“The heart of Aristotle’s logic is the syllogism, the classic example of which is as follows: All men are mortal; Socrates is a man; therefore, Socrates is mortal. The syllogistic form of logical argumentation dominated logic for 2,000 years.”
(bold theirs)

“Dominated” - past tense?? I understand there are things like fuzzy logic and so on, but as far as I know, syllogism is still logic today, right?

The term “mortal” means will die. It does not mean, “is (already) dead”. So Socrates (like you, I hope!) is mortal even if he were not dead. (Just as someone can be a smoker even if he is not smoking at the moment.)

So. while Socrates lives he does “fit” the first premise.

But, in any case, the issue is irrelevant to Aristotelian logic, which is about the validity of the the argument, and not about whether or not the premises of the argument happen to be true or false.

Consider the following syllogism:

All dogs are reptiles.
All kangaroos are dogs

Therefore, all kangaroos are reptiles.

The above syllogism is a valid syllogism since the premises follow from the conclusion, which means that if the premises were true, then the conclusion would have to be true.

In fact, both the premises, and the conclusion are false. That is irrelevant.

It doesn’t matter how we know or even if we know. The fact is, that’s the definition of “mortal”. Do we REALLY know if all men are mortal? No. But even if you assume that premise one is false, it doesn’t change the fact that the aregument is valid because the conclusion follows from the premise. “How we know” that any particular premise is true or not, is not relevant to the question at hand.

About this thread in general…

Even if other forms of logic exist now, it still seems to me that these sorts of logical structures (Aristotelian if you will) are still the predominating, most common and standard form of logic out there. So, I’d still say it “dominates” the field of logic. Maybe I’m out of tune with the field though.

Aristotelian logic was unable to manage relations. Infact most of the euclidean demonstrations could not be reproduced yhrough syllogisms. With Frege through the use of multiple place predicates and variables we could finally obtain the formalization of those dimonstrations.

Anyway imi: don’t confuse an epistemological problem with a logical one. All logic has to do is to go from one sentence to another conservating the truth.

The premises of a syllogism need not be known to be true. In fact, they need not even be true. Neither of these has anything to do with the validity of the syllogism. As I pointed out earlier.

In a syllogism (or, for that matter, any other argument) if the premises are true and the argument is valid, then the conclusion must be true.
But notice: the above does not say or imply that the premises need to be known to be true, nor even that the premises need to be true. And, for that matter, it does not say or imply that the conclusion needs to be known to be true, nor even that it needs to be true. Logic concerns only what follows from what, and not what is true or false, or known to be true or false.

It should perhaps be pointed out that the syllogism is the ancestral form of the conditional branching structure used in computer programming languages, the If . . . then . . . else branching structure: If [set of conditions A] is true, then do B (i.e., B is true).

yes. otherwise you are simply guessing about an empirical event that is not in view- mortality… when one guesses about empirical events that are not in view one makes a leap of induction…