Negation of a statement with "most" and "conditional statements"

aaabbbccc

I am having a difficult time figuring out how to negate a sentence that is comprised of both "most" and "conditional statements."

For example, if one says, "most people who study at least 5 hours a day for LSAT will get 180," how can we negate this?

Thank you guys!

NYC12345

@aaabbbccc
SAL5H-----M----->Get180

NYC12345

/Get180----->/SAL5H

Pacifico

I don't think that's correct since you're removing the most element completely. You need to be able to account for the people that do study for 5 hours or more but don't get a 180. Your negation denies they exist. Take a look at the conversation I was having with another 7Sage user at the top of the comments here: http://7sage.com/lesson/quiz-negation-3-answers/#comment-30808

Since there is no word in English for the opposite of "most", you have to simply say "It's not the case that most people who study at least 5 hours for LSAT will get 180".

Jonathan Wang

Pacifico is right. "Most" means more than half, so if that's not true it's just half or less.

DumbHollywoodActor

Why isn't it "few"? Doesn't that mean less than half?

NYC12345

@Pacifico
@"Jonathan Wang"
so would it be...
/get 180--------->half or less SAL5H

Matt1234567

@alexandergreene93 said:
so would it be...
/get 180--------->half or less SAL5H

You can't use the contrapositive on a most statement.
The original statement was most people who study at least 5 hours for lsat will get 180.
Al5hours Most 180.

Negate this relationship: it's not the case that most people who study at least 5 hours for lsat will get 180. So, it basically means half or less. So half or less of the people who study at least 5 hours for lsat will get 180.

NYC12345

@Matt1234567
Thank you for clarifying.

aaabbbccc

Thank you for your help! @Pacifico @alexandergreene93 @Matt1234567

Seriousbird

@"Jonathan Wang" so the negation of "most" would be "some" then? I was under the perception that there is no negation for "most"

Sami

@sweetsecret

So the negation of "most" is definitely not "some". Most means 51-100%. Some means 1-100%.
When you negate something you want to split the statement into two neat logical halves. So here the complete logical opposite of "most" will be 0%-50%. But the word "some" leaves out 0% and goes beyond 50% and thats why its not the logical opposite of "most".

*That's why I think a better way to say this is "that it is not the case that most people will ____" Because I don't think, as also stated above, there is a word in english for the opposite of most.

and I don't think "few" would be the opposite either since "few" means more than 1. And this leaves out our 0-1% variable. We need a cleaner cut and thats why with most its better to say "its not the case ...".

dennisgerrard

I forget which post said "most" statement has no negation since it's ambiguous to say either way.

Sami

@dennisgerrard There is definitely a negation for "most". But you have to see it in terms of what your goal is when you do negation.

so if our goal is to find the logical opposite of 51-100%, we know that would be 0-50%. So the negation for most is 0-50% and it definitely exists. We just don't have a word for it.

Jonathan Wang

Whoever said there's no negation to a most statement is wrong. This is a classic example of memorizing vocabulary and failing to recognize the conceptual basis behind it.

"Most" just means more than half. Let's say there's a pool of 100 puppies. Is it possible for me to take more than half of them? Of course. Is it possible for me to not take more than half of them? Sure. Boom - you have an easy-to-remember example of most and of "not most" - its negation. Yes, there isn't a neat English word to put on it, but I'm willing to bet money that this concept is not new to you, or even particularly complicated when put in this way.

Another example I just used with Sami on Discord - the sentences "It's not true that most people have 30 legs" (meaning that 50% or less of people have 30 legs) and "Some people have 30 legs" (implying that at least 1 person has 30 legs) are not equivalent. See if you can figure out why.

Additionally, how is it even possible for a concept to not have a negation? What concept exists that I can't just slap a "not" in front of and deny its existence in a particular case? Apple? Not an apple. Shiny? Not shiny. Blue? Not blue. Majority? Not a majority. It's like trying to have an "in" without an "out".

dennisgerrard

thanks for clarification!!

Seriousbird

@Sami thank you for your input, I really like your use of 0-50% to explain why you cannot use some as some does not include 0%

@"Jonathan Wang" your examples were great too! Thank you. I think the answer to the 30 legs example is this:

It's not true that most people have 30 legs
This could be inclusive of 0 people because of the it's not true, most people

Some people have 30 legs
At least 1 person has to have 30 legs

They are not equivalent because one allows for 0 people while the other requires at least 1 person.

Thank you both! I really understand it now!! I think I was confusing how most does not have a contrapositive with most not being negated, and then when I went through some of the older lessons I saw a comment somewhere (I think) that most cannot be negated. It's good to receive confirmation though and know for sure. Also, Jonathan has an excellent point that anything can be negated.

ajcrowel

As an aside, surprisingly enough, this is one of the questions Kaplan usually asks people who interview with them.
You can't actually determine any relationships by negating the statement "most people who study at least 5 hours a day for LSAT will get 180." Speaking in the mumbo-jumbo, the aforementioned expresses quantification over a set (quantifier logic). Conditional logic deals with the sufficient and necessary relationship between sets and their objects. This relationship is airtight, if you will, because the relationship holds for the entire set. No such air-tightness exists in quantifier logic. Its negation would be the following: it is not the case that "most people who study at least 5 hours a day for LSAT will get 180," but because there's no 'flowing relationship' in that expression it's mostly useless.
P.S you don't need to know quantifier logic for the LSAT. If you think you need to negate that statement to get a question correct, you're probably missing something else.
Hope that helps!

Sami

@sweetsecret said:
I really like your use of 0-50% to explain why you cannot use some as some does not include 0%

Just don't forget the other half of the issue as well; "some" includes 1-100% which means it also includes "most" which is 51-100%. How is that even the opposite of most? It basically includes all the variables of "most".

When I say "some puppies are cute" I am not excluding the idea that "most puppies are cute" or even "all puppies are cute". They are not opposites and therefore not the negation of each other.