数学季刊 ›› 2013, Vol. 28 ›› Issue (3): 360-365.

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数学无穷与中介逻辑(下)——关于△y/△y有意义dy/dx是切线的斜率在中介逻辑中的逻辑数学解读与逻辑分析

  

  1. 1. School of Information Science and Technology, Nanjing University of Aeronautics and Astronautics 2. State Key Laboratory of Software Development Environment, Beihang University 3. School of Electronics and Information Engineering, Nanjing University of Technology4. Institute of Modern Logic and Applications, Nanjing University
  • 收稿日期:2011-04-01 出版日期:2013-09-30 发布日期:2023-02-23
  • 作者简介:ZHU Wu-jia(1934-), male, native of Yixing, Jiangsu, an professor of Nanjing University of Aeronautics and Astronautics, engages in logic, mathematic foundation and computer science; GONG Ning- sheng(1958-), male, native of Nanjing, Jiangsu, a professor of Nanjing University of Technology, engages in logic and computer science.
  • 基金资助:
    Supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2011KF-04)；Supported by the Beihang University and by the National High Technology Research and Development Program of China(863 Program)(2009AA043303)

Mathematical Infinity and Medium Logic (II)——Logical-mathematical Interpretation and Logical Analysis of...

  1. 1. School of Information Science and Technology, Nanjing University of Aeronautics and Astronautics 2. State Key Laboratory of Software Development Environment, Beihang University 3. School of Electronics and Information Engineering, Nanjing University of Technology4. Institute of Modern Logic and Applications, Nanjing University
  • Received:2011-04-01 Online:2013-09-30 Published:2023-02-23
  • About author:ZHU Wu-jia(1934-), male, native of Yixing, Jiangsu, an professor of Nanjing University of Aeronautics and Astronautics, engages in logic, mathematic foundation and computer science; GONG Ning- sheng(1958-), male, native of Nanjing, Jiangsu, a professor of Nanjing University of Technology, engages in logic and computer science.
  • Supported by:
    Supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2011KF-04)；Supported by the Beihang University and by the National High Technology Research and Development Program of China(863 Program)(2009AA043303)

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摘要： Ref [5] provides a logical-mathematical explanation of the incompatibility of Leibniz’s secant and tangent lines in medium logic. However, the expression(*)(Δy/Δx is meaningful and dy/dx is the tangent slope) derived from 7 and 8 in §4 of Ref [5] is unimaginable within the framework of two-valued logic, why shouldn’t the same conflicting conclusion be reached in the medium logic calculus? This paper has subjected these questions to careful logical analysis, and approached them from the perspective of logical mathematics. As the two approaches have led to the identical conclusion, the paper thereby rigorously and thoroughly answers these questions.

关键词: calculus, limit theory, medium logic, potential infinity, actual infinity

Abstract: Ref [5] provides a logical-mathematical explanation of the incompatibility of Leibniz’s secant and tangent lines in medium logic. However, the expression(*)(Δy/Δx is meaningful and dy/dx is the tangent slope) derived from 7 and 8 in §4 of Ref [5] is unimaginable within the framework of two-valued logic, why shouldn’t the same conflicting conclusion be reached in the medium logic calculus? This paper has subjected these questions to careful logical analysis, and approached them from the perspective of logical mathematics. As the two approaches have led to the identical conclusion, the paper thereby rigorously and thoroughly answers these questions.

Key words: calculus, limit theory, medium logic, potential in?nity, actual in?nity

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