Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is of which it is supposed to be true. If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics.
纯数学包含的就是这样一些论断:如果某某命题对某事物为真(不管是什么事物)，则另个某菜命题对该事物亦为真。重要的是,我们并不去讨论第一个命题是否的确为真，也不要涉及假设为真的该命题中的那个(任何)事物是什么。如果我们的假设对任何事物都适用,而不是仅适用于某一件或几件特殊的事物,则我们的演绎推理便构成了数学。
