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Mathematical Knowledge (mathematical + knowledge)

Distribution by Scientific Domains
Humanities and Social Sciences75%

Selected Abstracts

Is Reliabilism Compatible with Mathematical Knowledge?

PHILOSOPHICAL FORUM, Issue 4 2004
Mark McEvoy
First page of article [source]

Transfer of Mathematical Knowledge: The Portability of Generic Instantiations

CHILD DEVELOPMENT PERSPECTIVES, Issue 3 2009
Jennifer A. Kaminski
Abstract, Mathematical concepts are often difficult to acquire. This difficulty is evidenced by failure of knowledge to transfer to novel analogous situations. One approach to this challenge is to present the learner with a concrete instantiation of the to-be-learned concept. Concrete instantiations communicate more information than their abstract, generic counterparts and, in doing so, they may facilitate initial learning. However, this article argues that extraneous information in concrete instantiations may distract the learner from the relevant mathematical structure and, as a result, hinder transfer. At the same time, generic instantiations, such as traditional mathematical notation, can be learned by both children and adults and can, in turn, allow for transfer, suggesting that generic instantiations result in a portable knowledge representation. [source]

Foundations of Mathematics: Metaphysics, Epistemology, Structure

THE PHILOSOPHICAL QUARTERLY, Issue 214 2004
Stewart Shapiro
Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena for exploring relations and interactions between mathematical fields, their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics. [source]

A Survey of Portuguese Mathematics in the Nineteenth Century

CENTAURUS, Issue 4 2000
Luis M. Ribeiro Saraiva
Résumé La reforme de l'Université Portugaise en 1772, qui avait pour but la mettre au niveau des meilleures Universités d'Europe, n'a pas eu le temps de se développer, opposée par des forces rétrogrades. En conséquence de ce fait et du climat d'agitation politique et sociale qui a caractérisé la Portugal dans la première moitié du dixneuvième siècle, la production mathématique dans cette époque fut minimale. Les académies militaires étaient alors les principaux centres de transmission des connaissances mathématiques, et les articles de mathématique en ce temps étaient publiés dans sa majorité par l'Académie de Sciences de Lisbonne. Dans la deuxième moitié du dixneuvième siècle le Portugal entra dans une période de stabilité. La reforme de l'enseignement de 1836, et les nouveaux status de l'Académie de 1851 ont proporcionné un développement de l'activité mathématique, qui fut acompagnée de la restructuration des académies militaires ou de leur transformation en Ecoles Polytechniques; l'Ecole Polytechnique de Lisbonne fut spécialement importante. A partir de 1877, avec la publication du premier journal de mathématique qui ne dépendait pas de l'Académie, et qui avait pour but spécifique briser l'isolement des mathématiques portugaises, la recherche en ce champs s'est encore plus développée. Dans la dernière partie de cet article nous donnons quelques éléments sur la vie et l'oeuvre de deux importants mathématiciens portugais du dixneuvième siècle: Daniel Augusto da Silva (1814,1878) et Francisco Gomes Teixeira (1851,1933). Abstract The Portuguese University was briefly reformed in 1772, aiming to bring it to the level of its European counterparts; but this was soon cut short by the return to power of reactionary forces. As a consequence of this, and the political and social unrest that characterized the first half of the nineteenth century in Portugal, there was very little production of mathematics in this period. The military academies were the main centres of transmission of mathematical knowledge, and mathematical works were mostly published by the Lisbon Academy of Sciences. In the second half of the nineteenth century the country entered a period of stability. The education reform of 1836 and the Academy's new statutes of 1851 set in train a blossoming of mathematical activity, reflected in the restructuring of the military academies, or their transformation into Polytechnic Schools, of which the Polytechnic School of Lisbon is of particular importance. Mathematics research was further promoted from 1877 onwards by the publication of the first mathematics journal independent of the Academy, which aimed specifically at ending the isolation of Portuguese mathematics. In the final pages of this survey some data is given on the life and work of the two outstanding Portuguese mathematicians of the nineteenth century: Daniel Augusto da Silva (1814,1878) and Francisco Gomes Teixeira (1851,1933). [source]