Comments on Aristotle's Logic

Since all the other parts of Aristotle’s logic theory have been proved invalid,
I will only focus on the theory of syllogism.

To illustrate the inherent formal errors within Aristotle’s system, Russell
gives an invalid inference of “Every golden mountain is mountain” + “Golden
mountains are gold” → “Some mountains are gold”. He says that since there
cannot exist any golden mountain, then the conclusion is false even if both the
major and minor premises are true.

However, from my point of view, the major premise cannot be true if there
doesn’t exist any golden mountain. Otherwise, then the conclusion should also
be true. I know that this is based on the induction instead of deduction. But I
don’t think this is a formal error in Aristotle’s syllogism system.