I think it helps to think about it like order of operations.
If you dump some of you A's into your B's
then dump all of your B bucket into your C's, then you will definitely have some A's in your C's.
But if you dump all of your A's into your B's
and then dump some of your B's into your C's, then you won't necessarily have any A's in your C's, you could, but its not guaranteed. If it is not guaranteed then it is not valid.
I think this reasoning also work for the most rule as well.
It's really helpful for me to think of this and the previous flaw with the buckets scenario. Think of it, if you only take some of the A's and put them into B, but then you take that entire bucket and put it into C, then of course there will be A's in there. But if you take all the A's into B (remember, we don't know how many A's that is, it could be literally 2), then take only some of that entire bucket into C, it's less likely that there will be A's in C. Hope this helped!!
So in the previous lesson they said that A←s→B→C leads to a valid inference of A←s→C. This in plain English would be if some of A are B and all of B is C, then some of A are C. (For example, if some fish in the fish tank are red and all red fish are venomous then we can make the inference that some fish in the fish tank are venomous).
However, in this lesson they introduce the formal argument A←s→B←C (or in other words C→B←s→A). In this case, you would be saying that all of C is B and some of B are A. For this type of formal argument you CANNOT make an inference. When you first see this argument, you would want to make the inference A←s→C but this cannot be an inference made because it could be true but it could also be false.
Here's how that works. Imagine a circle diagram where B is a big circle and within B there is a smaller circle called C. Because the only thing that this lawgic statement tells us is that all of C is in B, the size of C can be large or small. So C could take up a big spot within B or it could be a small dot within the circle "B." However, the lawgic statement goes onto say that some of B are A. In this case, could we guarantee that at least some of C (in other words, at least one of C) will be a part of A? No. Because what if the "some of B" that is a A is a part of the circle that C does not cover? If within the circle "B," circle C and A does not overlap, it would mean that some of C is NOT A and this is a possible scenario.
For example, let's replace A with fish in the fish tank, B with red and C with venomous fish. We can make the exact same formal argument as above (A←s→B←C) by saying "all venomous fish are red and some red fish are in the fish tank." (in fish tank ←s→ red fish ← venomous) Here we can't say that some fish in the fish tank are venomous. This example argument only states that the only possible fish in the world that can be venomous are red (venomous → red). Does that mean all red fish are venomous(red → venomous)? No, that would be a mistaken reversal. The owner of the fish tank could have gotten very lucky or only picked red fish that are not venomous. In that case, are any fish in the fish tank venomous? No! Because the owner only picked the non-venomous red fish which is possible under this lawgic statement. So if the only fish in the world that are venomous are red fish and the fish tank has red fish, it does not necessarily mean that the fish tank has venomous fish.
The example is really obvious, but when I think about it, something like "All violinist at New York Philharmonic know how to play the violin. Some people who know how to play the violin like to tune their violins daily. Therefore some violinists at NYP like to tune their violins daily." will definitely trip me up if I'm not careful about it.
great point, I feel like this is one of those moments that reminds us we need to shirk common sense when looking specifically for argument structure. cause while it’s definitely likely (and as someone that played instruments, definitely true) that NY philharmonic musicians tune their instruments daily, that isn’t a valid conclusion that can be drawn from the premises.
I think it would really be helpful to use the scoops example from previous lessons across these as well. It started to click for me when I read someones comment about scoops!
I understood it by thinking of the Formal Arguments #4 and #6. They all have to have some or most before all because we needs As in the other three two buckets.
A <--s--> B --> C
A <--s--> C
Some As are Cs. Because there is some As in the C bucket.
Not like the invalid argument:
A -->B <--s--> C
A <-s-> C
How do I have some As if I put all of them B. It does not make a correct conclusion.
I appreciate these explanations in written format as we already had videos to watch on this! Sometimes it's easier to understand when watching the videos, so reading it through helps me synthesize and think through the different arguments.
@Gisellednava rjon27 comment really helped me understand. I think it possible that there are humans that have tails but there is no 100% chance there that some mammals that have tails happened to be human. The "some" could all be different mammals that are not humans.
Here's my attempt at an invalid and valid argument. Someone correct me if I'm going about it wrong!
Invalid: All peaches have pits. Some pits are rotten. Therefore, some peaches are rotten.
The reason why this is invalid is because we don't know the peach is rotten. It could be because the air had weird chemicals in it, or maybe a bug was hiding in the peach. Simply knowing that some peach pits are rotten isn't enough to know that the peach itself is rotten.
Valid: Some peaches have pits. All pits are rotten. Therefore, some peaches are rotten.
This is valid because we know ALL of B is true. If all pits are rotten and we know some peaches have pits, we at least know some of the peaches are rotten.
this confused me so i put it into something my brain could comprehend:
All flowers are plants. (A -> B)
Some plants grow strawberries. (B <-s-> C)
Therefore, some flowers grow strawberries. (A <-s-> C)
Think:
What makes you think flowers and strawberry plants overlap in the plant community? Is there proof in a premise that tells us there are strawberry-growing flowers? NO. So the LSAT has no reason to think that and it's invalid. Sometimes it helps to imagine you are arguing with the LSAT prompt. Like "What makes you think that? Where's your proof? No proof? Invalid."
You cannot infer that flowers are in the subset of plants that grow strawberries when there is no premise that provides that information. Your job is to only believe what the premises are telling you.
This argument has flawed logic because it is making an assumption about flowers based off of it's membership in the plant group. You know flowers are plants right? You know some plants grow strawberries? Then why are you assuming flowers grow strawberries just because both are plants!!
In my case, the word "all" in the first premise make it hard to think of flowers as a subset of plants. It helps in this stage to draw it out so your brain genuinely pictures how absurd this flawed logic is. Big circle is plants. Inside Big circle: Little circle #1: flowers and Little circle #2: strawberry growing plants. There is no info in the argument that says the two overlap so why is the conclusion assuming that?
All Options at Marys dessert shop is frozen yogurt, some frozen yogurt is mint flavored; therefore some of the Options at Marys shop is mint.
this in incorrect because the statement about mint is about all frozen yogurt, it doesn't tell us anything about if frozen yogurt at Marys dessert shop. It is just as likely she only serves vanilla and chocolate. we cannot disprove or prove she has mint, just that it is possible.
But because "some" is weaker than "most", wouldn't that actually help an argument in this case? If "most" violinists aren't exceptionally good at playing the violin, I'm struggling to see how changing "most" to "some" would be invalid just because the "most" argument is invalid.
I found it helpful to draw out the sets in a way where it makes sense why the invalid form doesn't work. Hope this helps someone who's struggling to understand!
Remember: a valid conclusion about intersecting sets can only be made if the some arrow appears before the all arrow.
Ex.
Artists in the master class are painters. Some people who call themselves painters suck at art. Therefore, some artists in the master class suck at art.
Art's -> Pnt's <-s-> Suck@it
____
Art's <-s-> Suck@it
Thus is NOT valid
Again, just because the first set shares a characteristic with the second (painters), does not mean you can equate the two.
Ex.
Some artists in the master class are painters. All people who paint suck at art. Therefore, some artists in the master class suck at art.
Art's <-s-> Pnt's -> Suck@it
____
Art's <-s-> Suck@it
Here, we know 100% of the subset (painters) ALL share the quality we are discussing (sucking at it). So, we can easily conclude that the portion of artists in the class that are painters definitely suck at it.
#help so we don't even need to read the conclusion to know it'll be invalid (if in this specific instance, all they're giving us are an all followed by a some premise?
This will help when you're doing flaw questions and the flaw is an invalid argument like this; knowing these will help you anticipate whether the answer choices are right/wrong...so sometimes you won't need to read the conclusion, but that won't be for a while i think
74 comments
I think it helps to think about it like order of operations.
If you dump some of you A's into your B's
then dump all of your B bucket into your C's, then you will definitely have some A's in your C's.
But if you dump all of your A's into your B's
and then dump some of your B's into your C's, then you won't necessarily have any A's in your C's, you could, but its not guaranteed. If it is not guaranteed then it is not valid.
I think this reasoning also work for the most rule as well.
Very helpful, thank you!
Hands down the best explanation I've found on here. Way better than what is in the lessons. Thank you !!
@A.Belle you are a BEAST. 7Sage should update this with your formula.
#YouRock
@A.Belle great explanation. I like this more than the "scoop" example 7sage has been using.
Add a video for these flaw explanations please.
@ChristinaCorbo !!!
why is there no video for the important subjects :'(
Here's my attempt at explaining:
All of A are B: all humans are mammals (A --> B)
Some B are C: some mammals have tails (B <s> C)
Therefore, some humans have tails (A <s> C)
We cannot conclude that some humans have tails just because all humans are mammals. I tried to use an example that was obvious, I hope this helps!
It's really helpful for me to think of this and the previous flaw with the buckets scenario. Think of it, if you only take some of the A's and put them into B, but then you take that entire bucket and put it into C, then of course there will be A's in there. But if you take all the A's into B (remember, we don't know how many A's that is, it could be literally 2), then take only some of that entire bucket into C, it's less likely that there will be A's in C. Hope this helped!!
@SheridanMcGadden thank you so much. This helped me understand it way better.
im going to need a video explanation on this one chief im starting to dive myself insane
Same! I'm so lost with these last 3 logic flaws.
Because I'm a watch nerd:
Premises:
All Submariner owners own Rolexes.
Some Rolex owners own Grand Seikos.
Can we conclude: Some Submariner owners own Grand Seikos?
NO
ALL must always be secondary........ In order to include the SOME AND MOST if they are placed first the smaller pools trickle into the larger ones. .
DRAW OR THINK OF VENN DIAGRAMS! It helps a lot :D
Can someone please explain this in English and not Lawgic?
So in the previous lesson they said that A←s→B→C leads to a valid inference of A←s→C. This in plain English would be if some of A are B and all of B is C, then some of A are C. (For example, if some fish in the fish tank are red and all red fish are venomous then we can make the inference that some fish in the fish tank are venomous).
However, in this lesson they introduce the formal argument A←s→B←C (or in other words C→B←s→A). In this case, you would be saying that all of C is B and some of B are A. For this type of formal argument you CANNOT make an inference. When you first see this argument, you would want to make the inference A←s→C but this cannot be an inference made because it could be true but it could also be false.
Here's how that works. Imagine a circle diagram where B is a big circle and within B there is a smaller circle called C. Because the only thing that this lawgic statement tells us is that all of C is in B, the size of C can be large or small. So C could take up a big spot within B or it could be a small dot within the circle "B." However, the lawgic statement goes onto say that some of B are A. In this case, could we guarantee that at least some of C (in other words, at least one of C) will be a part of A? No. Because what if the "some of B" that is a A is a part of the circle that C does not cover? If within the circle "B," circle C and A does not overlap, it would mean that some of C is NOT A and this is a possible scenario.
For example, let's replace A with fish in the fish tank, B with red and C with venomous fish. We can make the exact same formal argument as above (A←s→B←C) by saying "all venomous fish are red and some red fish are in the fish tank." (in fish tank ←s→ red fish ← venomous) Here we can't say that some fish in the fish tank are venomous. This example argument only states that the only possible fish in the world that can be venomous are red (venomous → red). Does that mean all red fish are venomous(red → venomous)? No, that would be a mistaken reversal. The owner of the fish tank could have gotten very lucky or only picked red fish that are not venomous. In that case, are any fish in the fish tank venomous? No! Because the owner only picked the non-venomous red fish which is possible under this lawgic statement. So if the only fish in the world that are venomous are red fish and the fish tank has red fish, it does not necessarily mean that the fish tank has venomous fish.
Hope that makes sense.
Awesome, thank you so much
The example is really obvious, but when I think about it, something like "All violinist at New York Philharmonic know how to play the violin. Some people who know how to play the violin like to tune their violins daily. Therefore some violinists at NYP like to tune their violins daily." will definitely trip me up if I'm not careful about it.
loved it.
great point, I feel like this is one of those moments that reminds us we need to shirk common sense when looking specifically for argument structure. cause while it’s definitely likely (and as someone that played instruments, definitely true) that NY philharmonic musicians tune their instruments daily, that isn’t a valid conclusion that can be drawn from the premises.
#feedback
I think it would really be helpful to use the scoops example from previous lessons across these as well. It started to click for me when I read someones comment about scoops!
I understood it by thinking of the Formal Arguments #4 and #6. They all have to have some or most before all because we needs As in the other three two buckets.
A <--s--> B --> C
A <--s--> C
Some As are Cs. Because there is some As in the C bucket.
Not like the invalid argument:
A -->B <--s--> C
A <-s-> C
How do I have some As if I put all of them B. It does not make a correct conclusion.
I appreciate these explanations in written format as we already had videos to watch on this! Sometimes it's easier to understand when watching the videos, so reading it through helps me synthesize and think through the different arguments.
@catintheLSAT There were videos for these???
So in this and the last one, to put it very simply, if there is an arrow before the ←s→ or ‑m→ it is invalid? The ←s→ and ‑m→ must be first.
Exactly!
who else is confused :p
@Gisellednava rjon27 comment really helped me understand. I think it possible that there are humans that have tails but there is no 100% chance there that some mammals that have tails happened to be human. The "some" could all be different mammals that are not humans.
Here's my attempt at an invalid and valid argument. Someone correct me if I'm going about it wrong!
Invalid: All peaches have pits. Some pits are rotten. Therefore, some peaches are rotten.
The reason why this is invalid is because we don't know the peach is rotten. It could be because the air had weird chemicals in it, or maybe a bug was hiding in the peach. Simply knowing that some peach pits are rotten isn't enough to know that the peach itself is rotten.
Valid: Some peaches have pits. All pits are rotten. Therefore, some peaches are rotten.
This is valid because we know ALL of B is true. If all pits are rotten and we know some peaches have pits, we at least know some of the peaches are rotten.
@kyorofan20 This was helpful thank you!
this confused me so i put it into something my brain could comprehend:
All flowers are plants. (A -> B)
Some plants grow strawberries. (B <-s-> C)
Therefore, some flowers grow strawberries. (A <-s-> C)
Think:
What makes you think flowers and strawberry plants overlap in the plant community? Is there proof in a premise that tells us there are strawberry-growing flowers? NO. So the LSAT has no reason to think that and it's invalid. Sometimes it helps to imagine you are arguing with the LSAT prompt. Like "What makes you think that? Where's your proof? No proof? Invalid."
You cannot infer that flowers are in the subset of plants that grow strawberries when there is no premise that provides that information. Your job is to only believe what the premises are telling you.
This argument has flawed logic because it is making an assumption about flowers based off of it's membership in the plant group. You know flowers are plants right? You know some plants grow strawberries? Then why are you assuming flowers grow strawberries just because both are plants!!
In my case, the word "all" in the first premise make it hard to think of flowers as a subset of plants. It helps in this stage to draw it out so your brain genuinely pictures how absurd this flawed logic is. Big circle is plants. Inside Big circle: Little circle #1: flowers and Little circle #2: strawberry growing plants. There is no info in the argument that says the two overlap so why is the conclusion assuming that?
Ok here is my attempt at an invalid argument.
All Options at Marys dessert shop is frozen yogurt, some frozen yogurt is mint flavored; therefore some of the Options at Marys shop is mint.
this in incorrect because the statement about mint is about all frozen yogurt, it doesn't tell us anything about if frozen yogurt at Marys dessert shop. It is just as likely she only serves vanilla and chocolate. we cannot disprove or prove she has mint, just that it is possible.
But because "some" is weaker than "most", wouldn't that actually help an argument in this case? If "most" violinists aren't exceptionally good at playing the violin, I'm struggling to see how changing "most" to "some" would be invalid just because the "most" argument is invalid.
Some Before All
A ←s→ B → C
________
A ←s→ C
THIS IS VALID
ALL before some IS NOT
I found it helpful to draw out the sets in a way where it makes sense why the invalid form doesn't work. Hope this helps someone who's struggling to understand!
Here's an example I made for myself if it helps:
Trap 5: Swapping "some" and "all" arrows:
Remember: a valid conclusion about intersecting sets can only be made if the some arrow appears before the all arrow.
Ex.
Artists in the master class are painters. Some people who call themselves painters suck at art. Therefore, some artists in the master class suck at art.
Art's -> Pnt's <-s-> Suck@it
____
Art's <-s-> Suck@it
Thus is NOT valid
Again, just because the first set shares a characteristic with the second (painters), does not mean you can equate the two.
Ex.
Some artists in the master class are painters. All people who paint suck at art. Therefore, some artists in the master class suck at art.
Art's <-s-> Pnt's -> Suck@it
____
Art's <-s-> Suck@it
Here, we know 100% of the subset (painters) ALL share the quality we are discussing (sucking at it). So, we can easily conclude that the portion of artists in the class that are painters definitely suck at it.
So basically, the smaller amount needs to come before the larger amount in order for an argument to be true
#help so we don't even need to read the conclusion to know it'll be invalid (if in this specific instance, all they're giving us are an all followed by a some premise?
This will help when you're doing flaw questions and the flaw is an invalid argument like this; knowing these will help you anticipate whether the answer choices are right/wrong...so sometimes you won't need to read the conclusion, but that won't be for a while i think