摘要
对哲学、数学中与无穷相关的存在问题进行开拓性系统研究,提出了"数性"、"本体数"、"形式数"、"应用无穷"等新概念.在"系统性"、"数性"、"数量形式"、"数、数值认知行为"和"科学性"的层面上,将千百年来悬而未决的芝诺悖论、贝克莱悖论和罗素悖论所揭示的问题联系起来作为一个"疑难怪症"进行研究,分析、研究极限论这种"处理无穷数学事物的技术与理论"是什么及其功能.结果表明,我们必须从错误的"实无穷-潜无穷"阴霾中走出,正确认识与科学的新"无穷观"、新数量理论相关的极限论的"本体-形式"论性质,修缮、重构现有的经典极限论及其相关的数学分析、集合论、实数理论(比如重新认识"戴德金-康托公理"和"连续统假设")等重要数学内容的基础理论,进一步开拓"数-数值理论"的研究.
What has been presented in this paper is the ＂applied infinitude＂, another significant part in infinitude system of philosophy and mathematics after 《On ＂Infinitude＂》and 《On ＂Infinitude Number＂》on the systematic pioneering researches to the existing problems relating to ＂Infinitude＂ （which decides the specialties of the style and the cited references of these serial papers）. Four new connotations of ＂ontological number＂, ＂formal number＂, ＂the nature of number＂ and ＂applied infinitude＂ are discovered. At the new level of ＂system＂ ,＂the nature of number＂, ＂the form of number＂ , ＂the number and numerical value cognizing behavior＂ and ＂the nature of science＂, the problems disclosed by suspended Zeno＇s Paradox, Berkeley＇s Paradox and Russell＇s Paradox are put together and investigated as a ＂difficult and complicated syndrome＂ and, one of the technique and theory of treating infinitude mathematical substances-limit theory is analyzed and studied： what it is and what it can do. A conclusion is drown： We must get out of the black shadow of ＂potential infinitude-actual infinitude＂, have a scientific understanding on the ＂ontology-form＂ nature of limit theory relating to the new scientific ＂infinitude theory＂ and new ＂number theory＂, renovate and reconstruct the basic theories of present ＂limit theory＂ and its related areas such as mathematical analysis, set theory, real number theory （re-understand the Dedekind-Cantor Axiom and Continuum Hypothesis and so on）, and open up the researches on the ＂number-numerical value theory＂.
出处
《喀什师范学院学报》
2012年第6期15-20,共6页
Journal of Kashgar Teachers College
关键词
数学基础
无穷理论体系
极限论
本体数
形式数
数性
应用无穷
数学实体
The foundation of mathematics
The system of infinitude theory
Limit theory
Ontological number
Formal number
The nature of number
Applied infinitude
Mathematical substance
