There is a well-known variety of contact paradoxes which are significantly linked to topology. The aim of this paper is to present a new paradox concerning contact with bodies composed of a denumerable infinity of parts. This paradox establishes the logical necessity, in a Newtonian context, of contact forces (herein called “phantom forces”) that violate what is probably our most basic causal intuition, embodied in what I call the Principle of Influence: any force exerted on a body B induces (causes) change of movement of B or (inclusive disjunction) the emergence of internal forces in B. However, the above paradox can be made strictly compatible with a Newtonian framework by introducing phantom forces as ideal elements in the Hilbert sense, though it will be seen that this does not solve all the problems.

有许多众所周知的接触悖论，它们与拓扑结构密切相关。本文的目的是提出一个新的悖论，该悖论涉及与由无数部分组成的物体的接触。这个悖论在牛顿语境中确立了接触力（这里称为“幻象力”）的逻辑必然性，这可能违反了我们最基本的因果直觉，体现在我所谓的影响原理中：施加在物体上的任何力B 引起（导致）B 的运动变化或（包含析取）B 中内力的出现。然而，通过引入幻象力作为希尔伯特意义上的理想元素，可以使上述悖论与牛顿框架严格兼容，尽管可以看出，这并不能解决所有问题。