Understanding what numbers are means knowing several things. It means knowing how counting relates to numbers (called the cardinal principle or cardinality); it means knowing that each number is generated by adding one to the previous number (called the successor function or succession), and it means knowing that all and only sets whose members can be placed in one-to-one correspondence have the same number of items (called exact equality or equinumerosity). A previous study (Sarnecka & Carey, 2008) linked children's (...) understanding of cardinality to their understanding of succession for the numbers five and six. This study investigates the link between cardinality and equinumerosity for these numbers, finding that children either understand both cardinality and equinumerosity or they understand neither. This suggests that cardinality and equinumerosity (along with succession) are interrelated facets of the concepts five and six, the acquisition of which is an important conceptual achievement of early childhood. (shrink)

This article focuses on how young children acquire concepts for exact, cardinal numbers. I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children’s number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey. In this framework, the (...) counting list and the counting routine form a placeholder structure. Over time, the placeholder structure is gradually filled in with meaning to become a conceptual structure that allows the child to represent exact numbers A number system is a socially shared, structured set of symbols that pose a learning challenge for children. But once children have acquired a number system, it allows them to represent information that they had no way of representing before. (shrink)

Rips et al.'s critique is misplaced when it faults the induction model for not explaining the acquisition of meta-numerical knowledge: This is something the model was never meant to explain. More importantly, the critique underestimates what children know, and what they have achieved, when they learn the cardinal meanings of the number words through.

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

Bridging the gap between the world of science and the realm of the spiritual, B. Alan Wallace introduces a natural theory of human consciousness that has its roots in contemporary physics and Buddhism. Wallace's "special theory of ontological relativity" suggests that mental phenomena are _conditioned_ by the brain, but do not _emerge_ from it. Rather, the entire natural world of mind and matter, subjects and objects, arises from a unitary dimension of reality that is more fundamental than these dualities, as (...) proposed by Wolfgang Pauli and Carl Jung. To test his hypothesis, Wallace employs the Buddhist meditative practice of _samatha_, refining one's attention and metacognition, to create a kind of telescope to examine the space of the mind. Drawing on the work of the physicist John Wheeler, he then proposes a more general theory in which the participatory nature of reality is envisioned as a self-excited circuit. In comparing these ideas to the Buddhist theory known as the Middle Way philosophy, Wallace explores further aspects of his "general theory of ontological relativity," which can be investigated by means of _vipasyana_, or insight, meditation. Wallace then focuses on the theme of symmetry in reference to quantum cosmology and the "problem of frozen time," relating these issues to the theory and practices of the Great Perfection school of Tibetan Buddhism. He concludes with a discussion of the general theme of complementarity as it relates to science and religion. The theories of relativity and quantum mechanics were major achievements in the physical sciences, and the theory of evolution has had an equally deep impact on the life sciences. However, rigorous scientific methods do not yet exist to observe mental phenomena, and naturalism has its limits for shedding light on the workings of the mind. A pioneer of modern consciousness research, Wallace offers a practical and revolutionary method for exploring the mind that combines the keenest insights of contemporary physicists and philosophers with the time-honored meditative traditions of Buddhism. (shrink)

This chapter first surveys general issues in the epistemic internalism / externalism debate: what is the distinction, what motivates it, and what arguments can be given on both sides. -/- The second part of the chapter will examine the internalism / externalism debate as regards to the specific case of the epistemology of memory belief.

The acquisition of a new skill usually proceeds through five stages, from novice to expert, with a sixth stage of mastery available for highly motivated performers. In this chapter, we re-state the six stages of the Dreyfus Skill Model, paying new attention to the transitions and interrelations between them. While discussing the fifth stage, expertise, we unpack the claim that, “when things are proceeding normally, experts don’t solve problems and don’t make decisions; they do what normally works” (Dreyfus & Dreyfus, (...) 1988, pp. 30 – 31). This leads us to offer an account of the “perspectival deliberation” that arises for experts and masters and that is distinct from the calculative deliberation characteristic of the lower stages of skillfulness. (shrink)

'The problem of the twentieth-century is the problem of the color-line.' Originally published in 1903, The Souls of Black Folk is a classic study of race, culture, and education at the turn of the twentieth century. With its singular combination of essays, memoir, and fiction, this book vaulted W. E. B. Du Bois to the forefront of American political commentary and civil rights activism. The Souls of Black Folk is an impassioned, at times searing account of the situation of African (...) Americans in the United States. Du Bois makes a forceful case for the access of African Americans to higher education, memorably extols the achievements of black culture (above all the spirituals or 'sorrow songs'), and advances the provocative and influential argument that due to the inequalities and pressures of the 'race problem', African American identity is characterized by 'double consciousness'. This edition includes a valuable appendix of other writing by Du Bois, which sheds light on his attitudes and intentions. ABOUT THE SERIES: For over 100 years Oxford World's Classics has made available the widest range of literature from around the globe. Each affordable volume reflects Oxford's commitment to scholarship, providing the most accurate text plus a wealth of other valuable features, including expert introductions by leading authorities, helpful notes to clarify the text, up-to-date bibliographies for further study, and much more. (shrink)

We presuppose a position of scientific realism to the effect (i) that the world exists and (ii) that through the working out of ever more sophisticated theories our scientific picture of reality will approximate ever more closely to the world as it really is. Against this background consider, now, the following question: 1. Do the empirical theories with the help of which we seek to approximate a good or true picture of reality rest on any non-empirical presuppositions? One can answer (...) this question with either a 'yes' or a 'no'. 'No' is the preferred answer of most contemporary methodologists -- Murray Rothbard is one distinguished counterexample to this trend -- who maintain that empirical theories are completely free of non-empirical ('a priori') admixtures and who see science as a matter of the gathering of pure 'data' obtained through simple observation. From such data scientific propositions are then supposed to be somehow capable of being established. (shrink)

What are the most fundamental features of the world? Do minds stand outside the natural order? Is a unified picture of mental and physical reality possible? The Mind in Nature provides a staunchly realist account of the world as a unified system incorporating both the mental and the physical. C. B. Martin, an original and influential exponent of 'ontologically serious' metaphysics, echoes Locke's dictum that 'all things that exist are only particulars', and argues that properties are powerful qualities. He also (...) spells out the implications of this view for philosophical conceptions of causation, intentionality, consciousness, and the mind-body problem. Martin emphasizes the importance of non-conscious 'vegetative' systems, which provide clear examples of intentionality in the form of representational use. The slide from representational use to consciousness involves a change in the material of use, but not the form of representation. A concluding chapter provides an argument for the view that an ontology of particular substances and properties leads ineluctably to monism: the bus we board with Locke takes us directly to the world of Spinoza and Einstein. Along the way, we are led to understand the nature of minds and conscious states of mind in a way that avoids both reductionism and dualism. (shrink)

In this concise yet powerful book, one of the twentieth century's most respected political philosophers presents a controversial reassessment of the political ideas and intellectual legacy of Edmund Burke. A practicing politician and powerful writer, full of ideas, Burke was intent on getting those ideas translated into government policies. But he was too much the impatient practitioner to set out his principles in a single book in the manner of Locke or Hume, leaving both admirers and opponents ample scope to (...) reinterpret his work in different ways. Macpherson, however, finds Burke's views on political economy to be the one consistent factor in his thinking. Today Burke is often viewed as one of modern conservatism's founding lights, and in an era of global capitalism unfettered by national borders, Macpherson's reassessment of Burke's ideas is perhaps more timely than ever. (shrink)

First published in 1986, Knowledge, Belief, and Witchcraft remains the only analysis of indigenous discourse about an African belief system undertaken from within the framework of Anglo-American analytical philosophy. Taking as its point of departure W. V. O. Quine's thesis about the indeterminacy of translation, the book investigates questions of Yoruba epistemology and of how knowledge is conceived in an oral culture.

On the doctrines of Madhva, 13th century exponent of the Dvaita school in Hindu philosophy.