心灵因果并非承重结构
本文挑战了心灵哲学中的一个核心假设：即心理状态（信念、欲望等）必须具有因果效力，才能解释人类行动。作者论证，即便心理因果性不充当“承重墙”，我们对行动、自由意志和道德责任的日常理解也不会崩塌。通过分析物理主义与因果排他性问题的张力，文章提出我们可以放弃心理因果的负载功能，转而采用更灵活的解释框架。
相关报道
A blog post discusses a mathematical identity where pentagonal numbers can be expressed in terms of triangular numbers. It highlights that while examples don't typically prove theorems, in this case the identity Pn = T(2n−1) − T(n−1) holds, showing that three examples can suffice for proving certain relationships.
John D. Cook describes how a sequence of his blog posts often follows a hidden thread, beginning with a post about the mathematical approximation exp(−x²) ≈ (1 + cos(sin(x) + x))/2, which some commenters incorrectly attributed solely to a first-order Taylor expansion.
The nth pentagonal number Pn follows the formula Pn = (3n² − n)/2 for positive integer n. For non-positive integer n, the same formula defines a generalized pentagonal number.
Partial fraction decomposition is commonly introduced in calculus as a technique for integrating rational functions by breaking P(x)/Q(x) into simpler terms. However, the post suggests that this method has applications beyond integration that are often overlooked in a typical calculus class.