Document Type : Research Paper
Authors
1
Department of Linguistics, Faculty of Letters and Humanities, Ferdowsi University of Mashhad, Mashhad, Iran.
2
Linguistics Department, Faculty of Letters and Humanities, Ferdowsi University of Mashhad, Mashhad, Iran.
Abstract
According to the hypothesis of embodied mathematics, which is based on cognitive semantics, the basis and origin of mathematical concepts is human embodiment, and therefore opposing hypotheses such as mathematical Platonism, which assume the existence of mathematics independent of humans, are not supported by recent cognitive sciences. In this research, based on the descriptive-analytical method and based on the hypothesis of embodied mathematics, the cognitive origin of the concept of mathematical infinity, limit and other concepts derived from them such as transfinite numbers, derivative and integral have been examined descriptively. In this research, in addition to describing the concept of number and sets of numbers; The concept of infinity is described based on the basic metaphor of infinity, which is a type of conceptual metaphor, and on this basis, infinitesimals, the concept of limit, transfinite numbers, and finally differential and integral calculus, which is based on the two concepts of derivative or differential and integral, are analyzed. On this basis, the role of image schemas, conceptual structures such as metonymy, metaphor, and blending in the formation of basic concepts of arithmetic can be described based on linguistic intuition and in an introspective manner, and this research has conducted a descriptive study of the origin of basic concepts of arithmetic based on embodiment and conceptual structures derived from the second generation of cognitive sciences.
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