Howdy, Stranger!
It looks like you're new here. If you want to get involved, click one of these buttons!
Categories
- 33.6K All Categories
- 28.2K LSAT
- 17.1K General
- 5.2K Logical Reasoning
- 1.4K Reading Comprehension
- 1.7K Logic Games
- 70 Podcasts
- 192 Webinars
- 11 Scholarships
- 194 Test Center Reviews
- 2.2K Study Groups
- 112 Study Guides/Cheat Sheets
- 2.5K Specific LSAT Dates
- 36 November 2024 LSAT
- 18 October 2024 LSAT
- 9 September 2024 LSAT
- 38 August 2024 LSAT
- 28 June 2024 LSAT
- 4 April 2024 LSAT
- 11 February 2024 LSAT
- 22 January 2024 LSAT
- 38 November 2023 LSAT
- 43 October 2023 LSAT
- 14 September 2023 LSAT
- 38 August 2023 LSAT
- 27 June 2023 LSAT
- 30 Sage Advice
- 5K Not LSAT
- 4K Law School Admissions
- 13 Law School Explained
- 10 Forum Rules
- 647 Technical Problems
- 288 Off-topic
Related Discussions
What is the negation of "not many"?
Edmond.Dantes
Alum Member
How do you negate "not many"?
To me, you can't just dropped the "not". Here's my thought process:
"Not many" seems to be the same as "some not."
"Not many people like apple" = "Some people do not like apple."
The negation of "some people do not like apple" is "everyone likes apple," and this is very different from "many people like apple" (dropping the not in "not many").
So you can't just drop the "not" in front of "many" to negate "not many." Am I right?
To me, you can't just dropped the "not". Here's my thought process:
"Not many" seems to be the same as "some not."
"Not many people like apple" = "Some people do not like apple."
The negation of "some people do not like apple" is "everyone likes apple," and this is very different from "many people like apple" (dropping the not in "not many").
So you can't just drop the "not" in front of "many" to negate "not many." Am I right?
Comments
"Not many" negated is "Many."
"Not many people like apple" is not the same as "Some people do not like apple."
It is true that if I say that in my school of two thousand students "not many people like apple," you may conclude that "some people do not like apple." However, if in my school "some people do not like apple," you cannot conclude that "not many people like apple." "Some people" can include every student (in which case not many/nobody likes apple) or possibly only two of a thousand students (in which case many people like apple).
The fact that "some people do not like apple" can be derived from "Not many people like apple" does not mean that they are the same thing.
With most terms, negating them can be done simply by relying on intuition.
For instance, if someone walks up to you and says "Not many people go to this school" and you know that they are wrong, what would you say? Probably something like, "Uh, no, many people do go to this school."
First of all, I'm pretty sure I read somewhere (possibly on 7Sage) that many = some. If I think about it, it also makes sense. What is the definition of "many"? It's not zero. It's at least one and possibly all. But, it's very flexible.
If only 1 out of 2,000 students like apple (9,999 dislike), can we still say "many students like apple"? I think so. Many, unlike most or majority, is not a clear boundary. Maybe you really hate apples, and one person liking it is one too many.
An easier example might be: "many people suffer from poverty." This would make logical sense to me even if 1 person suffers from poverty.
I think to sum up: I don't know if many has a definitive boundary (like more than 5, or more than 2, or anything like that). It seems extremely subjective to me and in almost anyway equivalent to "some."
...many?.... lol
So, a given thing + its negation will encompass everything in existence, literally everything contained in the universe in addition to all ideas and abstractions. So when you're negating there can not be room in the equation for anything to exist outside of the binary cut. So an easy example. Apples + not apples = everything that ever was, is, will be, could be, and couldn't be. Give me anything you can possibly conceive of and I can classify it within one of those two groups. A negation MUST create that binary cut. "Many" and "few" don't do that.
(I believe! It's a big universe y'all!)
so, negating not many (zero) would mean some (1-100)
Second, if "many" really were equivalent to "some", then the negation of "many" would be equivalent to the negation of "some". But this is not true. "Not some" is equivalent to "all not". If "many" were equivalent to "some", then when I say "not many people were born with a purple tooth", I'm saying the equivalent of "all people are born without a purple tooth". But this is false, per our stipulation.
Third, if "many" were equivalent to "some", it would be a blatant contradiction to say "some, but not many, people were born with a purple tooth". But this is not a blatant contradiction, and we use the "some, but not many..." expression all the time in ordinary language.
You're right that "many" is context-sensitive, but that should be more evidence to you that "many" is *not* equivalent to "some". "Some" is not context-sensitive; it means the same thing in every context. "Some A's are B's" is true if there is only one A&B thing or a million A&B things. "Many A's are B's", on the other hand, is true depending not only on how many A&B things there actually are, but also on how many total relevant things there are. In this way, "many" and "some" do not behave similarly at all.
(1) A society that has some crimes has some laws
(2) A society that has many crimes has many laws
Now consider the following: A society that has no laws has no crimes.
Your task is to describe a circumstance in which either (1) or (2) could be false given the information above:
Could you describe a circumstance in which (1) could be false? No. "A society that has some crimes has some laws" is the contrapositive of "A society that has no laws has no crimes".
Could you describe a circumstance in which (2) could be false? Yes. Two crimes could be instances of breaking one law.
This was from PT 1.4.21 where (D) and (E) correspond to (1) and (2), respectively. What does this tell us? The LSAC does not treat “some” and “many” as equivalent. (E) is incorrect. And it is incorrect precisely because "many" must take on a value of greater than one. They also do not mean the same thing in ordinary language, as the posters above have demonstrated.
@BackoftheEnvelope and @quinnxzhang
I also begin to realize that many is not the same as some in the LSAT context. PT 62 S4 (towards the end, the film preservation question) also relies on the many and some distinction.
Anyways, thanks for the inputs. It might be good to just see the two as similar but distinct.
For 62.4.23 the answer choice isn't dependent on the Some vs Many, as it talks about the "films not being preserved" and requires a necessary assumption. Only D provides this, as if the films are already on other media, they will not fail to be preserved, destroying the argument. @"Jonathan Wang" or @"J.Y. Ping" any insight to add for the above comments about how many doesn't mean some?
For 1.4.21 it does have a distinction, but this is also test 1.
I think the point of this thread is to say that they are NOT the same. Because if you treat them as the same, you will probably run into trouble.
An example is PT62 S4 Film Preservation question, in which one of the trap answer is "not many films have already been transferred to acetate."
If you think many = some ("some films have not been transferred), then you would negate this as "all films have already been transferred to acetate", which would be the right answer. (Except it's not, because the negation of "not many" is "many").
many --> some
but, some --> many is wrong.
"All" becomes "Some Not"
All is a part of some, so it is not the logical opposite of it.
See: https://7sage.com/lesson/advanced-negate-some-statements/
Some films have not been transferred would negate to None, so no films have been transferred, which is not the right answer.
Some = Many
Many = Some
Some can mean at least 1 to 100 and according to our lessons Many means at least 1, where as Most means 51+ and we cant say that Many = Most as that is not true. Many could be 32, which is some. It could also be 1 which is Some, and it could also be 100, which is also Some.
So since the negation of Some is None, Many would also negate to None.
"All" Negates to "Some Not" so wouldn't that also be "Not Many or Many Not"
Saying Not Many is Many would be like saying Not Some (Some Not) is Some, which we have learned is not a binary cut, so not the logical opposite. Unless I am way off base.
This seems like a great lesson to add @"J.Y. Ping"
No. "Not many" is not the logical opposite of "all". The logical opposite of "all" is "not all" or equivalently "some not".
Not many people have property A.
It is not the case that many people have property A.
It is not the case that at least two people have property A.
Some person (only one) has property A.
Let's say property A refers to being fat.
Not many people are fat.
Some person is fat.
Imagine being in a room of three people. Two are thin. One is fat. Not many people in this room are fat (it is not the case that at least two people in this room are fat). But, some person is fat (it is the case that one person is fat).
Here is a good paper from Jon Barwise on this (the first few sections are the most relevant): http://isites.harvard.edu/fs/docs/icb.topic980565.files/Sept 21/Barwise and Cooper 1981.pdf
And he (she?) also acknowledged that for LSAT purposes it might be the case that the existential component of both is the only one that matters, so for all LSAT intents and purposes JY might be right that one can consider many to be equal to some without deleterious effects (even though that's not really the case). Likely because the difference is context driven, and the LSAT writers are not going to have answers that depend on where each test taker draws the line between "some" and "many", and conversely "none" and "not many".
In the case of the question mentioned (PT 62, S4, Q23), the incorrect answer C states:
"Not many old movies have already been transferred to acetate"
If many=some, then "not many"="not some"="none"
So, answer C would effectively state "no old movies have already been transferred to acetate" and it's clearly not a necessary assumption. (Negating it would yield "some movies have already been transferred to acetate", which wouldn't destroy the argument).
Alternatively you can go about analyzing answer C without worrying about many and some.
Just negate "not many" to "many" (see how similar this is to negating "none" to "some"?)
"Not many old movies have already been transferred to acetate" negated would yield "Many old movies have already been transferred to acetate". Nope, this still doesn't destroy the argument, whether you think "many" is one, or 20%, or 99.9% so C is still not a necessary assumption.
If many = some, then this should be the same as "SOME old movies have NOT been transferred to acetate" (logically equivalent to above).
The negation of this second sentence is "ALL old movies have NOT been transferred to acetate", or in other words, "NO old movies have been transferred to acetate."
To me, this does weaken the argument.
--
The only way to get around this is by recognizing that "many" is not "some".
So "Not many old movies have been transferred to acetate" negates to
"Many old movies have been transferred to acetate", which is logically equal to
"Some old movies have been transferred to acetate"
--
Do you see how, depending on whether many = some, the negation yields different results. To me, this proves that "many" is not the same as "some."
The negation of "some have been transferred" is not "some have not been transferred"; it's "none have been transferred".
Similarly, the negation of "some have not been transferred" is not "all have not been transferred", it's "all have been transferred".
I'm pointing this out because regardless of the many=some discussion (which is going to be involved in a minuscule number of questions), the negation of some will come up repeatedly.
The negation of "Some A's are X" is never "Some A's are NOT X"; it's "All A's are not X" or "No A's are X" (either replace some with all and X with /X or just replace some with no/none)
The negation of "Some A's are NOT X" is not "Some A's are X" it's "All A's are X"
Now, because you applied the negation of "some" the wrong way twice, you actually arrived to the right form of the negation of answer C: "no movies have been transferred to acetate".
You think that it weakens the argument, but this is NOT a weakening question. It's a necessary assumption question. "No old movies have been transferred to acetate" does not destroy the argument. I'm not even sure it weakens it a great deal, but it certainly doesn't destroy it.
Maybe none have been transferred to acetate because they've all been transferred to polypropylene film in the 70's and while polypropylene is not as good as acetate it still buys them another 20 years of longevity.
The correct answer, D, precludes this. D states "some films are only in their original, vulnerable state". The negation "no films exist only in their original vulnerable state" is in fact a necessary assumption.
"C: Not many films from the earliest years of Hollywood have already been transferred to acetate."
IF many = some, then C is logically equivalent to "SOME films from the earliest years of Hollywood have NOT already been transferred to acetate." The negation should be:
"ALL films from the earliest years of Hollywood have already been transferred to acetate."
So my earlier translation was wrong (apologies), but I think this last negation does weaken the argument. If all old films have already been transferred to acetate, then of course the argument that "some films will not be preserved" is wrong.
As frustrated as you probably are over this, I think it actually represents a really positive progression in your prep. You’ve outgrown the “tricks” and are thinking more deeply and fundamentally about the logical principles. If JY says many = some, he’s saying that for people just starting out to help them wrap their minds around a challenging concept. This isn’t you anymore. You’ve progressed beyond that, so time to set aside the learning devices for the more difficult, higher level understanding. I think this demonstrates it really well actually. Forget the rule and just think about it. Does not many = not some? Of course it doesn’t.
When I first read this, I was pissed about being wrong, but yeah, of course, thinking about it just a little bit reveals that you many implies some, but not many cannot equate not some. Your point about the false binary helps put it into perspective, especially after reviewing the common flaws page today and its mention of a false dichotomy.
It's either old-timers who wrote it before this brand of LSAT began, people in law school now who mention how little they use some of the skills of the test throughout their programs, or people who don't understand and "zone out" halfway through my long-winded explanations. I'm grateful for every opportunity to re-assess my thinking about be challenged by the material, especially when it comes to the nuances of the test like this one!
My view is that "not many" is close to "a few" and @BackoftheEnvelope gets at this when he says the "not many" doesn't rule out the possibility of "some." However, when you negate the few statement hoping to reach what you would expect to be the result of a "many," you end up with the possibility of none, which is not correct.
I believe it might be more useful to treat such statements by looking at the scope of their negation, which is much more intuitive rather than formal. This reinforces the idea that these quantifiers deal with natural language rather than strict logic.
Not many films have been transferred.
It is not the case that many films have been transferred.
Not(Many films have been transferred).
NOT( F some T).
F->/T *
*this step is rough. It suggests that "Not many films have been transferred" is equivalent "no films have been transferred." I don't think that is what the original statement is actually conveying and has to do with the idea that the upper bound of "many" is considered to be a majority by some people, but is highly subjective. So when you read "not many films have been transferred" you think that there could still be some number that were transferred. This is why I feel that "few" is implied by "not many," because "few" entails some, but less than half.
Note that NOT( F some T) is different than treating "not many" as "some are not" which would translate to F some /T.
And negating NOT(F some T) removes the NOT() to get F some T, which is what we would expect from the translation of a "many" statement.
/some films were transferred = No films were transferred = All films have NOT been transferred.
NOT SOME A's are X is never equivalent to SOME A's are NOT X. It's equivalent to ALL A's are NOT X (or NO A's are X).
In the end, it doesn't really matter, if you use common sense. There's no necessary assumption about the number of movies that have been transferred to acetate.
The LSAT writers used "not many" instead of a more precise term because it doesn't matter how many "not many" is. C could tell us "no movies have been transferred" "some movies have been transferred", "most movies have been transferred" or "all movies have been transferred" and it would still not be a necessary assumption.
The only necessary assumption is that some movies still exist only in a vulnerable form (like their original form, for instance). Answer D covers that.
Thanks a million. 30 posts later and there's the rub!