The classic exemplar of logic is supposed to be the following syllogism:
1: All men are mortal.
2: Socrates is a man.
3: Therefore, Socrates is mortal.
If you are very careful, then it is correct to say that, if you know that statements 1 and 2 are true, then it follows that statement 3 is true.
But it is quite a different thing to say that the syllogism above is an example of correct reasoning. Statement 1 is not true...that is, it asserts something as a truth that is in fact merely an inductive guess. All men, so far, well all the men I know of, well, there are many dead men, and it seems like it has happened indiscriminately, and there aren't any men 200 years old, and ... well, I would say everyone is going to die because all the dead people were once alive. This is quite a different statement from saying "There is no largest prime number." It is a statement, primarily intended to refer to not-dead men, derived from the observation of some now-dead former men, and making a prediction with no logical validity. So, how do we know Socrates must die? Because all men must die. How do we "know" all men must die? Because those men who have died, ...did die.
Moreover, this syllogism can hardly be said to be an example of thinking at all. If we suppose that the reasoner already accepts the truth of statements A and B, then no natural born person, mortal or not, save a newly baptized logician, would argue that statement C represents any kind of new or clarified knowledge. If a salesman came to my door, and I told him that all men are mortal and Socrate is a man, and he responded that if I only bought a box of his new logical machine, I would be able to determine that Socrates was mortal, then I would simply slam the door on him.
And really, the issue is that Aristotle is pretending that we can derive new knowledge from syllogisms. It's as though we could mutter, yes, all men are mortal, that's obvious, and Socrates is a man, so, wait a minute, that means that Socrate will have to die! Part of the force of this invalid conclusion comes from the fact that it is actually not obvious that anyone alive has to die. So it is sort of new knowledge...because it's NOT LOGICALLY CORRECT.
To see that the assertion, unsupported by fact, of universal human mortality, is an issue here, think for a moment of what a poor example we would have if our main premise became "All men are male." Leaving aside the fact that we have modified our interpretation of "men", the remainder of the logical syllogism is now exposed as laughably threadbare.
We must mention, however, that Aristotle is not responsible for this particular bad example. The syllogism in question is described in his text in abstract terms:
1: All A are B.However, this stark version of the syllogism, while unassailable in form, now suggests how unuseful such forms of reasoning are for practical thinking, that is, in the real world, as opposed to fictional worlds defined by mathematician, or logicians, in which we cannot rely on experience for knowledge, but instead are handed a bunch of logical axioms from which we really do need to construct a kind of understanding of what's going on.
2: C is an A.
3: Therefore, C is a B.