a mistake in which something is said or believed to be in one category (= group) when in fact it belongs to another

To treat atheism as a belief system alongside varieties of religious belief is simply a category mistake. 把无神论视为一种信仰，等同于各种宗教，是一种范畴错误。

a mistake in which something is said to have a particular quality, or be able to do a particular thing, that only members of another category (= group) of things can have or do

It is a category mistake to talk about a research programme as being falsified, because only theories can be falsified - research programmes can at most be discredited. 如果认为研究项目可以被证明是虚假的，这就犯了一种范畴错误，因为只有理论可能是虚假的，研究项目只能被推翻其可信度。