数学学习是现代人的基本学科训练之一，数学在人们对数和空间的认识方面无疑是十分重要的，除此之外，还有人强调数学在逻辑推理方面的作用也很大。其实，数学在逻辑推理方面的作用言过其实，其作用未必比逻辑学更佳。约翰·斯图尔特·穆勒（John Stuart Mill）在其自传《我的知识之路》（Autobiography of John Stuart Mill）中说到有关数学对思维和逻辑推理方面的作用时，它根本不能与经院逻辑学相提并论。因为数学过程中正确的推理根本不会产生真正的困难。数学由于并不需要学生通过经验和思考缓慢获得自己有价值思想这个前提条件，因而数学学习适合哲学学生早期阶段的教育。详见下文：

 

The first intellectual operation in which I arrived at any proficiency, was dissecting a bad argument, and finding in what part the fallacy lay: and though whatever capacity of this sort I attained was due to the fact that it was an intellectual exercise in which I was most perseveringly drilled by my father, yet it is also true that the school logic, and the mental habits acquired in studying it, were among the principal instruments of this drilling. I am persuaded that nothing, in modern education, tends so much, when properly used, to form exact thinkers, who attach a precise meaning to words and propositions, and are not imposed on by vague, loose, or ambiguous terms. The boasted influence of mathematical studies is nothing to it; for in mathematical processes, none of the real difficulties of correct ratiocination occur. It is also a study peculiarly adapted to an early stage in the education of philosophical students, since it does not presuppose the slow process of acquiring, by experience and reflection, valuable thoughts of their own. They may become capable of disentangling the intricacies of confused and self-contradictory thought, before their own thinking faculties are much advanced; a power which, for want of some such discipline, many otherwise able men altogether lack; and when they have to answer opponent, only endeavour, by such argument as they can command, to support the opposite conclusion, scarcely even attempting to confute the reasonings of their antagonists; and, therefore, at the utmost, leaving the question, as far as it depends on argument, a balanced one.

 

从我个人的阅读经验来看，许多学过数学及高等数学的现代文科学者，在论证其论点或反驳别人观点的时候，也并没有多少出色的逻辑和推理表现，更不用说理科学者在这方面的表现。也就是说，学习数学中的那些规矩在论证实战中并无多大威力。

 

 

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