力学原理的真理性反思——以虚功原理为例

Reflections on the Truth of the Mechanical Principles——Taking the Principle of Virtual Work as an Example

在虚功原理的具体语境中,关于数学证明是否可能的探讨引出了力学原理的真理性地位问题。把虚功原理的发展历史看作是概念的明晰化过程,拉格朗日正是利用前人的基本概念进行了还原模型证明。但是,证明过程中仍然出现了无限小位移、平衡等模糊概念,引起普安索、雅可比等众多科学家的批判。不同的是,普安索主张采用回避模糊概念、退回纯几何问题的方法获得证明,而雅可比认为力学原理只是假定与自然一致的约定,不可能存在严格的数学证明。最后进一步深化雅可比的约定思想,无法证明的力学原理既不是必然真理,也不是偶然真理,而是一种协调真理。

In the concrete context of the Principle of Virtual Work（ PVW）,discussions about the possibility of the mathematical justification lead to the question of the truth of the mechanical principles. The history of PVW can be regarded as a process of conceptual clarification. By these clarified concepts,Lagrange proved PVW through a pulley model. However,some fuzzy concepts still have arisen,such as infinitesimal displacement and equilibrium,which were criticized by Poinsot,Jacobi and many other scientists. While Poinsot’s proposal was to obtain pure geometric proof by evading the fuzzy concepts,Jacobi believed that the mechanical principles are conventions which are assumed to be identical with nature,and there are not strict mathematical proofs. We attempt to deepen Jacobi’s ideas and believe that the mechanical principles are not necessary truth or contingent truth but a kind of concert truth.