If a some dogs like bacon is MBT, then given that some is reversible, cant some bacon like dogs? This is a stupid sentence, but I am just wondering in terms of our logic rules.
I don't understand all implying some. If all dogs like bacon, and this implies that some dogs like bacon, doesn't that mean that all dogs like bacon implies some dogs do not like bacon?
If this is the case, then how is the range of some and most include 100% of something? If All is a bigger claim then the other two, then the other two must not include all right?
#feedback https://7sage.com/lesson/quantifier-inferences/?ss_completed_lesson=25459 says: "All" is a subset of "most." That's why it implies "most." Similarly, "most" is a subset of "some." That's why it implies "some." Is this a typo?
BC While all implies most, most does not necessarily imply all—which means all is not a subset of most, but rather most is a subset of all in terms of quantity.
The way I like to see this to help me understand is reflecting it off of criminal law burdens to meet.
Beyond every reasonable doubt is ALL. Preponderance of Evidence is Most Probable Cause is Some.
Beyond a reasonable doubt is the highest burden a jury can find. So, if the jury has believed a defendant is beyond a reasonable doubt of lets say Grand Theft, then we can also infer that they have met preponderance of evidence, and probable cause because they are lower burdens to meet and those have to be met already to get to the highest burden.
This may help some, for me in my criminal brain, it helps to visualize it like this.
Kevin Lin has a GREATTT video on Youtube about this as well.
https://www.youtube.com/watch?v=JkQ2ZRizWIE
An example I came across that helps me a bit:
In the context of combining statements containing quantifiers, you can remember the golden rule by thinking of the “4 S Rule”: The Sufficient of the Stronger statement must be Shared, and the conclusion is a “Some” statement.
Here’s how it works in practice – take the following example:
1. Everyone who is studying for the LSAT is stressed.
2. Some people who are studying for the LSAT are abstaining from alcohol.
In this case, we have an “all” statement (sentence #1) and a “some” statement (sentence #2). The stronger of those two statements is the first one, the “all” statement. The sufficient condition of the stronger statement is “studying for the LSAT”; in order for us to be able to combine these statements, they must both share that condition. Fortunately, the “some” statement also references people who are studying for the LSAT, so we’re good to go.
The conclusion, as we know from our golden rule, is going to be a “some” statement — in this case, that “Some people who are stressed are abstaining from alcohol.”
These combinations work because at least one of the premises is relatively strong. However, there are two combinations that will never, EVER work, simply because the premises are too weak to support a conclusion. You can never combine a “most” statement with a “some” statement, and you can never combine two “some” statements.
There are other variations that this video and Kevin's video breaks down that is super helpful.
To clarify, can I think of "some" as necessary for both "most" and "all?" Or do we consider all as /some b/c of the fact that some = implies at least 1 & all = means all?
I also found this very confusing, the only way I can make it clearer in my mind is to stop thinking about one circle inside of the other and instead think that "ALL" is Sufficient for "MOST" as a necessary, and "MOST" is Sufficient for "SOME" as a Necessary. By this logic they are subsets to supersets. Am I wrong in thinking this way?
Why is it that all→most = subset→superset? would "all" not be the superset and "most" be the subset? visually, "most" would be a circle contained within the larger "all" circle.
How is "all" a subset of "most" ? And how is "most" a subset of "some" ?
#help! can someone re-explain why "all" is a subset of "most" instead of the other way around, "most" being a subset of "all"? So like going back to cats & mammals, cats is the subset for mammals bc being a cat would imply it is a mammal but mammal is the broader category so why isn't "all" the broader category/superset? Does my question make sense or am I rambling lol
Because many implies some due to the fact that some means at least one, it must be true that some of a thing is a valid inference to many of that thing. Most also validly implies some for similar reasons. But many cannot validly imply most because of how subset and superset are viewed for their relationships. The idea that there is many of something means its lower boundary (at least 3 or more) falls outside of the superset of most where its lowest boundary encompasses 51% or more of that thing. If it was entirely encompassed by the superset, then it would be valid to imply many→most. Most implies many because it does encompass its entire range of boundaries.
It all has to do with the fact that you can equate many to some as a falsehood to better see the relationship between them. Just because you have a large amount of something "many," it doesn't imply that you have most of that thing. The most relationship indicates a proportion of something, whereas many only has to be 3 or more. Few as a quantifier means some, but not many and typically implies "most not." You can't equate many and few with each other.
I like to use the example: Many people love the color blue. If many people love blue, then it is valid to say that some people like blue because there is at least 1 person that likes blue. It wouldn't make sense to say that because many people like blue, then most people like blue too due to the fact that "most" would mean that 51% of people like blue. We only know that at least 3 people like blue with the "many" quantifier. It must be true that some people like blue, but it COULD BE TRUE that most people like blue. For your diagrams, I think the one on the right is correct. If you still need more help, I can try to come up with more examples that may work better for you. Quantifier relationships are difficult and super easy to miss little changes, so I completely understand not quite getting it. I still struggle with it at times. lol
"All" implies "Most" because if something is true for all, it is also true for most.
"Most" implies "Some" because if something is true for most, it is also true for at least some.
"Some" is not a subset of "Most":
"Some" and "Most" are not in a subset relationship. "Some" does not necessarily imply "Most" because "some" could be a small portion, and it doesn't have to encompass the majority.
If you say "Some," it means at least one but not necessarily a majority.
If you say "Most," it implies a majority but not necessarily all.
So, the key point is that while "Some" includes the possibility of "Most," it doesn't guarantee it. "Some" can indeed be most in certain cases, but it's not a strict implication. It depends on the specific context and proportions being referred to.
In set theory terms, "If all the members of a set A are also members of a set B, we say that A is a subset of B." Let A be "most" and B be "all." We then obtain the statement: "if all members of the set "most" are also members of the set "all," then set "most" is a subset of set "all." So I think the statement in the lesson is backwards.
I'm not sure I understand why all is a subset of most. I understand that if all, then most, this makes sense to me. Logically i understand that. However, when we put it in terms of all being the subset and most being the superset that falls apart in my mind. Doesnt all encompass many? #help
You can't have many → most but you could have most → many because many's bounds encapsulate most's bounds. Is this reasonable? #help
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58 comments
Can we add the quantifier word few in the lawgic chain and make it : all -> most -> some -> few?
If a some dogs like bacon is MBT, then given that some is reversible, cant some bacon like dogs? This is a stupid sentence, but I am just wondering in terms of our logic rules.
wait but didn't the last lesson just say some does not equal most??
xY
but
x-m->/Y
is what the last lesson said no? was I confusing m as Most instead of Many???
I don't understand all implying some. If all dogs like bacon, and this implies that some dogs like bacon, doesn't that mean that all dogs like bacon implies some dogs do not like bacon?
If this is the case, then how is the range of some and most include 100% of something? If All is a bigger claim then the other two, then the other two must not include all right?
#feedback https://7sage.com/lesson/quantifier-inferences/?ss_completed_lesson=25459 says: "All" is a subset of "most." That's why it implies "most." Similarly, "most" is a subset of "some." That's why it implies "some." Is this a typo?
BC While all implies most, most does not necessarily imply all—which means all is not a subset of most, but rather most is a subset of all in terms of quantity.
The way I like to see this to help me understand is reflecting it off of criminal law burdens to meet.
Beyond every reasonable doubt is ALL. Preponderance of Evidence is Most Probable Cause is Some.
Beyond a reasonable doubt is the highest burden a jury can find. So, if the jury has believed a defendant is beyond a reasonable doubt of lets say Grand Theft, then we can also infer that they have met preponderance of evidence, and probable cause because they are lower burdens to meet and those have to be met already to get to the highest burden.
This may help some, for me in my criminal brain, it helps to visualize it like this.
Kevin Lin has a GREATTT video on Youtube about this as well.
https://www.youtube.com/watch?v=JkQ2ZRizWIE
An example I came across that helps me a bit:
In the context of combining statements containing quantifiers, you can remember the golden rule by thinking of the “4 S Rule”: The Sufficient of the Stronger statement must be Shared, and the conclusion is a “Some” statement.
Here’s how it works in practice – take the following example:
1. Everyone who is studying for the LSAT is stressed.
2. Some people who are studying for the LSAT are abstaining from alcohol.
In this case, we have an “all” statement (sentence #1) and a “some” statement (sentence #2). The stronger of those two statements is the first one, the “all” statement. The sufficient condition of the stronger statement is “studying for the LSAT”; in order for us to be able to combine these statements, they must both share that condition. Fortunately, the “some” statement also references people who are studying for the LSAT, so we’re good to go.
The conclusion, as we know from our golden rule, is going to be a “some” statement — in this case, that “Some people who are stressed are abstaining from alcohol.”
These combinations work because at least one of the premises is relatively strong. However, there are two combinations that will never, EVER work, simply because the premises are too weak to support a conclusion. You can never combine a “most” statement with a “some” statement, and you can never combine two “some” statements.
There are other variations that this video and Kevin's video breaks down that is super helpful.
dog bacon
Some dogs like bacon.
bacon dog
Some that like bacon are dogs.
To clarify, can I think of "some" as necessary for both "most" and "all?" Or do we consider all as /some b/c of the fact that some = implies at least 1 & all = means all?
all → most → some
all is sufficient for most.
most is sufficient for some.
I also found this very confusing, the only way I can make it clearer in my mind is to stop thinking about one circle inside of the other and instead think that "ALL" is Sufficient for "MOST" as a necessary, and "MOST" is Sufficient for "SOME" as a Necessary. By this logic they are subsets to supersets. Am I wrong in thinking this way?
Why is it that all→most = subset→superset? would "all" not be the superset and "most" be the subset? visually, "most" would be a circle contained within the larger "all" circle.
How is "all" a subset of "most" ? And how is "most" a subset of "some" ?
Is it wrong to think of the quantifiers in this order from least to greatest?
some→few→many→most→overwhelming majority→all
I understand all-> most-> some, but can most imply many? why or why not?
Is it also accurate to say:
All → Most
Most → Some
as well as
Many → Some
Few → Some
Can you take the contrapositive of "all → most → some" and assume that
"/some → /most→ all"?
#help! can someone re-explain why "all" is a subset of "most" instead of the other way around, "most" being a subset of "all"? So like going back to cats & mammals, cats is the subset for mammals bc being a cat would imply it is a mammal but mammal is the broader category so why isn't "all" the broader category/superset? Does my question make sense or am I rambling lol
Because many implies some due to the fact that some means at least one, it must be true that some of a thing is a valid inference to many of that thing. Most also validly implies some for similar reasons. But many cannot validly imply most because of how subset and superset are viewed for their relationships. The idea that there is many of something means its lower boundary (at least 3 or more) falls outside of the superset of most where its lowest boundary encompasses 51% or more of that thing. If it was entirely encompassed by the superset, then it would be valid to imply many→most. Most implies many because it does encompass its entire range of boundaries.
It all has to do with the fact that you can equate many to some as a falsehood to better see the relationship between them. Just because you have a large amount of something "many," it doesn't imply that you have most of that thing. The most relationship indicates a proportion of something, whereas many only has to be 3 or more. Few as a quantifier means some, but not many and typically implies "most not." You can't equate many and few with each other.
I like to use the example: Many people love the color blue. If many people love blue, then it is valid to say that some people like blue because there is at least 1 person that likes blue. It wouldn't make sense to say that because many people like blue, then most people like blue too due to the fact that "most" would mean that 51% of people like blue. We only know that at least 3 people like blue with the "many" quantifier. It must be true that some people like blue, but it COULD BE TRUE that most people like blue. For your diagrams, I think the one on the right is correct. If you still need more help, I can try to come up with more examples that may work better for you. Quantifier relationships are difficult and super easy to miss little changes, so I completely understand not quite getting it. I still struggle with it at times. lol
#Help
This doesn't imply that this subset & superset relationship is a sufficient and necessary one does it?
"All" → "Most" → "Some":
"All" implies "Most" because if something is true for all, it is also true for most.
"Most" implies "Some" because if something is true for most, it is also true for at least some.
"Some" is not a subset of "Most":
"Some" and "Most" are not in a subset relationship. "Some" does not necessarily imply "Most" because "some" could be a small portion, and it doesn't have to encompass the majority.
If you say "Some," it means at least one but not necessarily a majority.
If you say "Most," it implies a majority but not necessarily all.
So, the key point is that while "Some" includes the possibility of "Most," it doesn't guarantee it. "Some" can indeed be most in certain cases, but it's not a strict implication. It depends on the specific context and proportions being referred to.
In set theory terms, "If all the members of a set A are also members of a set B, we say that A is a subset of B." Let A be "most" and B be "all." We then obtain the statement: "if all members of the set "most" are also members of the set "all," then set "most" is a subset of set "all." So I think the statement in the lesson is backwards.
I'm not sure I understand why all is a subset of most. I understand that if all, then most, this makes sense to me. Logically i understand that. However, when we put it in terms of all being the subset and most being the superset that falls apart in my mind. Doesnt all encompass many? #help
#feedback typo --> If "most A are B," then "some A are B."
You can't have many → most but you could have most → many because many's bounds encapsulate most's bounds. Is this reasonable? #help