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不可或缺性论证在强调数学与科学之整体性的基础上,试图借助数学在科学中的不可或缺性证实数学实体的存在性,成为求解数学真理困境的巧妙方案。然而,不可或缺性不能等同于经验确证,数学实在与否并不在于数学在科学中是否或缺,二者分属于不同的问题域。本文在阐明不可或缺性论证的基本形式及其对数学真理困境的求解策略的基础上,进一步指出了该论证的缺陷、得出了其对求解数学真理困境的有益启示,即要想突破数学真理困境,就需要洞察数学与科学的之间的关联性,揭示二者一致的实在本性,使数学能真正地具有与科学同等的本体论和认识论地位。
Indispensability Argumentation An attempt to prove the existence of a mathematical entity with the indispensability of mathematics in science by emphasizing the integrity of mathematics and science has become an ingenious solution to the dilemma of mathematical truth. However, indispensability can not be equated with empirical confirmation. Whether mathematics is true or not does not lie in whether mathematics is or is not lacking in science, and the two belong to different problem domains. On the basis of clarifying the basic forms of indispensable argumentation and its solving tactics for the dilemma of mathematics truth, this article further points out the defects of this argument and draws its beneficial enlightenment for solving the dilemma of mathematics truth, that is, It is necessary to understand the connection between mathematics and science and reveal the consistent real nature of the two so that mathematics can really have the same ontological and epistemological status as science.