Not many comments on this video, but that says nothing about the material. I found the two videos immensely helpful in putting into a larger framework of philosophy, logic, mathematics, and political history, my knowledge, observations, and a few ideas from going through parts of Frege's "Grundgesetze der Arithmetik." Truly, much thanks. It's too bad there is not more widely known some of the underlying ideas of mathematics and logic.
Nice lecture. Wish the speaker would spend more time explaining some of the ideas. Too happy just posting slides and rushing through the lecture without really giving examples and making real sense. Yes, Frege's work was decimated by Russel's Paradox, but Russel's work and some of Hilbert work was decimated by Godel's work. What goes around comes around.
Sure but Godel's work didn't, so far as I know, decimate the portions of Russell's work that Priest mentioned in the video. So its a bit besides the point, isn't it?
How long do you want the lecture to be? 3 hours? To go into immense detail in the format of a lecture wouldn't be practical. Go back and read the mathematicians/philosophers work in question to gain the best understanding possible of the ideas hinted at in the talk.
It's not clear to me why the two examples @23:02 express different notions. Is it agreed upon that reversing the order of the quantified variables conveys some different meaning, or did Priest merely mis-type? To be clear, I understand that the sentence "everyone saw somebody" has multiple (and distinct meanings), but do the translations into first-order logic really convey these two meanings? If so, why?
Yes, it's agreed that they convey those meanings, so far as I know. The order of the quantifiers change the scope, and so change how we interpret what's being said. To explain: "*∀x∃y xSy*" - The existential quantifier is in the scope of the universal quantifier, so this is translated as "For every x (every student), there is some y (some person which exists) such that each student saw some person". In other words, for each student, it is the case that they saw a person. Think of the "There is some Y" as extending FROM every student. The existential quantifier is bound to the universal quantifier here. "*∃y∀x xSy* - The universal quantifier is now within the scope of the existential quantifier, so this is translated as "There is some y (a singular person) such that every x saw that person y". In other words, think of the universal quantifier as extending FROM the existential quantifier, from a particular person, to being seen by every student. I hope that was helpful!
very helpful and informative. thank you for this post.
Not many comments on this video, but that says nothing about the material. I found the two videos immensely helpful in putting into a larger framework of philosophy, logic, mathematics, and political history, my knowledge, observations, and a few ideas from going through parts of Frege's "Grundgesetze der Arithmetik."
Truly, much thanks.
It's too bad there is not more widely known some of the underlying ideas of mathematics and logic.
Everybody saw someone? Everybody was Kung-Fu fighting.
Nice lecture. Wish the speaker would spend more time explaining some of the ideas. Too happy just posting slides and rushing through the lecture without really giving examples and making real sense.
Yes, Frege's work was decimated by Russel's Paradox, but Russel's work and some of Hilbert work was decimated by Godel's work. What goes around comes around.
Sure but Godel's work didn't, so far as I know, decimate the portions of Russell's work that Priest mentioned in the video. So its a bit besides the point, isn't it?
How long do you want the lecture to be? 3 hours? To go into immense detail in the format of a lecture wouldn't be practical. Go back and read the mathematicians/philosophers work in question to gain the best understanding possible of the ideas hinted at in the talk.
It's not clear to me why the two examples @23:02 express different notions. Is it agreed upon that reversing the order of the quantified variables conveys some different meaning, or did Priest merely mis-type? To be clear, I understand that the sentence "everyone saw somebody" has multiple (and distinct meanings), but do the translations into first-order logic really convey these two meanings? If so, why?
Yes, it's agreed that they convey those meanings, so far as I know. The order of the quantifiers change the scope, and so change how we interpret what's being said. To explain:
"*∀x∃y xSy*" - The existential quantifier is in the scope of the universal quantifier, so this is translated as "For every x (every student), there is some y (some person which exists) such that each student saw some person". In other words, for each student, it is the case that they saw a person. Think of the "There is some Y" as extending FROM every student. The existential quantifier is bound to the universal quantifier here.
"*∃y∀x xSy* - The universal quantifier is now within the scope of the existential quantifier, so this is translated as "There is some y (a singular person) such that every x saw that person y". In other words, think of the universal quantifier as extending FROM the existential quantifier, from a particular person, to being seen by every student.
I hope that was helpful!