关于莱布尼茨微积分的哲学背景

On the Philosophical Background of Leibniz's Calculus

有一种影响普遍的看法 ,认为莱布尼茨的微积分是以单子论为其哲学背景的 .通过对“单子”和无穷小量这两个概念的分析 ,说明这一看法是缺乏根据的 .进而通过对莱布尼茨数学哲学观的简要评述 ,说明其数学工作和哲学思想之间的相互联系主要表现在认识论和方法论层面的“普遍文字”和“数理算法” 。

By a comparative study on the concepts of Leibniz's monad and his infinitesimal,this article argues that the view of attributing philosophically Leibniz's invention of hte calculus to his theory of monod is deficient in good grounds.By the further analysis of Leibniz's thoughts of mathematical philosophy we try to show that one should look for the philosophical roots of Leibniz's mathematical work mainly in his epistemology and methodology,in particular his `universal character',but not from a superficial analogy between his monad and infinitesimal in the ontological sense.