“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.
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.
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."
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?
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.
So are you saying this argument is invalid, since you're embellishing the invalid "Opera" argument? It would be helpful to say if it is or isn't, instead of being cryptic. Thanks.
“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
C: Draco Malfoy (Wizard) → Friend
versus…
“Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is Harry Potter's friend, is probably a wizard.”
#feedback I'd recommend removing the word "because" in the "Let's review" section here. The two clauses in this sentence are linked, but the second clause is not a comprehensive explanation for the first.
So are "conclusions" that can be inferred from the Opera example that:
1) there are some trained who cannot recite the lyrics
2) there are some who can recite the lyrics who are not trained
And with Harry:
1) some of Harry's friends are not wizards
2) some wizards are not Harry's friends
If not, why not?
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81 comments
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.
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.
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.
Can someone explain to me this lesson, but with another example? Thank you!
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."
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!
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?
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.
So are you saying this argument is invalid, since you're embellishing the invalid "Opera" argument? It would be helpful to say if it is or isn't, instead of being cryptic. Thanks.
so, is the Harry Poter example valid? I think it is. The use of 'probably' indicates that Draco Malfoy might or might not be Harry Poter's friend.
#feedback It might be helpful to put quotation marks around "Most" in the title of this page
“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
C: Draco Malfoy (Wizard) → Friend
versus…
“Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is Harry Potter's friend, is probably a wizard.”
P1: Friends ‑m→ Wizards
P2: /Friends ‑m→ /Wizards
C: Friend → Draco Malfoy (Wizard)
#feedback I'd recommend removing the word "because" in the "Let's review" section here. The two clauses in this sentence are linked, but the second clause is not a comprehensive explanation for the first.
7sage, STOP using "reason why" it is redundant and makes this program seem unprofessional. I would not trust an attorney using this phrase.
-
So are "conclusions" that can be inferred from the Opera example that:
1) there are some trained who cannot recite the lyrics
2) there are some who can recite the lyrics who are not trained
And with Harry:
1) some of Harry's friends are not wizards
2) some wizards are not Harry's friends
If not, why not?