Essentially I saw this is a flipped conditional now reciting the waltz is necessary for being classically trained which is not the case. As the previous lesson stated triggering the Necessary condition yields no valid conclusion.
Another way I thought of it more in an intuitive way was: Okay lets say 51% of classically trained opera singers can recite the waltz and 51% of those who are no classically trained cannot recite the waltz. This doesn't mean that Anna cannot be apart of that group that is classically trained and cannot recite the waltz.
the fact that this entire unit has zero videos is really pissing me off. I paid for a course with videos and instruction, not examples I could ask AI to do for me for free lol.
Based on the sizes of the supersets and "most people who have not received such training cannot" - "It seems likely that Anna was classically trained" sounds pretty reasonable to me
@KaraSwider dude if ur gonna be choosing the size w bias ofc but this is the lsat where its not cut and stone. I can draw the same diagram but with differently sized circles and different amount shaded and cna get the oppisite
In regards to the opera example, I think at the end of the day, there are some problems where you cant look at it from an objective lawgic view and should use your real-world thinking because when I tried to diagram that, I was lost on finding my conclusion :((
@xyzana YES. sometimes using your intuition is a better tool than mapping it out. These modules are just other tools that can help prevent you from confusing sufficiency and necessity, because most times on the test your intuition may not help. These are good to rely on when all else fails.
“Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend.”
P1: Friends ‑m→ Wizards
P2: /Friends ‑m→ /Wizards
BUT don't confuse this. You cannot take the counter positive of "most" arguments. They will ALWAYS BE INVALID.
Wizards -m --> Friends
This says... Most wizards are Harry's friends...
Wizards are a BIGGER group than Harry's friends. It's absurd then, to think that most of the wizarding world is Harry's friends.
C: Draco Malfoy (Wizard) → Friend (FALSE)
This is invalid...because in the first premise most of Harry's friends are wizards. The conclusion confuses sufficiency for necessity.
Just because Malfoy is a wizard doesn't mean he is Harry's friend! In the first premise we cannot switch the sufficient condition and the necessary condition It is the same for the 2nd premise as well.
The conclusion is false because those conditions aren't met by the premises.
How would "Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend." look like in a subset superset visual? I understand the lawgic but visually I get confused. #help
Most senior-level staff in our office hold graduate-level degrees in Economics or Public Policy. Therefore, Samantha, who has a graduate degree in Economics, is likely to become a senior-level staff member.
For the opera Problem can someone just confirm that this is the correct interpretation
Trained -M> Recite
/Trained -M> /Recite
But the argument is
Recite -> Trained
This is not a valid conclusion because we cannot take the contrapositive of the second premise: /Trained -M> /Recite to be Recite -M> Trained because there are no contrapositives of most staements.
@DanielNahum This is an example of the one too many instances where the "lessons" omit crucial steps in an attempt to slow the progress of the students.
can someone please explain the last argument about harry potter and draco malfoy? I'm confused as to whether this lesson is saying it is a valid or invalid argument.
The conclusion says that because Draco Malfoy is a Wizard, he is probably Harry Potter's friend. This is invalid. Being a wizard is not sufficient for being Harry Potter's Friend. If you read the Lawgic backwards you might think that it is true, but it is false because we are not able to do this.
I am hoping to get clarification on this as I can't remember if it was spoken to in the lessons on most/some etc. If the argument says: "Most of Harry Potter's friends are wizards," could I write the contrapositive as "most people who are not wizards are not harry potter's friends" ?
In the second example within this lesson it says "Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards" so (HPF ‑m→ W) (/HPF ‑m→ /W). I am assuming this is a standalone clause and not the contrapositive of the former argument. If anyone can confirm this I would really appreciate it.
Most classically trained opera singers can recite the lyrics to Musetta's Waltz and most people who have not received such training cannot. It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained.
CTOS = classically trained opera singers
RLMW = can recite the lyrics to Musseta's Waltz
/CTOS = Most people who have not received such training ("such training" is a referential for "classically trained opera singers")
/RLMW = cannot (another referential. This time it refers to "recite the lyrics to Musseta's Waltz", negating it.)
A= Anna
So the Lawgic translation is:
CTOS ‑m→ RLMW
/CTOS ‑m→ /RLMW
A RLMW
---------------------
A CTOS
This is invalid because it's reading the ‑m→ arrow backwards as RLMW ‑m→ CTOS when it is the other way around.
For the conclusion to be valid it would've had to read "It seems likely, therefore, that Anna, who was classically trained, can recite the lyrics to Musetta's Waltz."
It helps to think about this visually in terms of intersecting sets. Let's look at the HP example. We can imagine two sets: wizards and Harry Potter's friends.
What we're told is that most of Harry's friends are wizards. So, let's imagine a circle that makes up Harry's friends and a larger circle that makes up all wizards. There will be an intersection between these two circles that contains more than half of Harry's friends. The majority of Harry's friends fall within the superset of being wizards. Therefore, some wizards are Harry's friends, but we are not told the ratio of the wizards set that intersects with Harry's friends.
Therefore, "Most of Harry Potter's friends are Wizards" does not imply that most wizards are Harry's friends. That would mean that the set of Harry's friends would contain more than half of all wizards, which is not stated and does not make intuitive sense – there are probably many more wizards than Harry's friends within the Wizarding World.
So the last paragraph, "Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend." is invalid?
I thought about it in terms of sufficient vs necessary. Satisfying the necessary condition of being a wizard, per the first premise, is not enough to guarantee satisfying the sufficient (being Harry Potter's friend).
It's a statistical generalization flaw. For example: Most of my friends are human. You are a human, so you are probably my friend.
Are we friends? Realistically, no. Just because you are a human doesn't mean you will likely be my friend. It's overgeneralizing my relationship with most of my friends to you, which makes this argument logically invalid.
Most of my friends have blue eyes. Most people who are not my friends dont have blue eyes, therefore if someone has blue eyes they are likely my friend.
Its hard for me to explain why that is incorrect but I think we call all see how its an absurd claim to say that since someone has blue eyes (which is like hundreds of millions of people) they are likely my friend.
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93 comments
One thing I've noticed is that they try to trick you with "Most." Most can leave an exception for some.
where are the videos for these? :/
How do we deal with "probably" claims, like in the opera example?
could we also say in the opera example, that the conclusion is confusing sufficiency for necessity. In other words, lawgic says:
Classically trained -m-> recite musetta Waltz
/classically trained -m-> /recite musetta Waltz
Conclusion: Recite Musetta waltz (Anna) --> Classically trained
Essentially I saw this is a flipped conditional now reciting the waltz is necessary for being classically trained which is not the case. As the previous lesson stated triggering the Necessary condition yields no valid conclusion.
Another way I thought of it more in an intuitive way was: Okay lets say 51% of classically trained opera singers can recite the waltz and 51% of those who are no classically trained cannot recite the waltz. This doesn't mean that Anna cannot be apart of that group that is classically trained and cannot recite the waltz.
Gosh sorry for the all words!
the fact that this entire unit has zero videos is really pissing me off. I paid for a course with videos and instruction, not examples I could ask AI to do for me for free lol.
#feedback
I think it helps clear this up to say: It could be likely — but it could also be unlikely. and thats the nuance of the LSAT.
@KaraSwider dude if ur gonna be choosing the size w bias ofc but this is the lsat where its not cut and stone. I can draw the same diagram but with differently sized circles and different amount shaded and cna get the oppisite
@JKang bro it literally says "Classically trained opera singers number in the thousands. People who are not so trained number in the billions."
no wonder you guys need videos to make it through - was just trying to add visuals to a section with all text. best wishes.
This entire unit is messed up, why am I paying for lessons I could just ask ChatGPT for or make flash cards for.
In regards to the opera example, I think at the end of the day, there are some problems where you cant look at it from an objective lawgic view and should use your real-world thinking because when I tried to diagram that, I was lost on finding my conclusion :((
@xyzana YES. sometimes using your intuition is a better tool than mapping it out. These modules are just other tools that can help prevent you from confusing sufficiency and necessity, because most times on the test your intuition may not help. These are good to rely on when all else fails.
For the last example...for those WHO NEED HELP:
“Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend.”
P1: Friends ‑m→ Wizards
P2: /Friends ‑m→ /Wizards
BUT don't confuse this. You cannot take the counter positive of "most" arguments. They will ALWAYS BE INVALID.
Wizards -m --> Friends
This says... Most wizards are Harry's friends...
Wizards are a BIGGER group than Harry's friends. It's absurd then, to think that most of the wizarding world is Harry's friends.
C: Draco Malfoy (Wizard) → Friend (FALSE)
This is invalid...because in the first premise most of Harry's friends are wizards. The conclusion confuses sufficiency for necessity.
Just because Malfoy is a wizard doesn't mean he is Harry's friend! In the first premise we cannot switch the sufficient condition and the necessary condition It is the same for the 2nd premise as well.
The conclusion is false because those conditions aren't met by the premises.
How would "Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend." look like in a subset superset visual? I understand the lawgic but visually I get confused. #help
It makes sense to me at first, but then when I try to apply Lawgic to explain it, I start to confuse myself lol
Back again with another explanation in hopes of it helping you because it might help me.
The key take away here: Don't read unidirectional arrows backwards
Just because most A are B, does not mean most B are A
Example:
Most of the water I drink is freshwater. Therefore, most freshwater is drank by me.
Lawgic:
Water I drink -m-> Freshwater
-----
Freshwater -m-> Drank by me
Is this valid? Does the premise being true make the conclusion true? NO! THIS IS INVALID.
Just because most of the water I drink is freshwater, DOES NOT MEAN that most of the freshwater is drank by me.
Just because most A are B, DOES NOT MEAN most B are A.
I wish they had videos for these lessons. I'm wasting way too much time trying to confirm if I got the examples right. This is so annoying.
Example:
Most senior-level staff in our office hold graduate-level degrees in Economics or Public Policy. Therefore, Samantha, who has a graduate degree in Economics, is likely to become a senior-level staff member.
Down with the unidirectional trickery! And the therefore and the assumptions of conclusions!
Most of the food I eat is Cheetos, therefore most of the Cheetos that exist are eaten by me.
For the opera Problem can someone just confirm that this is the correct interpretation
Trained -M> Recite
/Trained -M> /Recite
But the argument is
Recite -> Trained
This is not a valid conclusion because we cannot take the contrapositive of the second premise: /Trained -M> /Recite to be Recite -M> Trained because there are no contrapositives of most staements.
@DanielNahum This is an example of the one too many instances where the "lessons" omit crucial steps in an attempt to slow the progress of the students.
Why?
@DanielNahum Thats what I put too! I wanted confirmation but didnt recieve it :(
can someone please explain the last argument about harry potter and draco malfoy? I'm confused as to whether this lesson is saying it is a valid or invalid argument.
Harry Potter's Friends ‑m→ Wizard
/Harry Potter's Friends ‑m→ /Wizard
Draco Malfoy →Wizard
The conclusion says that because Draco Malfoy is a Wizard, he is probably Harry Potter's friend. This is invalid. Being a wizard is not sufficient for being Harry Potter's Friend. If you read the Lawgic backwards you might think that it is true, but it is false because we are not able to do this.
I am hoping to get clarification on this as I can't remember if it was spoken to in the lessons on most/some etc. If the argument says: "Most of Harry Potter's friends are wizards," could I write the contrapositive as "most people who are not wizards are not harry potter's friends" ?
In the second example within this lesson it says "Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards" so (HPF ‑m→ W) (/HPF ‑m→ /W). I am assuming this is a standalone clause and not the contrapositive of the former argument. If anyone can confirm this I would really appreciate it.
there is no contrapositive
Can someone explain to me this lesson, but with another example? Thank you!
For example,
Most dogs love to dig. Most things that are not dogs do not like to dig. Bob the Builder, who loves to dig, is probably a dog.
You see how the assumption is made that the human bob the builder is probably a dog just bc he likes to dig?
Let me know if the example helped!
l
Most classically trained opera singers can recite the lyrics to Musetta's Waltz and most people who have not received such training cannot. It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained.
CTOS = classically trained opera singers
RLMW = can recite the lyrics to Musseta's Waltz
/CTOS = Most people who have not received such training ("such training" is a referential for "classically trained opera singers")
/RLMW = cannot (another referential. This time it refers to "recite the lyrics to Musseta's Waltz", negating it.)
A= Anna
So the Lawgic translation is:
CTOS ‑m→ RLMW
/CTOS ‑m→ /RLMW
A RLMW
---------------------
A CTOS
This is invalid because it's reading the ‑m→ arrow backwards as RLMW ‑m→ CTOS when it is the other way around.
For the conclusion to be valid it would've had to read "It seems likely, therefore, that Anna, who was classically trained, can recite the lyrics to Musetta's Waltz."
Thank you!
After seeing so many lesson on negating and reversing claims to see the valid conclusion. It confuses me now that we are like do not negate "most"
This makes absolutely no sense to me!
It helps to think about this visually in terms of intersecting sets. Let's look at the HP example. We can imagine two sets: wizards and Harry Potter's friends.
What we're told is that most of Harry's friends are wizards. So, let's imagine a circle that makes up Harry's friends and a larger circle that makes up all wizards. There will be an intersection between these two circles that contains more than half of Harry's friends. The majority of Harry's friends fall within the superset of being wizards. Therefore, some wizards are Harry's friends, but we are not told the ratio of the wizards set that intersects with Harry's friends.
Therefore, "Most of Harry Potter's friends are Wizards" does not imply that most wizards are Harry's friends. That would mean that the set of Harry's friends would contain more than half of all wizards, which is not stated and does not make intuitive sense – there are probably many more wizards than Harry's friends within the Wizarding World.
So the last paragraph, "Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend." is invalid?
I thought about it in terms of sufficient vs necessary. Satisfying the necessary condition of being a wizard, per the first premise, is not enough to guarantee satisfying the sufficient (being Harry Potter's friend).
It's a statistical generalization flaw. For example: Most of my friends are human. You are a human, so you are probably my friend.
Are we friends? Realistically, no. Just because you are a human doesn't mean you will likely be my friend. It's overgeneralizing my relationship with most of my friends to you, which makes this argument logically invalid.
Yes that is invalid. Here is another example:
Most of my friends have blue eyes. Most people who are not my friends dont have blue eyes, therefore if someone has blue eyes they are likely my friend.
Its hard for me to explain why that is incorrect but I think we call all see how its an absurd claim to say that since someone has blue eyes (which is like hundreds of millions of people) they are likely my friend.