For the second example, after the diagramming, I found myself wanting to flip and negate the serves decaf -> serves tea to try and chain it that way. How would I recognize that this is something incorrect to do?
Anyone else a little disturbed by the floating letter buzzing around? Reminds me of insects 😵💫. They feel unnaturally alive which is uncanny since letter should not be alive!
I am so thankfuk for 7sage. I took the lsat with minimal prep and couldnt pass a 155. These lessons are opening my eyes and genuinely making me excited to learn. This makes so much sense. ROTATE THE SOME AND PUT THE PUZZLE TOGEHER!!!
Some Laker players are basketball stars. All basketball stars are invited to the All star game. Therefore, some Laker players where invited to the All star game
Another good visualization is combining the venn diagrams from previous some sections with the set & superset visualization from the beginning of foundations:
A and B have overlapping venn diagrams.
--- ( A () B )
B is also a subset of the C superset.
--- ((B) C )
---Where the parentheses are the subset within superset bubbles used in previous videos
This means that A is overlapping with C in the same way that A is overlapping with B
--- ( A ( ( ) B ) C ) [kind of hard to illustrate without the actual circles]
I followed this section easier than the previous idk how many. Like I could've explained this concept before I got the explanation. I needed this win lol. My brain hurts after concept on concept on concept.
For the last one if I got: Tea <-- Decaf <- some -> Source from Blue Mountain Roasters, isn't this logically correct too? Just drawn differently or making an invalid inference but coming to the right conclusion?
Just wanted to say the visual example was super effective, thank you for that! I've been trying to make visuals for a lot of the more complicated topics we've covered and used a similar beaker analogy for sufficiency/necessity. I'd love for more lessons to include visual comparisons like these!
Since the some relationship is reversible, this means that some C are A, can you please explain how that works with the bucket visualization or why some cafes that serve tea source their beans from BMR? I am confused because there were no Cs in the A bucket/teas in the BMR bucket, so I don't understand why the relationship is reversible in these cases. Thanks!
Yeah, when it comes to the reversibility of the "some" inference we get from two other statements, the bucket visual kind of breaks down. That's because the visual keeps the "A"s that are in the "C" bucket as distinct "A"s that just seem to be bouncing around in the "C"s. So it's hard to see how that translates to the idea of some "C"s bouncing around in the "A" bucket.
Another way to visualize these relationships is with overlapping circles. Some A are B = there's an overlap between the A circle and the B circle. All Bs are C = the entire B circle is contained within the C circle. This means a portion of the A circle must also be part of the C circle. And, a portion of the C circle must also be part of the A circle. This is why the "some" relationship between A and C is reversible.
If we stick with the bucket visual, then rather than thinking of the "A"s bouncing around in the "C" bucket as individual entities, think of the "A"s bouncing around as if they were attached to a corresponding "C" that's also bouncing around. This makes it easier to understand why "Some Cs are A" also makes sense. There are some A-C pairs. So some things are both A and C.
I recommend having a tab with the negating lessons for some most all and just regular statements and doing it, asking yourself self how they got to it in the lesson and how you work it out and write out the translation. Then when you go through the answers for all three pages, it makes his reasoning easier to understand. I find I still made mistakes by forgetting about the earlier indicators, but it helps with the confusion if you do not understand at first like me. Hope this helps.
Nothing really changed. In the first example, you can also kick "students" up to the domain. If you're not within the domain of students (talking about students), the argument doesn't work.
So you're correct in your observations that there was an opportunity to kick something up into the domain in the first example.
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59 comments
Thats a great explanation
A ←s→ B → C
In the thinking of nesting dolls, some of A is in B and some of B is in C, Therefore some of A is in C?
@Oblivion Thinking about it in terms of nesting dolls could work.
But in your written statement it has to be "some of A is in B, and all of B is in C, therefore some of A is in C."
You can't chain what you wrote: "some of A is in B and some of B is in C"
A <--s--> B, B <--s--> C
cannot become A <--s--> C
For the second example, after the diagramming, I found myself wanting to flip and negate the serves decaf -> serves tea to try and chain it that way. How would I recognize that this is something incorrect to do?
Anyone else a little disturbed by the floating letter buzzing around? Reminds me of insects 😵💫. They feel unnaturally alive which is uncanny since letter should not be alive!
@Tombee64 like the bugs that disguise themselves as another species, to break into a nest and eat all their larvae
I am so thankfuk for 7sage. I took the lsat with minimal prep and couldnt pass a 155. These lessons are opening my eyes and genuinely making me excited to learn. This makes so much sense. ROTATE THE SOME AND PUT THE PUZZLE TOGEHER!!!
Some Laker players are basketball stars. All basketball stars are invited to the All star game. Therefore, some Laker players where invited to the All star game
@LamontNarcisse Luka 60 ball last night!!
@Kevin_Lin
Can we also then conclude here both A & B are both sometimes C. Cant we just replace the entire argument as
Premise- A-s-B
A or B-C
Conclusion: A or B-s-C
Another good visualization is combining the venn diagrams from previous some sections with the set & superset visualization from the beginning of foundations:
A and B have overlapping venn diagrams.
--- ( A () B )
B is also a subset of the C superset.
--- ((B) C )
---Where the parentheses are the subset within superset bubbles used in previous videos
This means that A is overlapping with C in the same way that A is overlapping with B
--- ( A ( ( ) B ) C ) [kind of hard to illustrate without the actual circles]
if they did bucket examples on most of the sections, i think i would have grasped the concepts more quickly, imo
I followed this section easier than the previous idk how many. Like I could've explained this concept before I got the explanation. I needed this win lol. My brain hurts after concept on concept on concept.
The bucket visual was so helpful.
For the last one if I got: Tea <-- Decaf <- some -> Source from Blue Mountain Roasters, isn't this logically correct too? Just drawn differently or making an invalid inference but coming to the right conclusion?
@tjsmithpa03 Don't focus on the form of lawgic too much IMO. Just make sure you understand the actual Logic.
If this helps: The first 3 three formal arguments:
1) If A → B,A,∴ B 2) If A → B, not B,∴ not A
3) If A → Band B → C then A → C.
this visual is great
If I had just watched this before doing my drill set I would've gotten a question right
formal argument 4 - some before all:
a b
b-> c
--------
a c
Just wanted to say the visual example was super effective, thank you for that! I've been trying to make visuals for a lot of the more complicated topics we've covered and used a similar beaker analogy for sufficiency/necessity. I'd love for more lessons to include visual comparisons like these!
He's flyingggg through this one. Had to slow down the video.
the bidirectional some is remind me of the subscript letters we made use of in other lessons. Do they function the same way?
John is in Group A
can be expressed
John > Group A
AND would be just as true to say
Johnₐ
Is this accurate?
The bucket visualizer was actually super helpful.
Totally agree, this was the most helpful visual aid for me so far in the course
Since the some relationship is reversible, this means that some C are A, can you please explain how that works with the bucket visualization or why some cafes that serve tea source their beans from BMR? I am confused because there were no Cs in the A bucket/teas in the BMR bucket, so I don't understand why the relationship is reversible in these cases. Thanks!
Yeah, when it comes to the reversibility of the "some" inference we get from two other statements, the bucket visual kind of breaks down. That's because the visual keeps the "A"s that are in the "C" bucket as distinct "A"s that just seem to be bouncing around in the "C"s. So it's hard to see how that translates to the idea of some "C"s bouncing around in the "A" bucket.
Another way to visualize these relationships is with overlapping circles. Some A are B = there's an overlap between the A circle and the B circle. All Bs are C = the entire B circle is contained within the C circle. This means a portion of the A circle must also be part of the C circle. And, a portion of the C circle must also be part of the A circle. This is why the "some" relationship between A and C is reversible.
If we stick with the bucket visual, then rather than thinking of the "A"s bouncing around in the "C" bucket as individual entities, think of the "A"s bouncing around as if they were attached to a corresponding "C" that's also bouncing around. This makes it easier to understand why "Some Cs are A" also makes sense. There are some A-C pairs. So some things are both A and C.
So, for example, if I say "Some B are A. All B are C. Therefore, some A are C."
Is that valid?
Lawgic:
B ←s→ A
B → C
--------------
A ←s→ C
Basically,
B ←s→ A gets rotated to A ←s→ B which then gets chained to B → C
Which leads to the conclusion A ←s→ C
Rotated: A ←s→ B → C
---------------
A ←s→ C
I understand the concept, I just want to know if the English translation "Some B are A. All B are C. Therefore, some A are C." is valid.
grok
I had to turn the captions on and rewind because I was like, "No way he just dropped Grok in there"
I recommend having a tab with the negating lessons for some most all and just regular statements and doing it, asking yourself self how they got to it in the lesson and how you work it out and write out the translation. Then when you go through the answers for all three pages, it makes his reasoning easier to understand. I find I still made mistakes by forgetting about the earlier indicators, but it helps with the confusion if you do not understand at first like me. Hope this helps.
For anyone else who was confused by the bucket/scoop analogy, this is how I visualized it:
I went back to JY's subset superset circle diagram for the B → C relationship, so you have superset circle C subsuming subset circle B.
At the bottom, where the edges of B and C line up, there is overlap with the intersecting set A. That little cross-section is A ←s→ C.
Some A are B. B is sufficient for C. So some A are triggering the necessary condition C, and then we get A ←s→ C.
Why was a domain explicitly stated for example 2, but not for the initial example? What changed between the two examples?
Nothing really changed. In the first example, you can also kick "students" up to the domain. If you're not within the domain of students (talking about students), the argument doesn't work.
So you're correct in your observations that there was an opportunity to kick something up into the domain in the first example.