Syllogisms, Premises, and Conversion Rules | Prior Analytics (cc. 1-3) | Aristotle

- What is a syllogism, a premiss, a term?
- What are the conversion rules for assertoric, apodeictic, and problematic propositions?

[tjsurname]

Whoa ! Thank you. It will take me months to digest the basics of this. Anyone who grasped it on the first two or three watches - you must be brilliant beyond my imaginings ! But alas ! Where natural brilliance fails me. . . . hard work and devotion to comprehending this will prevail. . . .eventually I pray ! Thank you. I wish I had learned this at school. With the right teacher, this could have been made wonderful. Thank you for being the right teacher, albeit many decades after I wished I had learned this knowledge and developed my skills with the benefit of having known of it earlier! God Bless you and Peace be with you Dear Prof. Elliot Polsky and Friends reading this. AMAZING. I am addicted to this channel.

[MT-]

Wonderful discovery in YT... This content is GOLD.

[AndresOnu]

Thanks for these videos. Great help for our discussion group as we work through the Complete Works as total amateurs!

[WoolleyWoolf]

This is an amazing and pedagogical way of reading…kudos mate

[arshia]

Now I understand why I read it and didnt understand

[axelbatalha]

It's highly confusing when a necessary proposition is called apodeictic while the demonstrative proposition is called αποδεικτικός by Aristotle.

[TruthNerds]

The conversion of a universal affirmative ("Every swan is white") is a particular affirmative ("Something white is a swan")? I'm not willing to accept that because the latter requires swans to exist (at least if something white exists) but the original statement does or should not.

Now, of course, we know that swans and white things exist, but the entire point of the exercise is to look at the structure only, so we should be able to say, neutrally, "Everything A is B" and the alleged conversion "Something B is A".

Also, we can essentially define that "every A is B" shall imply that at least one A exists. But I don't think that's a good idea for the following reasons:

FIrst, the conventions I personally know, e.g. in programming (all function in Haskell, std::all_of in C++) or first-order logic (∀x: A(x) → B(x) is true if there is no x such that A(x))

Second, in mathematics, it is quite useful to construct statements of the form "Every _something that doesn't exist_ is …" for the purpose of proof by contradiction.

Third, and I admit that's rather technical, if we don't consider "Every A is B" to imply the existence of an A, and we need that, though, we can easily add an axiom to our axiomatic system that says "There is an A". However, if we do consider that "Every A is B" implies this and we do not want this additional axiom, we need to remove it with an implication: "If there is an A, then every A is B." and an implication translates to a disjunction ("There exists no A or every A is B."), which can't be a separate axiom because axioms are effectively combined in a conjunction (logical and).

(Maybe I'm missing something, of course…)