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