Most lecturers and books would've just throw the mathematical definition of wff to students and move on. Kudos for thoroughly explaining this topic! This channel is very underrated!
@v1z4 that's the book my prof used in my first logic class! Yeah, I think some of these authors are so smart they think some of these ideas are too obvious to cover. Luckily, I don't have that problem! Wait...
Thank you for your help! So, Will the following be considered as WFF. 1. C v~ C v. 2. ~ A * ~~ B 3. ~(Z- -> Z) 5. (A --> B) --> (C ≡ D) --> (E v F --> G) 6. A --> (E D) 7. ~A --> (A v ~ A) 8. ~~A --> (A v A) 9. Z v BB 10. ~Z v ~BB Thank you for your help and support.
1 should be (Cv~C). The extra v at the end definitely makes it not a wff 2 is technically not a wff because it doesn’t have outer parentheses. dropping those parentheses is a standard abbreviation, but unless you have that abbreviation written into your syntax, it’s not technically speaking a wff 3 is a wff 5 is missing several parentheses. Notice that it’s ambiguous if the last part should be ((EvF)->G) or (Ev(F->G))
Actually now I’m noticing none of these have outer parentheses, so my comment on 2 is probably not important. Your prof is probably using a syntax with that built in
6, 9, and 10 have basic propositions set right next to each other with no connectives in between. Some syntaxes use this for a conjunction, but it looks like you guys are using a dot? Is that what the asterisk stands for in 2? If so, 6, 9, and 10 are not wffs
Hello, Thanks for your help. I have another question please advise. Please are the following substitution instances on the substitution form(logical form) I listed below ? Substitution instance: ~ ~ ( A v ~A) v ~ ~ B Substitution form: P P v q
You do have the form PvQ: P = ~~(Av~A) Q= ~~B Both formulae are well-formed, so PvQ is well-formed. However, in order to be a case of P PvQ you would have to have P written out before PvQ. So, it should look like this: ~~(Av~A) ~~(Av~A ) v ~~B This is important because saying that P is true entails that PvQ is true. It's kind of weird, but the idea is that "PvQ" means "at least one of these two things P or Q is true, possibly both". So, if we claim P is true first, then it is already the case that at least one of those two things is true, namely P. It's weird because it sounds like we can use this to prove something about Q, which is just some random proposition we threw in there, but with the disjunction you can't conclude anything unless you can negate one of the disjuncts, and we just affirmed P, so we can't do anything with Q.
Most lecturers and books would've just throw the mathematical definition of wff to students and move on. Kudos for thoroughly explaining this topic! This channel is very underrated!
Thanks so much for that! Part of my mission is to make logic accessible, so I really appreciate that you noticed!
@v1z4 that's the book my prof used in my first logic class! Yeah, I think some of these authors are so smart they think some of these ideas are too obvious to cover. Luckily, I don't have that problem! Wait...
Awesome video, it helps me a lot, thank you so much!!!
Juan Andrés Flores Gutiérrez thanks so much for letting me know! Stoked to be of help!
12:00 But is it not just 1.iii that allows us to put parentheses in WFFs and preserve validity?
1.iii just tells you the symbols, not the rules for how to use them
Thank you for your help!
So, Will the following be considered as WFF.
1. C v~ C v.
2. ~ A * ~~ B
3. ~(Z- -> Z)
5. (A --> B) --> (C ≡ D) --> (E v F --> G)
6. A --> (E D)
7. ~A --> (A v ~ A)
8. ~~A --> (A v A)
9. Z v BB
10. ~Z v ~BB
Thank you for your help and support.
1 should be (Cv~C). The extra v at the end definitely makes it not a wff
2 is technically not a wff because it doesn’t have outer parentheses. dropping those parentheses is a standard abbreviation, but unless you have that abbreviation written into your syntax, it’s not technically speaking a wff
3 is a wff
5 is missing several parentheses. Notice that it’s ambiguous if the last part should be ((EvF)->G) or (Ev(F->G))
Actually now I’m noticing none of these have outer parentheses, so my comment on 2 is probably not important. Your prof is probably using a syntax with that built in
Chico the Philosurfer Thank you very much!!!
I really appreciate it, I will drop my questions in the comment section if I have any other questions.
Once again, Thank you very much!
6, 9, and 10 have basic propositions set right next to each other with no connectives in between. Some syntaxes use this for a conjunction, but it looks like you guys are using a dot? Is that what the asterisk stands for in 2? If so, 6, 9, and 10 are not wffs
Hello,
Thanks for your help.
I have another question please advise.
Please are the following substitution instances on the substitution form(logical form) I listed below ?
Substitution instance:
~ ~ ( A v ~A) v ~ ~ B
Substitution form:
P
P v q
You do have the form PvQ:
P = ~~(Av~A)
Q= ~~B
Both formulae are well-formed, so PvQ is well-formed.
However, in order to be a case of
P
PvQ
you would have to have P written out before PvQ. So, it should look like this:
~~(Av~A)
~~(Av~A ) v ~~B
This is important because saying that P is true entails that PvQ is true. It's kind of weird, but the idea is that "PvQ" means "at least one of these two things P or Q is true, possibly both". So, if we claim P is true first, then it is already the case that at least one of those two things is true, namely P. It's weird because it sounds like we can use this to prove something about Q, which is just some random proposition we threw in there, but with the disjunction you can't conclude anything unless you can negate one of the disjuncts, and we just affirmed P, so we can't do anything with Q.