@isabellagirjikian Wholeheartedly agree with @bellaens18 here, boss. You shouldn't rely on AI. Along with being bad for the environment (amongst other moral concerns, yeesh), you're also denying yourself understanding when handing it off to a bot. Thousands of generations before you people figured out math, science, tool use, exploration from the lowest valleys, highest mountaintops, densest rain forests and life-parched deserts. You come from these people. You are wholeheartedly capable of learning without the bot, and you should. To be the best you, you don't need a crutch. KICK LIFE IN THE TUCHUS, @isabellagirjikian !!
@isabellagirjikian NP boss. A lot of folks are quick to dunk/admonish AI users rather than encouraging them better alternatives. Using AI wont hurt you, but its like using a calculator for basic addition when you're totally capable of just doing it in your head. Good luck, and I wish for you nothing less than perseverence
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.
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 =(
When I read the example it makes total sense but I don't know how he got to that mapping can someone help me? (Only birds migrate south in winder example)
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?
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!
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'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.
"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.
My flawed logic: Monarch butterfly is not a bird. Therefore, it can't migrate south. < WRONG (butterflies might still fly south ... being a bird is not the only way.)
This last paragraph before the review seems relatively ambiguous, although I may be too confused to grasp the thrust of it. Is the premise we made up of B→A just a common pitfall that people make in translating the given scenario, or is it actually a correct translation but wrong in the larger context of the previous example?
Is the second argument, which uses the term only, logically distinct from the first argument? If it is logically distinct, then how is the premise still A→B. If not, then I don't see how the use of the term only doesn't change the premise to B→A. It seems valid for there to be some member of the set of birds which doesn't migrate south in the winter, but it would not be valid to say that there is a member of the set of not-birds which migrates south in the winter. Therefore B is a subset of A. With that, membership in the set of animals that migrate south for the winter is sufficient to guarantee that said element must be a bird. I.e. B→A.
I hope that my question(s) make sense, please let me know if I can clarify anything.
The last paragraph was super confusing. It's meant to show the formal logic we learned to highlight what specific trap the testmakers are constructing, but the wording is poor in those last couple sentences.
The word only does make the second argument logically distint.
Whereas "ALL birds migrate south in winter" makes 'birds' sufficient ( B --> MSw), "ONLY birds migrate south in winter" makes 'birds' necessary. Only is a Group 2 indicator, so we get: MSw --> B. This leads us to a valid contrapositive argument.
Let's look at the last paragraph again:
"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."
Here he's referring to the mistake people may have made with example 1 (ALL birds), confusing sufficiency for necessity, rather than saying example 2 is correct and immediately negating that statement. Instead of "all birds migrate south in winter," he's saying people may have interpreted it as "all things that migrate south in winter are birds," ultimately changing the roles of the two conditions.
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96 comments
I think about it like this: denying the existence of a square does not deny the existence of rectangles.
Flawgic
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.
If this helps from what I gathered on chatgbt:
All A are B = A → B
Every A is B = A → B
Any A is B = A → B
They ALL mean the same thing: 👉 if A, then B
Where your confusion is coming from
You’re probably thinking:
👉 “All” sounds like it’s talking about EVERYTHING
But it’s not.
It’s only talking about: 👉 the group A (birds)
It’s NOT saying anything about: 👉 things that are NOT A (non-birds)
@isabellagirjikian critically think instead of using ai pls it is unnecessary and is so bad for the environment :(
@isabellagirjikian Wholeheartedly agree with @bellaens18 here, boss. You shouldn't rely on AI. Along with being bad for the environment (amongst other moral concerns, yeesh), you're also denying yourself understanding when handing it off to a bot. Thousands of generations before you people figured out math, science, tool use, exploration from the lowest valleys, highest mountaintops, densest rain forests and life-parched deserts. You come from these people. You are wholeheartedly capable of learning without the bot, and you should. To be the best you, you don't need a crutch. KICK LIFE IN THE TUCHUS, @isabellagirjikian !!
@ManusWeber Appreciate your honesty!!
@isabellagirjikian NP boss. A lot of folks are quick to dunk/admonish AI users rather than encouraging them better alternatives. Using AI wont hurt you, but its like using a calculator for basic addition when you're totally capable of just doing it in your head. Good luck, and I wish for you nothing less than perseverence
@ManusWeber Thank you!
So...
Bird -> Migrate
butterfly /Bird
____
butterfly /Migrate Invalid
If it would have said the monarch butterfly doesn't migrate in the winter, then it would have been
Bird -> Migrate
butterfly /Migrate
____
butterfly /Bird
Which is valid because if you aren't in the necessary condition, you fail the sufficient.
Stated another way, multiple things can migrate south, but if you don't migrate south, you're not a bird.
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.
yeah i’m lost i feel like i used to understand this and now i don’t :/
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
i need the videos!! My brain reacts better to "someone" telling me the story, than me reading the story.
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 =(
Help!
When I read the example it makes total sense but I don't know how he got to that mapping can someone help me? (Only birds migrate south in winder example)
@LauraBolivar I believe mapped out it looks like:
MSW (Migrate south in winter) -> B (bird).
mb/B (Monarch butterfly is not a bird).
Conclusion: mb/MSW (Monarch butterfly does not migrate south in Winter)
the butterfly can fly around the necessary condition circle and make his way down south he doesn't have to be a bird
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?
The instructions and written explanations made sense until you did the lawgic.
I think having the explicit forms of the predicate indicators in the lawgic form will help the confusion
I don't really understand why everyone is saying this lesson is unclear.
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!
Haha the ending... you made up your own premise
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.
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 This is the first lesson I've seen so far that I believe needs to be updated and improved.
"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
My flawed logic: Monarch butterfly is not a bird. Therefore, it can't migrate south. < WRONG (butterflies might still fly south ... being a bird is not the only way.)
Train your mind to:
- Avoid assumptions.
- Pay attention to clues (Only, All, etc.).
Okay... this is kinda confusing.
This last paragraph before the review seems relatively ambiguous, although I may be too confused to grasp the thrust of it. Is the premise we made up of B→A just a common pitfall that people make in translating the given scenario, or is it actually a correct translation but wrong in the larger context of the previous example?
Is the second argument, which uses the term only, logically distinct from the first argument? If it is logically distinct, then how is the premise still A→B. If not, then I don't see how the use of the term only doesn't change the premise to B→A. It seems valid for there to be some member of the set of birds which doesn't migrate south in the winter, but it would not be valid to say that there is a member of the set of not-birds which migrates south in the winter. Therefore B is a subset of A. With that, membership in the set of animals that migrate south for the winter is sufficient to guarantee that said element must be a bird. I.e. B→A.
I hope that my question(s) make sense, please let me know if I can clarify anything.
The last paragraph was super confusing. It's meant to show the formal logic we learned to highlight what specific trap the testmakers are constructing, but the wording is poor in those last couple sentences.
The word only does make the second argument logically distint.
Whereas "ALL birds migrate south in winter" makes 'birds' sufficient ( B --> MSw), "ONLY birds migrate south in winter" makes 'birds' necessary. Only is a Group 2 indicator, so we get: MSw --> B. This leads us to a valid contrapositive argument.
Let's look at the last paragraph again:
"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."
Here he's referring to the mistake people may have made with example 1 (ALL birds), confusing sufficiency for necessity, rather than saying example 2 is correct and immediately negating that statement. Instead of "all birds migrate south in winter," he's saying people may have interpreted it as "all things that migrate south in winter are birds," ultimately changing the roles of the two conditions.