| 微积分发展史上的逻辑要素 |
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| 引用本文： | 李经文.微积分发展史上的逻辑要素[J].邵阳学院学报(社会科学版),2002(6). |
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| 作者姓名： | 李经文 |
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| 作者单位： | 邵阳学院数学系 湖南邵阳 |
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| 摘 要： | 亚里斯多德是逻辑学的奠基人 .逻辑为数学分析的发展提供了演绎的方法论 .但合乎逻辑的未必是科学的 ,因为人类知识积累的顺序与逻辑的顺序未必一致 .微积分是在不很严格、讲究实用的基础上 ,而不是在欧几里得严密思想的基础上发展起来的 .然而 ,科学最终是要讲究严格的 .通过许许多多人的努力 ,微积分建立在极限理论的基础上 ,而根限又建立在实数连续统基础上 ,整个微积分终于走上了严格逻辑的轨道 .
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| 关 键 词： | 微积分 逻辑 亚里斯多德 欧几里得 极限理论 实数连续统 |
The Key Logic Elements on the History of Calculus Development |
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| LI Jing-wen.The Key Logic Elements on the History of Calculus Development[J].Journal of Shaoyang University:Social Science,2002(6). |
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| Authors: | LI Jing-wen |
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| Abstract: | Aristotle was a man of laying a foundation on logic.The logic provided the deductive methodology for mathematical analysis,but the things tallying with logic were not all the best,because the order of knowledge accumulation of humanity might not be identical with that of logic.The development of calculus was based on not very strict but practical thought instead of Euclid's strict thought.Nevertheless science was finally very strict.As many people made great effforts,calculus was founded on limit theory,while the latter was founded on continuum of real number. The whole calculus finally headed for strict logic. |
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| Keywords: | calculus logic Aristotle Euclid limit theory continuum of real number |
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