Some Historical Issues and Paradoxes Regarding the Concept of Infinity: An Apos-Based Analysis: Part 1 View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2005-03

AUTHORS

Ed Dubinsky, Kirk Weller, Michael A. Mcdonald, Anne Brown

ABSTRACT

This paper applies APOS Theory to suggest a new explanation of how people might think about the concept of infinity. We propose cognitive explanations, and in some cases resolutions, of various dichotomies, paradoxes, and mathematical problems involving the concept of infinity. These explanations are expressed in terms of the mental mechanisms of interiorization and encapsulation. Our purpose for providing a cognitive perspective is that issues involving the infinite have been and continue to be a source of interest, of controversy, and of student difficulty. We provide a cognitive analysis of these issues as a contribution to the discussion. In this paper, Part 1, we focus on dichotomies and paradoxes and, in Part 2, we will discuss the notion of an infinite process and certain mathematical issues related to the concept of infinity. More... »

PAGES

335-359

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10649-005-2531-z

DOI

http://dx.doi.org/10.1007/s10649-005-2531-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1008344527


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