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
(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, 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
(...)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.
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
Can you elaborate on what exactly Dillahunty gets wrong about logic in the video that I think above? — Need Logic Help
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.