This concept seems to become easier to grasp once you start thinking about it as set theory. At least, it seems to come easier to me that way. Gonna have to see if it works on the drills and questions later!
I'm confused with the way this sentence is written and including "all". If you say some pets are cats, technically that could mean all pets are cats because it just needs to be at least 1 with no upper boundary. But, we know that's not true because dogs are pets, fish are pets, etc. This doesn't make sense to me
@mayamcd125 Remember, don't go off your worldly knowledge.
Going off of the logical stand point (without going straight to our assumptions):
Since the arrow goes both ways, yes, it could mean that all pets are cats,orall cats are pets. Of course "some" only means at least one. We're going purely off of what the text gives us. If we say at "least one," thats reasonable. As we start to move to "all", then it becomes increasingly unreasonable.
I know its weird to think of at first, but its about thinking logically and very literally, based off of what we're reading. The more we practice seeing things that way, the more it will become a second nature to us.
im confused. "Some students in Mrs. Stoops's class can read," can also mean "Some students that can read are in Mrs. Stoops's class." However, when you mapped it, you said that students and read are two different sets. However, the translation seems to merge these two and is now "students reading" and "Mrs. stoops's class." Am I wrong?
@KyleWelch the only student's we're referring to are the ones in Mrs Stoops class. some of them can read. He only used "students" in the lawgic translation to simplify. remember, the shorter & more simple, the faster you go. Of course the tradeoff that is spoken of in earlier lessons is missing some of the critical context.
Hi all, I made another flashcard set. This time for memorizing Quantifiers. Flashcards are what really helped me in undergrad and so I decided to make them to companion my 7sage studies. Thought I'd share to help others who would benefit :) made a folder that I will most likely add more sets to as I go. Much Love and happy studying! https://quizlet.com/user/ehoffmanwallace/folders/lsat-7sage-flashcards
@JDMurphy If you see it virtually you will understand: let's say pets include dog cat and rat in a ratio of 40:38:22
so if some cats are pets its saying 38% of cats are pet why? and what?; well cats includes all tigers, lions and cats at a ratio of 40:40:20 see of those only 20 are pets means 20% of cats are pet but those 20% constitute as 38% in pets world,
Now, in the second sentence pets who are they dog, cat and rat and some of them aka 38% are still cats.
one more example
like some Asians are Indian
some Indian are Asian use the above concept you will understand.
In this lesson, we start using our language of Lawgic when dealing with relationships involving the quantity “some”. “Some” must include at least “one” or could include up to “all”.
In Lawgic, the quantifier “some” is represented with this bi-direction arrow ( ←S→ ) with an S in the middle of it. The “S” in this arrow is to distinguish it from the bi-conditional arrow ( ← → ).
The quantifier some ( ← S → ) which expresses an intersection. Let’s look at an example…..
“Some students in Mrs. Stoops’s class can read.”
Step 1: Identify that this is a statement, this is a claim that is amenable to translation. The way to do that is to (first) identify/notice the quantifier. Or the intersection indicator. In this instance it’s the word “Some”.
Step 2: Identify the two concepts. Typically, they are sets. The [first concept] is “students in Mrs. Stoops’'s class” & the [second concept] is “student or people can read”.
Step 3: Assign Symbols to represent these two sets. (Student) to represent students in Mrs. Stoops’s class & (Read) to represent the student/people who can read.
Translation Into Lawgic : Add the “Some” arrow! (student) ← S → (read) This means you can read this arrow either from left to right or from right to left. What that means is that this statement here, “student ← S → read,” is identical to the statement “read ← S → student.” In Lawgic, these two claims are the same.
Translating Back Into English: What it means is that “Some students in Mrs. Stoops’s class can read” is identical in meaning to “Some student that can read are in Mrs. Stoops’s class.”
Example→ “Some cats are pets” is identical to the claim that “Some pets are cats.” Translate into Lawgic: (c ← S → p) (p ← S → c) All four of these expressions are getting at the exact same idea, which, again, is just the idea of an intersection between two sets.
RECAP:
To translate “some” claims to Lawgic, use the bi-directional “some” arrow (← S →). The arrow is bi-directional because the intersection relationship works both ways: “some A are B” is identical to “some B are A.”
I was confused at first but I think I know why some can include all:
Some students pass the LSAT only if they study everyday.
In order for the necessary condition to be true it has to include at least 1 student, but can also include all students, that is, even if we say all students have to study everyday for passing LSAT, does not fail the necessary condition. So it can include all!
Essentially we need to look for anything can cause the necessary condition to fail and exclude that interpretation.
i get how some can mean all, but how does this help with lsat questions. I feel like from my limited experience, rarely are lsat answers with 'All' correct because they are too extreme.
"Some" covers an intersect and that's why it can go both ways.
Some cats are pets and Some pets are cats
These mean the same thing because they both have the same intersection in the middle where pets and cats overlap. Once you are in that intersection part in the middle you are part of both groups so it doesn't matter.
The word some means "at least one" so once I am in that middle group then yah, at least one cat is a pet, and at least one pet is a cat. Some can include all, sure. BUT it doesn't have to. All some has to do is mean "At least one"
Ex. I am a cat who is also a pet. I am in that middle intersection group so that means I can also say I am a pet who is a cat. On the flip lets pretend I am not a cat, but I am a pet. This means I can't be part of the that intersection in the middle. I am only part of the "pets" circle.
@EmilyMacaluso no it does not. The relationship is different. The if/then is a sufficiency and necessity (a guarantee if you have the sufficient) and the some is of intersection (more of an over lap).
When you break down the Stoops's sentence, it would be better not to use "students" as one of the main concepts, since when you bring it back together students is in both concepts. It would be better to break that first main concept into "Mrs. Stoops's class."
omg yes finally - the last few lessons in the last unit were just awful. Im scared to continue studying just bc how hare those were -- just impossible. I hope it gets more doable now
this might be answered in a future lesson, but i'm just curious. are there situations where "some" means "all" like the previous lesson said, and are used qualifiers as a sufficient condition? i know the example here is "some people who can read are students in the class, some students in the class are people who can read," but if we were provided more context before or after that statement that would include "all" as the meaning of "some" students in the class (the meaning being "all students can read in the class"), are there cases that the LSAT expects you to use this as a sufficient condition?
I can't figure out if this is more or less intuitive than just using (∃x) in the usual language of logic. Learning predicate logic is very different than what I'm learning here on 7sage.
If we used it in this class example it would be like:
S = Stoop's class
R = predicate (can read)
∃x = what is called the "existential quantifier"
(∃r)[Sr]
(∃r)[Sr] is true when Sr is true for at least one value of r
I'm not understanding how we introduce a biconditional symbol in there for this lesson.
I took some logic as well, so that existential modifier brought back a lot of memories haha. But I think it is just approaching the propositions from a different angle. Using the existential modifier is bringing it to a higher level of logic then is necessary for understanding the passage. Also it doesn't fit as well with the rest of the logical language we are using, as you pointed out. The 'some' biconditional that 7sage uses, doesn't fit into the syntax of first or second order logic, so that is why it isn't "translatable." However, the phrase you expressed is saying the same thing. Simply that there are two sets, and there is at least one object that shares the attributes of these two sets. Could be more, but we know for sure that there is at least one. Which is what the existential modifier is saying, as well as the 'some' biconditional.
@ColinErickson I agree this is going to take some getting used too lol, I have taught predicate logic to college freshman for 3 years and this new style threw me through a loop
Also I'm pretty sure using the existential as a logical connective inevitably leads to a contradiction within a logical system that includes it (from Russell's "On Denoting") however, it may still be practical?
54 comments
This concept seems to become easier to grasp once you start thinking about it as set theory. At least, it seems to come easier to me that way. Gonna have to see if it works on the drills and questions later!
does this mean we are forgoing sufficient and necessary conditions here then? if the arrow can go both ways? gulp
ahhhhhHHhHHHHHHHHHHHHHHHHHHHHHH what
@yesterdayseeker and this is just the foundations lol
My God there's so many layers to everything
I'm confused with the way this sentence is written and including "all". If you say some pets are cats, technically that could mean all pets are cats because it just needs to be at least 1 with no upper boundary. But, we know that's not true because dogs are pets, fish are pets, etc. This doesn't make sense to me
@mayamcd125 Remember, don't go off your worldly knowledge.
Going off of the logical stand point (without going straight to our assumptions):
Since the arrow goes both ways, yes, it could mean that all pets are cats, or all cats are pets. Of course "some" only means at least one. We're going purely off of what the text gives us. If we say at "least one," thats reasonable. As we start to move to "all", then it becomes increasingly unreasonable.
I know its weird to think of at first, but its about thinking logically and very literally, based off of what we're reading. The more we practice seeing things that way, the more it will become a second nature to us.
Cheers.
@GabrielLerma thank you this actually helped me to understand better cause I had the same question
im confused. "Some students in Mrs. Stoops's class can read," can also mean "Some students that can read are in Mrs. Stoops's class." However, when you mapped it, you said that students and read are two different sets. However, the translation seems to merge these two and is now "students reading" and "Mrs. stoops's class." Am I wrong?
@KyleWelch the only student's we're referring to are the ones in Mrs Stoops class. some of them can read. He only used "students" in the lawgic translation to simplify. remember, the shorter & more simple, the faster you go. Of course the tradeoff that is spoken of in earlier lessons is missing some of the critical context.
Separate the subject from the predicate.
Hope this helped. Cheers.
Hi all, I made another flashcard set. This time for memorizing Quantifiers. Flashcards are what really helped me in undergrad and so I decided to make them to companion my 7sage studies. Thought I'd share to help others who would benefit :) made a folder that I will most likely add more sets to as I go. Much Love and happy studying! https://quizlet.com/user/ehoffmanwallace/folders/lsat-7sage-flashcards
This is how they get you — ‘it’s easy!’… 5 minutes later I’m solving advanced algebra with no numbers, just vibes and letters.
@JDMurphy If you see it virtually you will understand: let's say pets include dog cat and rat in a ratio of 40:38:22
so if some cats are pets its saying 38% of cats are pet why? and what?; well cats includes all tigers, lions and cats at a ratio of 40:40:20 see of those only 20 are pets means 20% of cats are pet but those 20% constitute as 38% in pets world,
Now, in the second sentence pets who are they dog, cat and rat and some of them aka 38% are still cats.
one more example
like some Asians are Indian
some Indian are Asian use the above concept you will understand.
Step by step breakdown:
In this lesson, we start using our language of Lawgic when dealing with relationships involving the quantity “some”. “Some” must include at least “one” or could include up to “all”.
In Lawgic, the quantifier “some” is represented with this bi-direction arrow ( ←S→ ) with an S in the middle of it. The “S” in this arrow is to distinguish it from the bi-conditional arrow ( ← → ).
The quantifier some ( ← S → ) which expresses an intersection. Let’s look at an example…..
“Some students in Mrs. Stoops’s class can read.”
Step 1: Identify that this is a statement, this is a claim that is amenable to translation. The way to do that is to (first) identify/notice the quantifier. Or the intersection indicator. In this instance it’s the word “Some”.
Step 2: Identify the two concepts. Typically, they are sets. The [first concept] is “students in Mrs. Stoops’'s class” & the [second concept] is “student or people can read”.
Step 3: Assign Symbols to represent these two sets. (Student) to represent students in Mrs. Stoops’s class & (Read) to represent the student/people who can read.
Translation Into Lawgic : Add the “Some” arrow! (student) ← S → (read) This means you can read this arrow either from left to right or from right to left. What that means is that this statement here, “student ← S → read,” is identical to the statement “read ← S → student.” In Lawgic, these two claims are the same.
Translating Back Into English: What it means is that “Some students in Mrs. Stoops’s class can read” is identical in meaning to “Some student that can read are in Mrs. Stoops’s class.”
Example→ “Some cats are pets” is identical to the claim that “Some pets are cats.” Translate into Lawgic: (c ← S → p) (p ← S → c) All four of these expressions are getting at the exact same idea, which, again, is just the idea of an intersection between two sets.
RECAP:
To translate “some” claims to Lawgic, use the bi-directional “some” arrow (← S →). The arrow is bi-directional because the intersection relationship works both ways: “some A are B” is identical to “some B are A.”
This makes sense so far. I'm waiting for something to hit that throws away all that sense.
@JessM FELT
I was confused at first but I think I know why some can include all:
Some students pass the LSAT only if they study everyday.
In order for the necessary condition to be true it has to include at least 1 student, but can also include all students, that is, even if we say all students have to study everyday for passing LSAT, does not fail the necessary condition. So it can include all!
Essentially we need to look for anything can cause the necessary condition to fail and exclude that interpretation.
it takes me so long to draw the some symbol smh
'Some cats are pets' and 'some pets are cats' do not seem identical to me.
I wonder where he is going with this lesson
i get how some can mean all, but how does this help with lsat questions. I feel like from my limited experience, rarely are lsat answers with 'All' correct because they are too extreme.
"Some" covers an intersect and that's why it can go both ways.
Some cats are pets and Some pets are cats
These mean the same thing because they both have the same intersection in the middle where pets and cats overlap. Once you are in that intersection part in the middle you are part of both groups so it doesn't matter.
The word some means "at least one" so once I am in that middle group then yah, at least one cat is a pet, and at least one pet is a cat. Some can include all, sure. BUT it doesn't have to. All some has to do is mean "At least one"
Ex. I am a cat who is also a pet. I am in that middle intersection group so that means I can also say I am a pet who is a cat. On the flip lets pretend I am not a cat, but I am a pet. This means I can't be part of the that intersection in the middle. I am only part of the "pets" circle.
Doess this apply to 'several' or 'many' or a few'?
#help
so i just want to be clear that this does not mean p>c as well as c>p
if it is a pet, then it is a cat,
if it is a cat, then it is a pet.
the <s> does not translate into if/then?
@EmilyMacaluso no it does not. The relationship is different. The if/then is a sufficiency and necessity (a guarantee if you have the sufficient) and the some is of intersection (more of an over lap).
@8M_M8 ^^^
are there cats that are not pets?!
@OrcaPark Yes. Some cats are feral street cats. Some are wild tigers. Not all are pets.
When you break down the Stoops's sentence, it would be better not to use "students" as one of the main concepts, since when you bring it back together students is in both concepts. It would be better to break that first main concept into "Mrs. Stoops's class."
Finally a lesson that's intuitive in my brain!
omg yes finally - the last few lessons in the last unit were just awful. Im scared to continue studying just bc how hare those were -- just impossible. I hope it gets more doable now
this might be answered in a future lesson, but i'm just curious. are there situations where "some" means "all" like the previous lesson said, and are used qualifiers as a sufficient condition? i know the example here is "some people who can read are students in the class, some students in the class are people who can read," but if we were provided more context before or after that statement that would include "all" as the meaning of "some" students in the class (the meaning being "all students can read in the class"), are there cases that the LSAT expects you to use this as a sufficient condition?
i hope this question makes sense!
I can't figure out if this is more or less intuitive than just using (∃x) in the usual language of logic. Learning predicate logic is very different than what I'm learning here on 7sage.
If we used it in this class example it would be like:
S = Stoop's class
R = predicate (can read)
∃x = what is called the "existential quantifier"
(∃r)[Sr]
(∃r)[Sr] is true when Sr is true for at least one value of r
I'm not understanding how we introduce a biconditional symbol in there for this lesson.
I took some logic as well, so that existential modifier brought back a lot of memories haha. But I think it is just approaching the propositions from a different angle. Using the existential modifier is bringing it to a higher level of logic then is necessary for understanding the passage. Also it doesn't fit as well with the rest of the logical language we are using, as you pointed out. The 'some' biconditional that 7sage uses, doesn't fit into the syntax of first or second order logic, so that is why it isn't "translatable." However, the phrase you expressed is saying the same thing. Simply that there are two sets, and there is at least one object that shares the attributes of these two sets. Could be more, but we know for sure that there is at least one. Which is what the existential modifier is saying, as well as the 'some' biconditional.
@ColinErickson I agree this is going to take some getting used too lol, I have taught predicate logic to college freshman for 3 years and this new style threw me through a loop
Also I'm pretty sure using the existential as a logical connective inevitably leads to a contradiction within a logical system that includes it (from Russell's "On Denoting") however, it may still be practical?
@aldertree00644 I feel just taking ∩ from set theory could suffice alongside the existential quantifier.