کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10460191 923380 2005 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Creating mathematical infinities: Metaphor, blending, and the beauty of transfinite cardinals
موضوعات مرتبط
علوم انسانی و اجتماعی علوم انسانی و هنر زبان و زبان شناسی
پیش نمایش صفحه اول مقاله
Creating mathematical infinities: Metaphor, blending, and the beauty of transfinite cardinals
چکیده انگلیسی
The infinite is one of the most intriguing, controversial, and elusive ideas in which the human mind has ever engaged. In mathematics, a particularly interesting form of infinity-actual infinity-has gained, over centuries, an extremely precise and rich meaning, to the point that it now lies at the very core of many fundamental fields such as calculus, fractal geometry, and set theory. In this article I focus on a specific case of actual infinity, namely, transfinite cardinals, as conceived by one of the most imaginative and controversial characters in the history of mathematics, the 19th century mathematician Georg Cantor (1845-1918). The analysis is based on the Basic Metaphor of Infinity (BMI). The BMI is a human everyday conceptual mechanism, originally outside of mathematics, hypothesized to be responsible for the creation of all kinds of mathematical actual infinities, from points at infinity in projective geometry to infinite sets, to infinitesimal numbers, to least upper bounds [Lakoff, George, Núñez, Rafael, 2000. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. Basic Books, New York]. In this article I analyze the BMI in terms of a non-unidirectional mapping: a double-scope conceptual blend. Under this view “BMI” becomes the Basic Mapping of Infinity.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pragmatics - Volume 37, Issue 10, October 2005, Pages 1717-1741
نویسندگان
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