Mathematics emphasizes logic, but philosophical syllogism emphasizes truth beyond logic. In mathematics, the following reasoning process is correct or accurate regardless of whether the starting point (that is, the basis of starting) is established or not. However, in philosophy, because the starting point and process of syllogism are limited by truth, it must be discussed in an accurate and single category.

At that time, Russell pointed out a famous example: "The mountain made of gold is a mountain, and the mountain made of gold is gold, so at least one mountain is gold." It is completely consistent with Aristotle's syllogism, but it is easy to prove wrong by mathematical logic.

However, this does not mean that Aristotle's syllogism is wrong. Gold is a matter, and mountains are a form, which are two different categories, so we can't draw a correct conclusion. Philosophically, this is a change of concept. Mathematically, this actually equates "mountain" with "gold", but logically, this reasoning is correct in form.

Different fields pay attention to different problems, and when dealing with different problems, of course, we must use different methods. In addition, mathematical proof can ensure the basic rigor of logical reasoning, and philosophy is needed.