"All birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Apply group 1 because of "All" indicator, so the sufficient condition is A = Birds, and the necessary is B = (migrate south in winter) to get Lawgic rule of A -> B. Otherwise stated using if conditional, this is "If something is a bird, then it migrates south in the winter."
Contrapositive would then be !B -> !A, or "if something does not migrate south in the winter, then it is not a bird."
Then we have "The monarch butterfly is not a bird," which maps onto the necessary condition of the contrapositive form ("...it is not a bird."). We cannot make any kind of assumption from this, as a necessary condition being met does not imply anything about the existence of any corresponding sufficient condition being met, thus the conclusion that "the monarch butterfly does not migrate south in winter" is not valid.
This makes sense, however the following example of the text does not. Changing the modifier from "all" to "only" switches the conditions that are presented as being sufficient and necessary. The "only" modifies the things that fly south in the winter to be birds and birds alone, meaning birds are transformed into the necessary condition and things that fly south in the winter into the sufficient. This gives us B -> A (using the same variable mapping as above). When the end of the problem states "The only problem is that you made up your own premise B → A. The actual premise is A → B. You confused sufficiency for necessity," it ignores that the new wording of the premise has actually flipped the sufficient and necessary conditions, and therefore the reasoning of the argument is valid. See below:
"Only birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Apply group 2 because of "Only" indicator, so "only" indicates necessary condition A = Birds, and makes B = "migrate south in winter" the sufficient. This gives the rule:
B -> A, otherwise stated using if conditional as "if something migrates south in the winter, then it is a bird."
The contrapositive of this would then be:
!A -> !B, or "if something is not a bird, then it does not migrate south in winter." Here, "The monarch butterfly is not a bird" clause satisfies the sufficient condition of the contrapositive, meaning we can indeed draw a conclusion that it does also fit the necessary, being that it does not fly south in winter.
Ok so I also found this lesson confusing. What I think the key take away here is that denying the sufficient condition tells you nothing about the necessary condition. That's it.
My example:
All students study at night. Timmy is not a student. Therefor, Timmy does not study at night.
Lawgic:
Student -> Study at night
Timmy = /Student
--
Timmy = /Study at night
This is invalid. WHY? Because we have no clue when Timmy studies. All we know is that Timmy ain't a student.
Denying the sufficient condition by saying Timmy is not a student tells you nothing about the necessary condition of studying at night.
Membership in the subset is sufficient for membership in the superset, BUT IT IS NOT NECESSARY. There could be other subsets under the superset of "studying at night" and Timmy could be part of those other subsets.
Denying the sufficient condition (the subset) tells you nothing about the necessary condition (the superset)
@Student101 This example makes sense, but in the last example of the lesson, "Only birds" seems a lot different and more like a necessary condition than if it were "All birds". Could somebody help explain this?
For all the folks who are having a hard time grasping this flaw, I've found it helpful to think about it in these terms: "Just because something isn't A, doesn't mean it can't be B." That's it.
I also find it helpful to recall one of the simple arguments from earlier,
If one is a cat, then one is also a mammal (C → M), meaning that being a cat is sufficient for being a mammal is necessary for being a cat.
Denying the sufficient in this case would be like saying that since animal X is not a cat animal X is not a mammal, a claim whose validity is not guaranteed since animal X can potentially be a pig or cow or dog, etc. All of which are still mammals while simultaneously failing the sufficient condition of being a cat.
This is SUPER confusing. If you are not going to have a video, then the written explanations must be clear. If the written explanations are not clear, then you must have a video.
I rather watch the videos, understanding this by my own feels like I am not paying for the course and I am learning with examples that Chat GPT could give =(
I'm so glad this Group 1-4 indicators thing is starting to stick because I see myself understanding the sufficient and necessity much faster than before. If you are still struggling, I would suggest skimming the video lessons and redoing the sufficient necessity practice with a fresh mind, and then repeating just the practice the next day again with a fresh mind before continuing.
Honestly, I used chat to help explain it in more details and it's explanation worked. Hope this helps:
Original Statement:
"Only birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Analysis:
Understanding "Only" in Logical Terms:
The phrase "Only birds migrate south in winter" can be interpreted as: If something migrates south in winter, then it must be a bird.
In formal logic, this is expressed as:
Migration South → Bird
In Lawgic terms: M → B
Contrapositive Form:
The contrapositive of M → B is:
If not a bird, then does not migrate south.
In Lawgic terms: /B → /M
Statement Breakdown:
Premise 1: Only birds migrate south in winter.
This is translated as: M → B (If it migrates south, then it is a bird).
Premise 2: The monarch butterfly is not a bird.
This is: /B (Not a bird).
Conclusion: The monarch butterfly does not migrate south in winter.
This is: /M (Does not migrate south).
Logic Flow:
From Premise 1 (M → B), we know that migrating south implies being a bird.
If something is not a bird (/B), it cannot migrate south (/M).
Thus, from /B (not a bird), we conclude /M (does not migrate south).
Confusing Sufficiency for Necessity:
Premise Misinterpretation: If you confuse sufficiency with necessity, you might wrongly translate "Only birds migrate south" as: Birds → Migration South.
This misinterpretation would incorrectly suggest that being a bird is sufficient for migrating south, rather than understanding that migration south implies being a bird (which is the correct interpretation).
Correct Translation:
Correctly translating "Only birds migrate south" means understanding that being a bird is a necessary condition for migrating south. Thus, if something is not a bird, it cannot migrate south.
Summary:
Correct Logic: M → B (Migration South → Bird) and /B → /M (Not a Bird → Does Not Migrate South)
Incorrect Logic (Confusing Sufficiency for Necessity): Birds → Migration South, which misrepresents the logical relationship.
I understand this perfectly and this is exactly what I was thinking as well. I just don't understand why things were explained in such a confusing way in the last paragraph. I didn't confuse anything and yet it said I did.
omg i was so confused ab why it would be b -> a and then read the end lollll. but still a little confusing. but thank god for some commenters down here hehe yall rly helped <33 good luck, we got this!
So, technically, we aren't wrong in our translation process for the argument:
“All birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter.”
Birds → Migrate South in Winter
Monarch Butterfly → /Bird
Monarch Butterfly → /Migrate South in Winter
It seems that what makes this conclusion invalid is that it's assuming monarch butterflies don't migrate south in the winter simply because it's not a bird. So, it's not that our process is wrong, but rather that we're missing additional premises that would support the conclusion. We're making an assumption that isn't justified by the given information. All ≠ Only.
I'm confused --- "That's valid. In fact, that's the contrapositive argument form. The only problem is that you made up your own premise B → A. The actual premise is A → B. You confused sufficiency for necessity."
If we're following the contrapositve argument form, how then did we confuse the sufficiency for necessity?
@CLacey it's referring to the above example A > B. He's saying if you confused "all" to be "only", you'd end up confusing sufficient for necessary because you'd be working with a different argument.
107 comments
"All birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Apply group 1 because of "All" indicator, so the sufficient condition is A = Birds, and the necessary is B = (migrate south in winter) to get Lawgic rule of A -> B. Otherwise stated using if conditional, this is "If something is a bird, then it migrates south in the winter."
Contrapositive would then be !B -> !A, or "if something does not migrate south in the winter, then it is not a bird."
Then we have "The monarch butterfly is not a bird," which maps onto the necessary condition of the contrapositive form ("...it is not a bird."). We cannot make any kind of assumption from this, as a necessary condition being met does not imply anything about the existence of any corresponding sufficient condition being met, thus the conclusion that "the monarch butterfly does not migrate south in winter" is not valid.
This makes sense, however the following example of the text does not. Changing the modifier from "all" to "only" switches the conditions that are presented as being sufficient and necessary. The "only" modifies the things that fly south in the winter to be birds and birds alone, meaning birds are transformed into the necessary condition and things that fly south in the winter into the sufficient. This gives us B -> A (using the same variable mapping as above). When the end of the problem states "The only problem is that you made up your own premise B → A. The actual premise is A → B. You confused sufficiency for necessity," it ignores that the new wording of the premise has actually flipped the sufficient and necessary conditions, and therefore the reasoning of the argument is valid. See below:
"Only birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Apply group 2 because of "Only" indicator, so "only" indicates necessary condition A = Birds, and makes B = "migrate south in winter" the sufficient. This gives the rule:
B -> A, otherwise stated using if conditional as "if something migrates south in the winter, then it is a bird."
The contrapositive of this would then be:
!A -> !B, or "if something is not a bird, then it does not migrate south in winter." Here, "The monarch butterfly is not a bird" clause satisfies the sufficient condition of the contrapositive, meaning we can indeed draw a conclusion that it does also fit the necessary, being that it does not fly south in winter.
this is way better than the explanation they gave in the lesson. thank you!
@juliagvrooman Iconic
@juliagvrooman is only not a suff indicator?
I agree the last example was unclear whether it was valid or not. A video would be helpful on this one.
@ChristinaCorbo a video would help so much bc I got confused one what was happening in the text
@ChristinaCorbo This also really confused me.
Ok so I also found this lesson confusing. What I think the key take away here is that denying the sufficient condition tells you nothing about the necessary condition. That's it.
My example:
All students study at night. Timmy is not a student. Therefor, Timmy does not study at night.
Lawgic:
Student -> Study at night
Timmy = /Student
--
Timmy = /Study at night
This is invalid. WHY? Because we have no clue when Timmy studies. All we know is that Timmy ain't a student.
Denying the sufficient condition by saying Timmy is not a student tells you nothing about the necessary condition of studying at night.
Membership in the subset is sufficient for membership in the superset, BUT IT IS NOT NECESSARY. There could be other subsets under the superset of "studying at night" and Timmy could be part of those other subsets.
Denying the sufficient condition (the subset) tells you nothing about the necessary condition (the superset)
@Student101 This was very helpful, thanks!
@Student101 This example makes sense, but in the last example of the lesson, "Only birds" seems a lot different and more like a necessary condition than if it were "All birds". Could somebody help explain this?
#feedback This is the first lesson I've seen so far that I believe needs to be updated and improved.
Flawgic
i need the videos!! My brain reacts better to "someone" telling me the story, than me reading the story.
Can you guys write the lawgic in terms of the the actually question and not just use A and B?
For all the folks who are having a hard time grasping this flaw, I've found it helpful to think about it in these terms: "Just because something isn't A, doesn't mean it can't be B." That's it.
I also find it helpful to recall one of the simple arguments from earlier,
If one is a cat, then one is also a mammal (C → M), meaning that being a cat is sufficient for being a mammal is necessary for being a cat.
Denying the sufficient in this case would be like saying that since animal X is not a cat animal X is not a mammal, a claim whose validity is not guaranteed since animal X can potentially be a pig or cow or dog, etc. All of which are still mammals while simultaneously failing the sufficient condition of being a cat.
@shane.harilall This is such a good way to explain this, thank you! I appreciate the call back to the previous example.
yeah i’m lost i feel like i used to understand this and now i don’t :/
this one is making my brain hurt. we need a video asap for this.
I think about it like this: denying the existence of a square does not deny the existence of rectangles.
Yuhhh this lesson was indeed confusing...fml
This is SUPER confusing. If you are not going to have a video, then the written explanations must be clear. If the written explanations are not clear, then you must have a video.
@Amanhasnoname Never mind. I get it now.
now why would you make this one with no video and now i am confused
I rather watch the videos, understanding this by my own feels like I am not paying for the course and I am learning with examples that Chat GPT could give =(
Why would they put the rule and then say that its not correct. Just put the right lawgic translation to avoid an confusion.
In this example, the word all is a sufficient condition indicator, so I am going to put the first statement as:
bird --> migrate south in winter
Let's say:
A = Bird
B = migrate south in winter
The relationship would be:
A --> B
The wrong interpretation, however, would be:
migrate south in winter --> bird
Or,
B-->A
This is confusing sufficiecny for necessity.
If you take B-->A, then you would end up with another wrong interpretation or the wrong contrapositive which is:
/A-->/B
That is why your conclusion that if x/A, then x/B, is wrong.
I'm so glad this Group 1-4 indicators thing is starting to stick because I see myself understanding the sufficient and necessity much faster than before. If you are still struggling, I would suggest skimming the video lessons and redoing the sufficient necessity practice with a fresh mind, and then repeating just the practice the next day again with a fresh mind before continuing.
#feedback
Why use A and B when making these examples? Especially when reordering. It would be much more helpful to actually type it out.
In the second example, it mentions the premise is made up, but fails to explain those details.
Honestly, I used chat to help explain it in more details and it's explanation worked. Hope this helps:
Original Statement:
"Only birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Analysis:
Understanding "Only" in Logical Terms:
The phrase "Only birds migrate south in winter" can be interpreted as: If something migrates south in winter, then it must be a bird.
In formal logic, this is expressed as:
Migration South → Bird
In Lawgic terms: M → B
Contrapositive Form:
The contrapositive of M → B is:
If not a bird, then does not migrate south.
In Lawgic terms: /B → /M
Statement Breakdown:
Premise 1: Only birds migrate south in winter.
This is translated as: M → B (If it migrates south, then it is a bird).
Premise 2: The monarch butterfly is not a bird.
This is: /B (Not a bird).
Conclusion: The monarch butterfly does not migrate south in winter.
This is: /M (Does not migrate south).
Logic Flow:
From Premise 1 (M → B), we know that migrating south implies being a bird.
If something is not a bird (/B), it cannot migrate south (/M).
Thus, from /B (not a bird), we conclude /M (does not migrate south).
Confusing Sufficiency for Necessity:
Premise Misinterpretation: If you confuse sufficiency with necessity, you might wrongly translate "Only birds migrate south" as: Birds → Migration South.
This misinterpretation would incorrectly suggest that being a bird is sufficient for migrating south, rather than understanding that migration south implies being a bird (which is the correct interpretation).
Correct Translation:
Correctly translating "Only birds migrate south" means understanding that being a bird is a necessary condition for migrating south. Thus, if something is not a bird, it cannot migrate south.
Summary:
Correct Logic: M → B (Migration South → Bird) and /B → /M (Not a Bird → Does Not Migrate South)
Incorrect Logic (Confusing Sufficiency for Necessity): Birds → Migration South, which misrepresents the logical relationship.
This is a perfect explanation. Thank you so much.
I understand this perfectly and this is exactly what I was thinking as well. I just don't understand why things were explained in such a confusing way in the last paragraph. I didn't confuse anything and yet it said I did.
I am very confused with this lesson. Can you provide a video example or something? thank you.
what
omg i was so confused ab why it would be b -> a and then read the end lollll. but still a little confusing. but thank god for some commenters down here hehe yall rly helped <33 good luck, we got this!
So, technically, we aren't wrong in our translation process for the argument:
“All birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter.”
Birds → Migrate South in Winter
Monarch Butterfly → /Bird
Monarch Butterfly → /Migrate South in Winter
It seems that what makes this conclusion invalid is that it's assuming monarch butterflies don't migrate south in the winter simply because it's not a bird. So, it's not that our process is wrong, but rather that we're missing additional premises that would support the conclusion. We're making an assumption that isn't justified by the given information. All ≠ Only.
I'm confused --- "That's valid. In fact, that's the contrapositive argument form. The only problem is that you made up your own premise B → A. The actual premise is A → B. You confused sufficiency for necessity."
If we're following the contrapositve argument form, how then did we confuse the sufficiency for necessity?
@CLacey it's referring to the above example A > B. He's saying if you confused "all" to be "only", you'd end up confusing sufficient for necessary because you'd be working with a different argument.