From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in 'unmediated opposition' (P,﹁P ) whether in ZFC or not; it has further been proved that the m...From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in 'unmediated opposition' (P,﹁P ) whether in ZFC or not; it has further been proved that the manners in which a variable infinitely approaches its limit also satisfy the law of intermediate exclusion. With these results as theoretical bases, this paper attempts to provide an accurate and strict logical-mathematical interpretation of the incompatibility of Leibniz's secant and tangent lines in the medium logic system from the perspective of logical mathematics.展开更多
Abstract： Ref [5] provides a logical-mathematical explanation of the incompatibility ofLeibniz＇s secant and tangent lines in medium logic. However, the expression （＊）（△y/△x） ismeaningful and dy/dx is the tang...Abstract： Ref [5] provides a logical-mathematical explanation of the incompatibility ofLeibniz＇s secant and tangent lines in medium logic. However, the expression （＊）（△y/△x） ismeaningful and dy/dx is the tangent slope） derived from ⑦ and ⑧ in §4 of Ref [5] is unimaginablewithin the framework of two-valued logic, why shouldn＇t the same conflicting concluslon 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 thoroughlv answers these questions.展开更多
The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and it...The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and its extensions （MF^＊ and ME^＊ ） are not strong complete; and generally, ff a consistent formal system is not strong complete, then any consistent extensions of this forreal system are not strong complete either.展开更多
基金Supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2011KF-04)Supported by the National High Technology Research and Development Program of China (863 Program)(2009AA043303)
文摘From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in 'unmediated opposition' (P,﹁P ) whether in ZFC or not; it has further been proved that the manners in which a variable infinitely approaches its limit also satisfy the law of intermediate exclusion. With these results as theoretical bases, this paper attempts to provide an accurate and strict logical-mathematical interpretation of the incompatibility of Leibniz's secant and tangent lines in the medium logic system from the perspective of logical mathematics.
文摘Abstract： Ref [5] provides a logical-mathematical explanation of the incompatibility ofLeibniz＇s secant and tangent lines in medium logic. However, the expression （＊）（△y/△x） ismeaningful and dy/dx is the tangent slope） derived from ⑦ and ⑧ in §4 of Ref [5] is unimaginablewithin the framework of two-valued logic, why shouldn＇t the same conflicting concluslon 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 thoroughlv answers these questions.
文摘The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and its extensions （MF^＊ and ME^＊ ） are not strong complete; and generally, ff a consistent formal system is not strong complete, then any consistent extensions of this forreal system are not strong complete either.
