This right here is exactly why I love 7Sage, and will sing your praises until the end of time. For someone who truly learns visually, and couldn’t always connect the “lawgic” even when it was in video form from earlier once we hit the some, most, and all, inferences, these visuals helped immensely!
@Hfa More is not necessarily half +1. Anything more than 50% (more than half) is still considered most. I don't think that the example for #5 should be considered incorrect. In other problems, even if the majority is a large majority, it still is a majority (most)
This was the easiest and simplest module we’ve had so far....it’s literally one I understood the first time I read it, which is why I’m confused about why everyone else is having a hard time. Maybe the videos just aren’t for me.
I think this is a case where as many videos as 7Sage can make, drilling and consistent practice is the only way to master these concepts. Gotta put in the work
Here are some more complex examples of invalid arguments that you may see on the test:
(1) Confusing Sufficiency for Necessity:
All published constitutional scholars have advanced training in legal theory. Dr. Morales has advanced training in legal theory. Therefore, Dr. Morales is a published constitutional scholar.
(2) Denying the Sufficient Condition:
If a company qualifies for federal renewable-energy subsidies, then it uses solar or wind technology in its operations. GreenTech Industries does not qualify for federal renewable-energy subsidies. Therefore, GreenTech Industries does not use solar or wind technology.
(3) Affirming the Necessary Condition:
Any policy proposal that significantly reduces urban air pollution must limit emissions from private vehicles. The new proposal limits emissions from private vehicles. Therefore, the new proposal significantly reduces urban air pollution.
(4) Most Statements Are Not Reversible:
Most peer-reviewed articles in leading medical journals are written by researchers affiliated with major universities. Therefore, most articles written by researchers affiliated with major universities appear in leading medical journals.
(5) All Before Most:
All constitutional law professors are law professors. Most law professors publish articles on legal theory. Therefore, some constitutional law professors publish articles on legal theory.
(6) All Before Some:
All marine biologists working in coral reef conservation programs are members of the International Society for Marine Science. Some members of the International Society for Marine Science specialize in deep-sea hydrothermal vent ecosystems. Therefore, some coral reef conservation biologists specialize in hydrothermal vent ecosystems.
(7) Most Before Most:
Most urban commuters who rely on public transit read digital news during their commute. Most people who read digital news during their commute closely follow international political developments. Therefore, some urban commuters who rely on public transit closely follow international political developments.
(8) Some Before Some:
Some historical linguists specialize in ancient Indo-European languages. Some scholars who specialize in ancient Indo-European languages conduct field research on endangered modern dialects. Therefore, some historical linguists conduct field research on endangered modern dialects.
Another tip I got was to diagram every question or drill, even if I thought I understood it, until the patterns became intuitive. If you don't understand the reasoning, you can always memorize rules.
I know that the lack of videos made this set a bit hard to understand so here are my explanations that helped me understand. They are super dumbed down because I am dumb so hope it helps
Sufficiency for Necessity
A->B
----
B->A
WRONG. Why? Imagine this, All cats are mammals SO, all mammals are cats. Is this conclusion that all mammals are cats correct based off the premise that all cats are mammals. NO! The only thing the premise is telling us is that cats are mammals. We have no clue what mammals are and thus cannot say that mammals are cats because we would be confusing sufficient and necessity
Denying Sufficient Condition
A->B
/A
--
/B
Wrong. Why? Just because we deny the sufficient condition does not mean that the necessary condition is false. Remember from the earlier lessons that, Membership in the subset is sufficient for membership in the superset, but it's not necessary.
Example. All cats are mammals. Steve the lion is not a cat. Therefore, Steve the lion is not a mammal. Does the premise being true make the conclusion true? Is this valid? NO IT's NOT. All we know is that Cats are mammals. Steve the lion isn't a cat, ok cool that's fine, BUT does that mean he's not a mammals? We don't know. The premise doesn't tell us anything about Steve the lion not being a mammal.
Affirming the necessary condition
A->B
B
--
A
Wrong. Why? Just because we say the necessary condition is true does not immediately mean that the sufficient condition is true. Remember back to subset and superset. The circle within the circle. Just because I'm in the first circle does that mean I'm in the second one? NO.
Example. All cats are mammals. Steven the lion is a mammal. Therefore, Steve the lion is a Cat. Does this premise being true make the conclusion true? Is this valid? NO! Just because Steve the lion is a mammal tells us nothing about if he is a cat or not. Maybe to become a cat one needs to have stripes and Steve the lion doesn't have strips so we can't say that just because he satisfies the necessary condition that he is cool with the sufficient condition.
Most statement are not reversible
A-m->A
--
B-m->A
Wrong. Why? Just because most A are B, does not mean most B are A.
Example. Most cats are mammals. Therefore, most mammals are cats. Based off the premise of "most cats are mammals" can we say it's valid that most mammals are cats? NO WE CAN'T. We have no clue what most mammals are. All we know is that most cats are mammals
Wrong. Why? Lets imagine it like this. All 2 of my red cars are trucks. Most of my 100 trucks are made by ford. Therefore, some of my red cars are made by ford. I hope this helps to show were the gap is. The reason it's invalid is because we have no clue if some of my red cars are made by ford or not. Maybe 98 of my trucks (which would satisfy most) are made by ford and 2 of my trucks (the red ones) are made by 7Sage auto. Then yah we can't say that some of my red trucks are made by ford, because this is incredibly weak. It could be the change that my 2 red trucks are not part of that most that is made by ford.
All before Some
A->B<-s->C
--
A<-s->C
Wrong. Why? Lets imagine it like this. All of my 3 cats are from London. Some cats from London enjoy drinking tea. Therefore, some of my cat's enjoy drinking tea. This is Invalid because what if for all we know my 3 cats from London are allergic of tea.
Another way to think about it is like this. All A are B. Some B are C. Thus, some A are C. Think of it like exclusions and inclusions. Just because all of my A are now in B does not mean that some of those A's made it all the way to C. They could have been left behind and so we can't say that some A are C
If so, can someone please explain why this form is invalid? Thanks in advance!
Is the explanation that '←S→' is implied within 'All' and we already know that 'all' cannot proceed '-M→' or ' ←S→'. If it does proceed either of those two quantifiers, the argument is invalid, is my basic understanding.
This lesson was helpful as it summarized exactly what I was doing wrong in previous drills, skill builders, etc. Yes, some of these flaws are implied, but something simply wasn’t clicking for me. I’m going to do a few drills now to make sure that I understand where I was going wrong. Overall, I feel a bit more confident in my understanding of the formal arguments.
I honestly don't think this lesson sucks at all. As DAVEMARINO said below, you need to have a strong grasp of the lessons on sets. I too was having problems recognizing formal logic flaws in drill and preptest questions until I went back and reviewed both of the sections on sets. One thing that significantly helped me was to write down each of the 8 formal logic flaws on a separate piece of paper (with their examples and Lawgic forms) and have this paper next to me as I drilled. Having the flaws in open view as I drilled helped to facilitate my pattern-recognition of these flaws whenever they appeared in questions. Eventually, you begin to recognize them instinctively. Above all, practice practice practice.
If you didn't fully grasp the "Logic of Intersecting Sets" section, this "Formal Logic Flaws" section is useless. Though this last lesson is a nice summation.
Would be more helpful if it was formatted the same way as LIS, and had videos.
This section on flaws needs some serious work. Videos would help clarify things to a greater degree than these pitifully written explanations. I had to go to another site to get clarification.
#feedback I feel it would be helpful to also include what the valid form of the arguments are so that in the review we can have a quick way to reference a valid/invalid argument for example, and see how the test writers try and trick us.
I have a question regarding the all arrows. If A --> B and A --> C lead to B some C because the all arrows can be converted into most arrows (aka the valid form: Two Split Mosts), is there any conclusion we can draw from having two statements such as B --> A and C --> A? In other words, when it's no longer the same sufficient term with two necessary terms but instead two different sufficient terms with the same necessary term. Would we just combine the two statements so that it becomes B + C --> A?
B+C->A in lawgic reads that two events are jointly sufficient for A. If the question does not add the conjunction “and” then consider both statements as two separate premises. The nect statement(s) or conclusion provided in the question will be the main factor(s) in deciding the validity of the argument.
If you switch to V1 and look for the section called "Invalid Argument Forms" they have some video lessons like this one: https://7sage.com/lesson/distinguish-valid-from-invalid-forms/
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78 comments
Where's my bestie that made those very helpful quizlets?
reading through this helped wayyy more than the previous lessons on the same topics
@StarBrooks 100% agree, the explanation with the use of visual aid is super helpful. Wish the previous modules were similar to this one.
This right here is exactly why I love 7Sage, and will sing your praises until the end of time. For someone who truly learns visually, and couldn’t always connect the “lawgic” even when it was in video form from earlier once we hit the some, most, and all, inferences, these visuals helped immensely!
Just a minor observation for Invalid Form #5, poodle example:
More than half for Friendly box should be 6 not 7 since the interpretation for most is half + 1.
The total no of dogs is 10.
half+1 of 10 is 6 ( 5+1).
I know it won't match with the total no of 10, but just sharing.
@Hfa More is not necessarily half +1. Anything more than 50% (more than half) is still considered most. I don't think that the example for #5 should be considered incorrect. In other problems, even if the majority is a large majority, it still is a majority (most)
Loved the visuals❤️
One of the best modules in the game change my mind
This was the easiest and simplest module we’ve had so far....it’s literally one I understood the first time I read it, which is why I’m confused about why everyone else is having a hard time. Maybe the videos just aren’t for me.
I think this is a case where as many videos as 7Sage can make, drilling and consistent practice is the only way to master these concepts. Gotta put in the work
Here are some more complex examples of invalid arguments that you may see on the test:
(1) Confusing Sufficiency for Necessity:
All published constitutional scholars have advanced training in legal theory. Dr. Morales has advanced training in legal theory. Therefore, Dr. Morales is a published constitutional scholar.
(2) Denying the Sufficient Condition:
If a company qualifies for federal renewable-energy subsidies, then it uses solar or wind technology in its operations. GreenTech Industries does not qualify for federal renewable-energy subsidies. Therefore, GreenTech Industries does not use solar or wind technology.
(3) Affirming the Necessary Condition:
Any policy proposal that significantly reduces urban air pollution must limit emissions from private vehicles. The new proposal limits emissions from private vehicles. Therefore, the new proposal significantly reduces urban air pollution.
(4) Most Statements Are Not Reversible:
Most peer-reviewed articles in leading medical journals are written by researchers affiliated with major universities. Therefore, most articles written by researchers affiliated with major universities appear in leading medical journals.
(5) All Before Most:
All constitutional law professors are law professors. Most law professors publish articles on legal theory. Therefore, some constitutional law professors publish articles on legal theory.
(6) All Before Some:
All marine biologists working in coral reef conservation programs are members of the International Society for Marine Science. Some members of the International Society for Marine Science specialize in deep-sea hydrothermal vent ecosystems. Therefore, some coral reef conservation biologists specialize in hydrothermal vent ecosystems.
(7) Most Before Most:
Most urban commuters who rely on public transit read digital news during their commute. Most people who read digital news during their commute closely follow international political developments. Therefore, some urban commuters who rely on public transit closely follow international political developments.
(8) Some Before Some:
Some historical linguists specialize in ancient Indo-European languages. Some scholars who specialize in ancient Indo-European languages conduct field research on endangered modern dialects. Therefore, some historical linguists conduct field research on endangered modern dialects.
What helped me was to read these and if they didn't intuitively make sense, sit with them for as long as it took until it clicked.
Write them down on paper, poke holes in the why, ask Chatgpt for more examples and drills, look up common answers for flaw questions, etc.
Another tip I got was to diagram every question or drill, even if I thought I understood it, until the patterns became intuitive. If you don't understand the reasoning, you can always memorize rules.
we WILL avoid trap answers, everybody 180
I know that the lack of videos made this set a bit hard to understand so here are my explanations that helped me understand. They are super dumbed down because I am dumb so hope it helps
Sufficiency for Necessity
A->B
----
B->A
WRONG. Why? Imagine this, All cats are mammals SO, all mammals are cats. Is this conclusion that all mammals are cats correct based off the premise that all cats are mammals. NO! The only thing the premise is telling us is that cats are mammals. We have no clue what mammals are and thus cannot say that mammals are cats because we would be confusing sufficient and necessity
Denying Sufficient Condition
A->B
/A
--
/B
Wrong. Why? Just because we deny the sufficient condition does not mean that the necessary condition is false. Remember from the earlier lessons that, Membership in the subset is sufficient for membership in the superset, but it's not necessary.
Example. All cats are mammals. Steve the lion is not a cat. Therefore, Steve the lion is not a mammal. Does the premise being true make the conclusion true? Is this valid? NO IT's NOT. All we know is that Cats are mammals. Steve the lion isn't a cat, ok cool that's fine, BUT does that mean he's not a mammals? We don't know. The premise doesn't tell us anything about Steve the lion not being a mammal.
Affirming the necessary condition
A->B
B
--
A
Wrong. Why? Just because we say the necessary condition is true does not immediately mean that the sufficient condition is true. Remember back to subset and superset. The circle within the circle. Just because I'm in the first circle does that mean I'm in the second one? NO.
Example. All cats are mammals. Steven the lion is a mammal. Therefore, Steve the lion is a Cat. Does this premise being true make the conclusion true? Is this valid? NO! Just because Steve the lion is a mammal tells us nothing about if he is a cat or not. Maybe to become a cat one needs to have stripes and Steve the lion doesn't have strips so we can't say that just because he satisfies the necessary condition that he is cool with the sufficient condition.
Most statement are not reversible
A-m->A
--
B-m->A
Wrong. Why? Just because most A are B, does not mean most B are A.
Example. Most cats are mammals. Therefore, most mammals are cats. Based off the premise of "most cats are mammals" can we say it's valid that most mammals are cats? NO WE CAN'T. We have no clue what most mammals are. All we know is that most cats are mammals
@Student101 Part 2 to follow up on these
All before Most
A->B-m->C
--
A<-s->C
Wrong. Why? Lets imagine it like this. All 2 of my red cars are trucks. Most of my 100 trucks are made by ford. Therefore, some of my red cars are made by ford. I hope this helps to show were the gap is. The reason it's invalid is because we have no clue if some of my red cars are made by ford or not. Maybe 98 of my trucks (which would satisfy most) are made by ford and 2 of my trucks (the red ones) are made by 7Sage auto. Then yah we can't say that some of my red trucks are made by ford, because this is incredibly weak. It could be the change that my 2 red trucks are not part of that most that is made by ford.
All before Some
A->B<-s->C
--
A<-s->C
Wrong. Why? Lets imagine it like this. All of my 3 cats are from London. Some cats from London enjoy drinking tea. Therefore, some of my cat's enjoy drinking tea. This is Invalid because what if for all we know my 3 cats from London are allergic of tea.
Another way to think about it is like this. All A are B. Some B are C. Thus, some A are C. Think of it like exclusions and inclusions. Just because all of my A are now in B does not mean that some of those A's made it all the way to C. They could have been left behind and so we can't say that some A are C
Is this below example an invalid argument?
A ←S→ B -M→ C
__________
A ←S→ C
If so, can someone please explain why this form is invalid? Thanks in advance!
Is the explanation that '←S→' is implied within 'All' and we already know that 'all' cannot proceed '-M→' or ' ←S→'. If it does proceed either of those two quantifiers, the argument is invalid, is my basic understanding.
@CrispyOats I'd encourage you to use examples or draw out a number of "As" "Bs" and "Cs" to flesh out why this is invalid.
Let's say we have 5 As and 10 Bs. Some of the As are Bs -- so let's say one of the As is also a B.
Most of the Bs are C.
Does that guarantee that some of the As must be C? Why not?
I just don't understand how the grammar lesson had so many thorough explanations with videos but not this lesson... very disappointing
if you were my greatest enemy, i would screenshot these invalid arguments and send them to you and tell you that they're valid
@emilylu you're mistaken to assume your greatest enemy isn't also on 7sage's core curriculum.
This lesson was helpful as it summarized exactly what I was doing wrong in previous drills, skill builders, etc. Yes, some of these flaws are implied, but something simply wasn’t clicking for me. I’m going to do a few drills now to make sure that I understand where I was going wrong. Overall, I feel a bit more confident in my understanding of the formal arguments.
I honestly don't think this lesson sucks at all. As DAVEMARINO said below, you need to have a strong grasp of the lessons on sets. I too was having problems recognizing formal logic flaws in drill and preptest questions until I went back and reviewed both of the sections on sets. One thing that significantly helped me was to write down each of the 8 formal logic flaws on a separate piece of paper (with their examples and Lawgic forms) and have this paper next to me as I drilled. Having the flaws in open view as I drilled helped to facilitate my pattern-recognition of these flaws whenever they appeared in questions. Eventually, you begin to recognize them instinctively. Above all, practice practice practice.
@gabrielfermin54 this sounds like a really great way to drill, thanks for the advice!
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The point of this section is to tell you that you WILL see these flaws on the test, and you need to be able to recognize them.
The valid forms of all of these arguments have already been taught to us in previous lessons.
If you didn't fully grasp the "Logic of Intersecting Sets" section, this "Formal Logic Flaws" section is useless. Though this last lesson is a nice summation.
Would be more helpful if it was formatted the same way as LIS, and had videos.
This section on flaws needs some serious work. Videos would help clarify things to a greater degree than these pitifully written explanations. I had to go to another site to get clarification.
.
exactly!! same
#feedback
Confusing Sufficiency for Necessity
A → B
_
B → A
Denying the Sufficient Condition
A → B
/A
_
/B
Affirming the Necessary Condition
A → B
B
A
Most Statements are Not Reversible
A —m→ B
_
B —m→ A
All Before Most
A → B —m→ C
_
A ←s→ C
All Before Some
A → B ←s→ C
_
A ←s→ C
Most Before Most
A —m→ B —m→ C
A ←s→ C
Some Before Some
A ←s→ B ←s→ C
A ←s→ C
Does this resolve the example?
A and /B → C
/C→/A or B
yes
#feedback I feel it would be helpful to also include what the valid form of the arguments are so that in the review we can have a quick way to reference a valid/invalid argument for example, and see how the test writers try and trick us.
I have a question regarding the all arrows. If A --> B and A --> C lead to B some C because the all arrows can be converted into most arrows (aka the valid form: Two Split Mosts), is there any conclusion we can draw from having two statements such as B --> A and C --> A? In other words, when it's no longer the same sufficient term with two necessary terms but instead two different sufficient terms with the same necessary term. Would we just combine the two statements so that it becomes B + C --> A?
#help
B+C->A in lawgic reads that two events are jointly sufficient for A. If the question does not add the conjunction “and” then consider both statements as two separate premises. The nect statement(s) or conclusion provided in the question will be the main factor(s) in deciding the validity of the argument.
If you switch to V1 and look for the section called "Invalid Argument Forms" they have some video lessons like this one: https://7sage.com/lesson/distinguish-valid-from-invalid-forms/
I found it to be helpful!