture and society. Telling each other information and showing each other how to do things comes naturally to us. A strong case has been made that declarative knowledge is the norm of assertion, which is our primary way of telling others information. This article presents an analogous case for the hypothesis that procedural knowledge is the norm of instructional demonstration, which is a primary way of showing others how to do things. Knowledge is the (...) norm of telling and showing. It is the prime pedagogical principle. (shrink)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...) or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...) from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas. (shrink)

Only human beings have a rich conceptual repertoire with concepts like tort, entropy, Abelian group, mannerism, icon and deconstruction. How have humans constructed these concepts? And once they have been constructed by adults, how do children acquire them? While primarily focusing on the second question, in The Origin of Concepts , Susan Carey shows that the answers to both overlap substantially. Carey begins by characterizing the innate starting point for conceptual development, namely systems of core cognition. Representations of core cognition (...) are the output of dedicated input analyzers, as with perceptual representations, but these core representations differ from perceptual representations in having more abstract contents and richer functional roles. Carey argues that the key to understanding cognitive development lies in recognizing conceptual discontinuities in which new representational systems emerge that have more expressive power than core cognition and are also incommensurate with core cognition and other earlier representational systems. Finally, Carey fleshes out Quinian bootstrapping, a learning mechanism that has been repeatedly sketched in the literature on the history and philosophy of science. She demonstrates that Quinian bootstrapping is a major mechanism in the construction of new representational resources over the course of childrens cognitive development. Carey shows how developmental cognitive science resolves aspects of long-standing philosophical debates about the existence, nature, content, and format of innate knowledge. She also shows that understanding the processes of conceptual development in children illuminates the historical process by which concepts are constructed, and transforms the way we think about philosophical problems about the nature of concepts and the relations between language and thought. (shrink)

We propose that the crucial difference between human cognition and that of other species is the ability to participate with others in collaborative activities with shared goals and intentions: shared intentionality. Participation in such activities requires not only especially powerful forms of intention reading and cultural learning, but also a unique motivation to share psychological states with others and unique forms of cognitive representation for doing so. The result of participating in these activities is species-unique forms of cultural cognition and (...) evolution, enabling everything from the creation and use of linguistic symbols to the construction of social norms and individual beliefs to the establishment of social institutions. In support of this proposal we argue and present evidence that great apes understand the basics of intentional action, but they still do not participate in activities involving joint intentions and attention. Human children's skills of shared intentionality develop gradually during the first 14 months of life as two ontogenetic pathways intertwine: the general ape line of understanding others as animate, goal-directed, and intentional agents; and a species-unique motivation to share emotions, experience, and activities with other persons. The developmental outcome is children's ability to construct dialogic cognitive representations, which enable them to participate in earnest in the collectivity that is human cognition. Key Words: collaboration; cooperation; cultural learning; culture; evolutionary psychology; intentions; shared intentionality; social cognition; social learning; theory of mind; joint attention. (shrink)

Thomas Reid , the Scottish natural and moral philosopher, was one of the founding members of the Aberdeen Philosophical Society and a significant figure in the Scottish Enlightenment. Reid believed that common sense should form the foundation of all philosophical inquiry. He criticised the sceptical philosophy propagated by his fellow Scot David Hume and the Anglo-Irish bishop George Berkeley, who asserted that the external world did not exist outside the human mind. Reid was also critical of the theory of ideas (...) propagated by Locke and Descartes, arguing that it was incompatible with physical and experiential facts. For Reid, our senses demonstrate that the external world must exist, and this work is organised in chapters examining each of the senses in turn. The book, based on his lectures, was first published in 1764 when Reid was a regent professor at King's College, Aberdeen, and was reissued in 1818. (shrink)

Intellectualism about knowledge-how is the view that practical knowledge is a species of propositional knowledge. I argue that this view is undermined by a difference in properties between knowledge-how and both knowledge-that and knowledge-wh. More specifically, I argue that both knowledge-that and knowledge-wh are easily transmitted via testimony while knowledge-how is not easily transmitted by testimony. This points to a crucial difference in states of knowledge. I also consider Jason Stanley's attempt to subsume knowledge-how under an account of de se (...) knowledge. I argue that there are crucial differences between de se knowledge and knowledge-how. Thus, this paper advances both the discussion of intellectualism and the literature on the nature of de se knowledge. (shrink)