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.
If these last several lessons are ever updated, it would be so helpful if you could replace the "A"s and "B"s in the Lawgic write-ups with the actual example being used (ie Harry Potter friends/wizards or Jedi/Force, etc.). It would make following along and comparing our own work much easier.
To understand that the conclusion in the second example is invalid, (Anna is classically trained), we just have to look at the word most.
From the lessons about the quantifier "most", we know that "most" can include "all", but not always. In this example, saying that Anna was classically trained because she can recite Musetta's Waltz is erroneous.
The example assumes that only classically trained opera singers can recite Musetta's Waltz and that people who are not classically trained cannot recite Musetta's Waltz. However, the example said most, not all.
By following these assumptions, the example also made the error of confusing necessity with sufficiency by saying that her ability to recite is a sufficient condition for her being classically trained.
If this example followed the assumption they made in the conclusion, the lawgic would be:
classically-trained --> recite
/classically-trained --> /recite
NOT
recite --> classically-trained
/recite --> /classically trained
As a whole, however, we cannot validate whether Anna was classically trained because we only know that the majority of classically trained opera singers can recite Musetta's Waltz and the majority can’t. Anna may be classically trained, but she also could be the large minority of un-trained people in the world who can recite it. The correct lawgic is:
Some people in the comments are saying using their own intuition helped them parse this example easier (which is great!), but if you write the example down, IMO the lawgic makes it incredibly simple.
trained -m-> MW
/trained -m-> /MW
To my knowledge, we have no valid argument forms that would apply here. Even if the second premise was formatted as a contrapositive, which it is not, we know that contrapositives don't apply to some, most, and many.
The way that I thought about the opera example in my own terms:
Most NBA players can dunk a basketball, and most people who are not NBA players cannot. Therefore, it seems likely that since I can dunk, I play in the NBA.
1- There are very few NBA players in the world. Just because I can dunk doesn't offset the very low statistical probability that I am an NBA player.
2- There are plenty of other people who can dunk but are not in the NBA (e.g. college basketball players or retired NBA players).
11
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77 comments
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?
If these last several lessons are ever updated, it would be so helpful if you could replace the "A"s and "B"s in the Lawgic write-ups with the actual example being used (ie Harry Potter friends/wizards or Jedi/Force, etc.). It would make following along and comparing our own work much easier.
To understand that the conclusion in the second example is invalid, (Anna is classically trained), we just have to look at the word most.
From the lessons about the quantifier "most", we know that "most" can include "all", but not always. In this example, saying that Anna was classically trained because she can recite Musetta's Waltz is erroneous.
The example assumes that only classically trained opera singers can recite Musetta's Waltz and that people who are not classically trained cannot recite Musetta's Waltz. However, the example said most, not all.
By following these assumptions, the example also made the error of confusing necessity with sufficiency by saying that her ability to recite is a sufficient condition for her being classically trained.
If this example followed the assumption they made in the conclusion, the lawgic would be:
classically-trained --> recite
/classically-trained --> /recite
NOT
recite --> classically-trained
/recite --> /classically trained
As a whole, however, we cannot validate whether Anna was classically trained because we only know that the majority of classically trained opera singers can recite Musetta's Waltz and the majority can’t. Anna may be classically trained, but she also could be the large minority of un-trained people in the world who can recite it. The correct lawgic is:
classically-trained --m--> recite
/classically-trained --m--> /recite
Some people in the comments are saying using their own intuition helped them parse this example easier (which is great!), but if you write the example down, IMO the lawgic makes it incredibly simple.
trained -m-> MW
/trained -m-> /MW
To my knowledge, we have no valid argument forms that would apply here. Even if the second premise was formatted as a contrapositive, which it is not, we know that contrapositives don't apply to some, most, and many.
The way that I thought about the opera example in my own terms:
Most NBA players can dunk a basketball, and most people who are not NBA players cannot. Therefore, it seems likely that since I can dunk, I play in the NBA.
1- There are very few NBA players in the world. Just because I can dunk doesn't offset the very low statistical probability that I am an NBA player.
2- There are plenty of other people who can dunk but are not in the NBA (e.g. college basketball players or retired NBA players).