Think tool sets. Consider the number and variety of tools a master mechanic owns or has access to. Compare that to the small sets of Craftsman tools Sears used to sell for $49.99 or the like. Aristotelian logic is like one of those same Craftsman tool sets. Excellent professional-quality tools, guaranteed, and enough for small jobs. But the small sets just plain not adequate for all jobs.

No magic or mystery whatsoever to it. Or like Newtonian physics. Perfectly good for getting all the ordinary work done. But just plain inadequate for a surprisingly large number of modern applications.

But how logic works can seem strange to a person new to it. Not a big deal. You just get used to it and soon enough, not only does it not seem strange any more, but you also come to know that whatever strangeness you may have thought was in it, was all you and not the logic at all.

So, here’s some context: Matt Dillahunty sometimes talks about how Aristotle and his buddies sat down 2000 years ago and discovered all the valid syllogisms. That’s all of them and if your argument doesn’t take one of those forms, it’s invalid or something like that. Alex Malpass is trying to communicate to him that there are a lot of other formal logical systems that cover things that Aristotle’s logic doesn’t (I think he mentions modal logic as an example a bit before the start of the clip). In this clip specifically, Alex tells Matt that in classical logic for all x Px doesn’t imply exists x Px (which is correct) to which Matt pushes back. — Need Logic Help

If Dillahunty did say that (don't know if he did, and don't have time to watch the video), then I do think he made a pretty bad mistake. Bertrand Russell already talked about this subject quite clearly in my opinion:

(2) Over-estimation of the syllogism . The syllogism is only one kind of deductive argument. In mathematics, which is wholly deductive, syllogisms hardly ever occur. Of course it would be possible to re-write mathematical arguments in syllogistic form, but this would be very artificial and would not make them any more cogent. Take arithmetic, for example. If I buy goods worth $4.63, and tender a $5 bill in payment, how much change is due to me? To put this simple sum in
the form of a syllogism would be absurd, and would tend to conceal the real nature of the
argument. Again, within logic there are non-syllogistic inferences, such as: "A horse is an animal, therefore a horse's head is an animal's head." Valid syllogisms, in fact, are only some among valid deductions, and have no logical priority over others. The attempt to give pre-eminence to the syllogism in deduction misled philosophers as to the nature of mathematical reasoning. Kant, who perceived that mathematics is not syllogistic, inferred that it uses extra-logical principles, which, however, he supposed to be as certain as those of logic. He, like his predecessors, though in a different way, was misled by respect for Aristotle.

So I do think that Dillahunty is wrong if he really said:

So, here’s some context: Matt Dillahunty sometimes talks about how Aristotle and his buddies sat down 2000 years ago and discovered all the valid syllogisms. That’s all of them and if your argument doesn’t take one of those forms, it’s invalid or something like that. — Need Logic Help

The issue seems to be that there are formal logical systems that Dillahunty was not paying adequate attention to, but how significant was this error of omission? — Need Logic Help

Ignoring new formal logical systems, such as modal logic and mathematical logic, is a pretty big deal, it amounts to saying (as I think Kant did if my memory serves right) that logic has not made progress since Aristotle, and in modern times some hold that those systems are not important in comparison to aristotelian logic or the subject-predicate logic.

There's no doubt that Aristotle was a genius, being the inventor of formal logic in its first form, but the genius of one man has limits, however great it may have been, and it seems quite arrogant and due to an excess of worship of Aristotle to say that he discovered all there was to discover about logic, since as Russell pointed out:

(...)a man whose opinions and theories are worth studying may be presumed to have
had some intelligence, but (...) no man is likely to have arrived at complete and final truth on any subject whatever.

Your concerns are well-founded. Using classical logic and its spin-off predicate logic, logics Dillahunty seems to be well-versed in, would mean thinking in the same way as Aristotle (roughly 2 millennia ago) and Gottlob Frege (approximately a century ago). That's like going to a modern pharmacy with a prescription made out by none other than Hippocrates who lived around the same time as Aristotle. Hippocrates may have been the go to person back then but his methods, not all but most of it, would be quackery to even a first year student of modern medicine.

Can you elaborate on what exactly Dillahunty gets wrong about logic in the video that I linked above?

I don't know how I could possibly repay you for showing me this; it's an enormous help you're giving me, and I don't know how to return the help! Just let me know any way I can make it up to you!

I'm very ignorant about logic, but I know that Dillahunty (and others) don't seem to interact much with the professionals, and so I always wonder if they're pushing bad logic or bad philosophy.

I don't know how I could possibly repay you for showing me this; it's an enormous help you're giving me, and I don't know how to return the help! Just let me know any way I can make it up to you! — Need Logic Help

:rofl:

Can you elaborate on what exactly Dillahunty gets wrong about logic in the video that I think above? — Need Logic Help

To the extent that I'm aware, the argument that DIllahunty is having with the gentlemen who appear with him in the video is all about the nature of universal claims (all As are Bs and No As are Bs) and particular claims (Some As are Bs and Some As are not Bs) in categorical logic, specifically their existential import (statements that imply the existence of members in a given category). I must warn you that my logic is rusty so do take what I have to say with a pinch of sodium chloride.

First, a non-empty subject categories and the four categorical syllogisms

1. All dogs are mammals
2. No dogs are mammals
3. Some dogs are mammals
4. Some dogs are not mammals

1 is true. Because 2 is the contrary of 1, 2 is false (contraries can't be both true). 3 is true because 3 is the subaltern of 1. Also, 3 is true because it's the contradictory of 2 which is false. 4 is false because it's the contradictory of 1. All relationships as described by Aristotle's traditional square of the opposition holds.

Second, an empty subject category and the four categorical syllogisms

5. All unicorns are horses
6. No unicorns are horses
7. Some unicorns are horses
8. Some unicorns are not horses

According to Peter Abelard, the word "some" implies existence of at least one. Therefore, according to Abelard, statements 7 and 8 are both false because unicorns don't exist. Immediately the subcontrary relationship is made null and void since both are false. By subalternation, statements 5 and 6 are also both false but that would mean 5 and 8 are no longer contradictories and neither are 6 and 7. This to logicians was not acceptable. Given two statements that contradict each other, one has to be true and the other necessarily false. Ergo, statements 5 and 6 are to be treated as simultaneously true, out goes the contrary relationship. Since 5 is true and 7 is false, 6 is true and 8 is false, the subalternation relation too is no longer tenable. Thus we're left with the contradictories 5 and 8, 6 and 7. However, 5 and 6 can't be true if they're seen as having existential import (there are no unicorns). Ergo, 5 and 6 have been stripped of existential import: 5 is translated as IF x is a unicorn THEN, x is a horse and 6 is translated as IF x is a unicorn THEN, x is not a horse. The modern square of the opposition takes shape.

Dillahunty's error is that he employs subalternation - moving from a statement like 5 (All Martians are green) to a statement like 7 (some Martians are green) - when the subject category (Martians) is empty [refer to the unicorns example vide supra]