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)
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.
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 am troubled with this example. I thought we needed to base our decisions on the facts of the stimulus (passage). I get it, the rule is flawed, but why would I assume outside of what the rule states. Make little sense to teach that you shouldn't assume for MSS or MBT, but here you should.
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 arrived at the answer to the monarch passage using different lawgic. Rather than specify membership in a set, I communicated relationships through conditionals. I wrote Monarch→/bird for the second premise and monarch→/migrate south for the conclusion. I figured out the argument was invalid because I determined /Monarch←s→ migrate south, and because some does not imply all, I deemed the argument invalid.
My two questions are: 1) Is this a valid way to determine the validity of the conclusion 2) does anybody have any good strategies for identifying membership in sets versus conditional relationships?
So pretty much the reason why the first example where it uses "ALL" is INVALID because all can mean most right? so more than half of the birds or all of the birds??? From what I am understanding is that when you use the word only it makes it valid because it being specific in terms of how many??
this one is making my brain hurt. we need a video asap for this.
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77 comments
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)
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)
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.
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.
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.
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 am troubled with this example. I thought we needed to base our decisions on the facts of the stimulus (passage). I get it, the rule is flawed, but why would I assume outside of what the rule states. Make little sense to teach that you shouldn't assume for MSS or MBT, but here you should.
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 arrived at the answer to the monarch passage using different lawgic. Rather than specify membership in a set, I communicated relationships through conditionals. I wrote Monarch→/bird for the second premise and monarch→/migrate south for the conclusion. I figured out the argument was invalid because I determined /Monarch←s→ migrate south, and because some does not imply all, I deemed the argument invalid.
My two questions are: 1) Is this a valid way to determine the validity of the conclusion 2) does anybody have any good strategies for identifying membership in sets versus conditional relationships?
Why would they put the rule and then say that its not correct. Just put the right lawgic translation to avoid an confusion.
I need more lessons for this my brain is having a hard time understanding :(
So pretty much the reason why the first example where it uses "ALL" is INVALID because all can mean most right? so more than half of the birds or all of the birds??? From what I am understanding is that when you use the word only it makes it valid because it being specific in terms of how many??
#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.
So is the second example valid or is it confusing sufficiency for necessity?
this one is making my brain hurt. we need a video asap for this.