[Logic] Predicate Logic

[@matejpavel2296]

I literally went from "I don't have a single clue what's going on" to a passable understanding in under 20 minutes. Hat's off.

[@Ulikela]

Even though u hv a 2 hours lecture, it's still have no clue what's going on

[@VictorianoOchoa]

The way you casually laughed at your mistake at 2:30 makes this video that much better.

[@anonymousmask4224]

8 Years and still best explanation ever on Why to use specific connectives for quantifiers. Kudos to you.

[@macestarwalk2474]

Oh my god for the first 2 and half minutes of the video I was confused AF because you wrote that he was immortal. I was trying to figure out how the heck that contradiction could possibly make sense 😂

[@zyansheep]

I just justified it to myself saying that the proposition "Socrates is immortal" is false based on the previous propositions.

[@lutfilutfi3310]

brilliant video man. Builds the need of why you need predicate logic instead of just handing out the formulas

[@hannahbogahi4684]

If you understand can you help me out

[@lutfilutfi3310]

@@hannahbogahi4684 sure which part dont you get?

[@hannahbogahi4684]

Both the negations and the predicate part

[@lutfilutfi3310]

@@hannahbogahi4684thats a bit too long of a long explanation , do you have a discord

[@hannahbogahi4684]

@@lutfilutfi3310 no I don't have any disagreement but it is just too tough

[@tiptoe1413]

Immortal? you caught it.

[@weijie7]

Hello, question. at 16:00, shouldn't Hx be 0 as your population has x that are sad too (not knowing they are men or women)? I know in the end the first conditional rule will still be true, but just to clarify this detail

[@isawilraen9816]

At around 13:00 and onwards where you were showing why we use different connectives for different quantifiers: You showed that, when MarkIsHappy, SteveIsHappy, JocelynIsSad, we get 0->1=1, and 0^1=0, respectively. So, Mx here means that x is a man. That will ofc be 0 for each. But, Hx here seemed to expressly mean that "man is happy"... which is 1 for each, yes, and thus the above statement =1, while the below one =0. So it checks out. But, it just seems confusing to think that Hx here means "man is happy" instead of "x is happy". I mean, for every object (x) that we check in our universe of xs, sure, Mx won't be true, so it's 0. But it seems strange that Hx is always 1. Like, how do we remember that Hx only checks whether the men are happy? Because there is afterall an x (Jocelyn) that is not happy. It feels much more intuitive to just think about it as follows: IS IT TRUE THAT IN THE CASE OF EACH x ie object in that universe 1) WHENEVER x is a man, x is also happy? Yes. 1) x is a man, AND x is happy? No. It is not true that in the case of each object in that universe x is a man and x is happy. The latter feels more intuitive, like I said, but of course, if what Hx MEANS is happy man, then that is correct as well. It's just that the meanings seem rather arbitrary. But this makes me wonder if I've missed something necessary, or if I'm just looking at convention that happens to be confusing to me.

[@mhdfrb9971]

Are you just assume their gender?

[@tomasmateus17]

I still cant get this shit 🙃 im going to fail so hard

[@bonbonpony]

00:31 You meant Socrates is MORTAL, right? Proving otherwise would be an indication of an error :q BTW how about introduction and elimination rules for these quantifiers?

[@unh0lys0da16]

Apparantly he didnt understand them so he didn't cover them

[@johantitulaer1052]

He wrote it wrongly because he was talking. He meant to say: "a mortal" but it sounds similar to immortal.

[@alvin3832]

Maybe Socrates is in fact immortal?

[@deborahiranezereza6040]

This might seem random, but thank you!! U just saved my life😭… my book was not doing a good job. God bless you!

[@faiza.s6509]

Thank you!!! I was so stuck over predicates and this really cleared things up! Thank youuuuu

[@georgejerry1545]

15:17 wouldn’t Hx still be 0? Isnt Hx symbolizes all x (not men) are happy? If that’s the case, then since Jocelyn is sad, then Hx is 0, no? Well, if that’s the case, it’s still fine since the antecedent Mx is false, making the statement still true, right?

[@arpi6054]

you’re literally a life saver

[@eliwidd]

crazy good teaching

[@NghiaNguyen-lp1us]

very clear, thank you!

[@mohammedal-shaboti7939]

The examples at the end help a lot, Thanks for sharing :)

[@PizzaPunt99]

Thanks!

[@rxrider1451]

Really helped with intuition. Thanks!

[@timmeeyh6523]

2:29 I was looking forward to an awsome proof by contraposition of some kind!

[@ThisIsNotMyHandle]

Excellent job!

[@proggenius2024]

man you are teaching math like a book! Keep it up.

[@mamtasingh8373]

Is general language different from language used in logic in terms of precisely defining things.

[@affumcollins3375]

Easy understandable 👍😀👍😀

[@farah-bq3rg]

you are amazing

[@aizazkhan5439]

You are a great teacher. If not for this, I would have to spend a full day looking into Predicate Logic. Thank you so much. **P.S: university lectures are dog shit.**

[@kamenzhelyazkov8575]

2:26 I just suggested that you are starting with the opposite, proving that it is wrong ;D

[@oskaraltman]

at 15:54 Does Hx mean x is happy for all x because of the quantifier? Because it doesn't make sense to me that Hx is true for all x even though Jocelyn is sad. It doesn't change the truth of the implication or the conjunction, however i am confused why Hx is true in this case.

[@oskaraltman]

unless Hx means something like if x is a man then x is happy or x is happy or a woman or something.

[@kyejocham483]

Amazing!

[@marinastamou4246]

could you create a video explaining the problem of improper definite descriptions? Thank you!

[@wecros3249]

Hi, thanks for the video. Could you elaborate on 15:15, please? If Steve was pointing to Sad, meaning Mark is happy and Steve sad, would that mean that ∀x(Mx -> Hx), where Mx is 0 and Hx is 0, means "All men are happy", even though they are not judging by common sense? Thank you!

[@PizzaPunt99]

Did you ever find the answer, I am stuck on this too

[@wecros3249]

@@PizzaPunt99 I passed the exam, that's all I remember now :D But go with your guts on this one, I think I was onto something here though.

[@PizzaPunt99]

I believe the answer is that when the left side of an implication is false we can just assume that the right side is true as it doesn't matter anymore because the statement we are making a conclusion out of is false

[@PizzaPunt99]

@@wecros3249 just had my exam, hope I passed

[@Logos59]

Actually the truth tables say this is true. Even if Mx is 0 and Hx is 0; "All men are happy" is true. I think the same as you; although by common sense you would say is false, the conditional says is true. This is actually troubling in my mind. I'm obsessed with logic but there are cases like this that make me mad. It's like is not connected to our reality.

[@apataoyinlade3033]

Thanks a lot for this

[@computerscience901]

When we use universal quantifiers for all ∀x , does that mean everyone in our domain of discourse of discourse is "x" ?

[@Trevtutor]

It depends what follows it. If we say "∀x Dog(x)", then that means everything in our universe is a dog. If we say "∀x (Dog(x)->Happy(x))", then that means that every dog in our universe is happy. ∀x is just like a variable statement, "for every x".. then something.

[@computerscience901]

Wow. Didn't expect the GREAT TrevTutor to respond to my comment. (bows down) . Thank you for your awesome response. One follow through question: ∀x Dog(x)->Happy(x) V ∀y Penguin(y)->Happy(y) What does this mean in respect to our domain of discourse ? Does that mean everyone in our domain is some form of hybrid penguin/dog ?

[@computerscience901]

∀x (Dog(x) -> Happy(x)) V ∀y (Penguin(y) -> Happy(y)) . For some reason the formula to the previous question go crossed off. (Formula above is for the previous question)

[@Trevtutor]

This means that "Every dog is happy or every penguin is happy". These are variables stating something like "For every x, if x is a dog then x is happy. OR. For every y, if y is a penguin, then y is happy." The conditional means "if-then", so we should treat it like "if variable satisfies this first part, then the variable also satisfies this second part."

[@vigneshkumar4546]

At 10:08 why can't we take cake and pie as a single unit?

[@Logos59]

Cause of the word "and" which is the ^ operator. It separates it in two.

[@paurushgargtube]

thnks

[@speconcloud9]

Tahnk you :)

[@timbarnbou372]

Amazing

[@liamtaylor5523]

Thanks for the video, question: how do you define Existential quantifier (backwards E) as “some” when it can also represent a single item having that property only which wouldn’t be some.

[@ajricherson1099]

think of it as "there exists some value(s) ..."

[@madhavi120]

A is brother of B if A is a male, A has father F and mother M and B has the same mother and father as A does. Translate these facts into formulae in predicate logic

[@alahuakbar4442]

man pls answer my question, all men like cake and pie can also be written. by “Ax(M(x)->Lx(c^p))?

[@alahuakbar4442]

“?*

[@paque-music]

no you cannot

[@alahuakbar4442]

Sven explain man

[@alahuakbar4442]

why not becoz the statement “Lx(c^p) is also men like cakes and pie

[@hypotheticallyspeaking]

∀x [(Mx -> (Lxc V Lxp)]. For every x is such that if x is a man, then x likes cake or a pie or both.

[@mamtasingh8373]

Help professor,this doubt is eating me up for days, Does dog refers to class/group of all animals satisfying dog properties or refers to every individual satisfying dog conditions

[@yoroo3000]

blessings

[@oOJw9gKX8YOTz8BHSdlmDg]

Bruh I thought I was tripping until 2:30

[@rumi2245]

Thx

[@nathanvanlent9407]

Sorry but isn’t scocrates mortal if he is a man and all men are mortal?

[@CaesarInVa]

Caught it about 2 seconds before you mentioned it.

[@efbdvtfbrt7027]

I now learned men likes pee

[@lekoicy]

Lojban

[@mastermind2971]

Its pie not p

[@mastermind2971]

Lol

[@BlightHeart]

I am not a happy man that's for sure.

[@leetheee]

all men aren't happy

[@lederpsta42]

You get a lot wrong in this.

[@zaccalvert7341]

Lucky he made this video 9 years ago. Him changing the name "Mary" to a "mans name" Mark? Dude would have been cancelled af

[@Trevtutor]

In 2024 anyone can be any gender so really I was just super progressive in hindsight 😉

[@rastisdiq4142]

​@@Trevtutor That is bull*it. If you have an xy chromosome you ARE a man. And If you have an xx chromosome you ARE a woman. That's simple biology

[@Salamanca-joro]

​@@rastisdiq4142damn 🥷🏾 its a joke

[@mamtasingh8373]

Help professor,this doubt is eating me up for days, Does dog refers to class/group of all animals satisfying dog properties or refers to every individual satisfying dog conditions

[@supernenechi]

I am by no means an expert, but from what I gathered he meant that for absolutely everything you can point to in the universe, if it is a dog then it satisfies that condition. It depends on the universe you're looking at. Your universe could be filled with only animals, or filled with mostly osmium atoms. If you pick a point, any point, and it's a dog, then it satisfies that condition