Types of Mathematical Explanation

Subject Areas : Philosophy

Received: 2015-04-22 Accepted : 2015-09-03 Published : 2015-08-23

Keywords: internal and external explanat, local and holistic explanation, demonstrative and non-demonstr, symbolic and non-symbolic expl, avoidable and unavoidable expl,

Abstract :

One good way to grasp the concepts is to study their instances. This article examines the types of mathematical explanation and introduces several new types of it. The two famous types of mathematical explanation are internal and external explanations. The local–holistic distinction is also a distinction used in philosophy of mathematics as a strategy of explanation. But it seems that we can distinguish a greater variety of mathematical explanations and thereby gain a better understanding of it. For example, demonstrative and non-demonstrative explanations can be separated. These two explanations are given, respectively, in the process of proving and such processes as modeling and idealization. This division is based on the theoretical or cognitive role of explanations, we can say. Moreover, we must separate the symbolic from the non-symbolic, the avoidable from the unavoidable, explanations. Some explanations can be removed from a process of reasoning, without prejudice to that process. They are given for educational or pragmatic purposes. But others are not avoidable, because the main burden of explanation is on them. This article separates this ten explanations and introduces several new types with different examples.

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