Hutchins examines a set of phenomena that have fallen between the established disciplines of psychology and anthropology, bringing to light a new set of relationships between culture and cognition.

In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

Behavioral scientists routinely publish broad claims about human psychology and behavior in the world's top journals based on samples drawn entirely from Western, Educated, Industrialized, Rich, and Democratic (WEIRD) societies. Researchers – often implicitly – assume that either there is little variation across human populations, or that these “standard subjects” are as representative of the species as any other population. Are these assumptions justified? Here, our review of the comparative database from across the behavioral sciences suggests both that there is (...) substantial variability in experimental results across populations and that WEIRD subjects are particularly unusual compared with the rest of the species – frequent outliers. The domains reviewed include visual perception, fairness, cooperation, spatial reasoning, categorization and inferential induction, moral reasoning, reasoning styles, self-concepts and related motivations, and the heritability of IQ. The findings suggest that members of WEIRD societies, including young children, are among the least representative populations one could find for generalizing about humans. Many of these findings involve domains that are associated with fundamental aspects of psychology, motivation, and behavior – hence, there are no obviousa priorigrounds for claiming that a particular behavioral phenomenon is universal based on sampling from a single subpopulation. Overall, these empirical patterns suggests that we need to be less cavalier in addressing questions ofhumannature on the basis of data drawn from this particularly thin, and rather unusual, slice of humanity. We close by proposing ways to structurally re-organize the behavioral sciences to best tackle these challenges. (shrink)

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

It is widely supposed that every entity falls into one of twocategories: Some are concrete; the rest abstract. The distinction issupposed to be of fundamental significance for metaphysics andepistemology. This article surveys a number of recent attempts to sayhow it should be drawn.

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.

Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.

Previous discussions of the origins of writing in the Ancient Near East have not incorporated the neuroscience of literacy, which suggests that when southern Mesopotamians wrote marks on clay in the late-fourth millennium, they inadvertently reorganized their neural activity, a factor in manipulating the writing system to reflect language, yielding literacy through a combination of neurofunctional change and increased script fidelity to language. Such a development appears to take place only with a sufficient demand for writing and reading, such as (...) that posed by a state-level bureaucracy; the use of a material with suitable characteristics; and the production of marks that are conventionalized, handwritten, simple, and non-numerical. From the perspective of Material Engagement Theory, writing and reading represent the interactivity of bodies, materiality, and brains: movements of hands, arms, and eyes; clay and the implements used to mark it and form characters; and vision, motor planning, object recognition, and language. Literacy is a cognitive change that emerges from and depends upon the nexus of interactivity of the components. (shrink)

Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such (...) as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work. (shrink)

A translation of Plato's dialogue on the nature of pleasure and its relation to thought and knowledge. It includes a cogent introduction, notes, and comprehensive bibliography.

Drawing on the material culture of the Ancient Near East as interpreted through Material Engagement Theory, the journey of how material number becomes a conceptual number is traced to address questions of how a particular material form might generate a concept and how concepts might ultimately encompass multiple material forms so that they include but are irreducible to all of them together. Material forms incorporated into the cognitive system affect the content and structure of concepts through their agency and affordances, (...) the capabilities and constraints they provide as the material component of the extended, enactive mind. Material forms give concepts the tangibility that enables them to be literally grasped and manipulated. As they are distributed over multiple material forms, concepts effectively become independent of any of them, yielding the abstract irreducibility that makes a concept like number what it is. Finally, social aspects of material use—collaboration, ordinariness, and time—have important effects on the generation and distribution of concepts. (shrink)

This text features nearly 200 entries which introduce basic mathematical tools and vocabulary, trace the development of modern mathematics, define essential ...

My contribution will focus on a central issue of Yehuda Elkana's anthropology of knowledge — namely, the role of reflectivity in the development of knowledge. Let me therefore start with a quotation from Yehuda's paper “Experiment as a Second-Order Concept.”.

Mathematics is a subject we are all exposed to in our daily lives, but one which many of us fear. In this introduction, Timothy Gowers elucidates the most fundamental differences, which are primarily philosophical, between advanced mathematics and what we learn at school, so that one emerges with a clearer understanding of such paradoxical-sounding concepts as 'infinity', 'curved space', and 'imaginary numbers'. From basic ideas, through to philosophical queries, to common sociological questions about the mathematical community, this book unravels some (...) of the mysteries of space and numbers. (shrink)