"Some" vs "Many"

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PDaddy
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Re: "Some" vs "Many"

Postby PDaddy » Fri Mar 19, 2010 11:27 pm

Leeroy Jenkins wrote:for the purposes of logic, quantity is described as 'None' 'All' or 'Some'. if you're trying to figure out where 'many' lies on that spectrum...you have more important things to worry about.


+1 Wherever he bumped into "many" the writers were playing games. "Many" equals "some" and should be approached that way. Many does not equal "all", nor does it equal no/none/zero, of course.

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Fri Mar 19, 2010 11:39 pm

I studied way too much formal logic ...

Warning: Sorry for the slapdash organization of my post, but it should answer your question pretty well if you read through it.

Here is what you need to know:
1) The distinction doesn't matter for the LSAT
2) There is only a small difference in that "many" means "not few" and "few" stands for only an insignificant upper limit of a sample, so "few" has no existential commitment and could be zero (for small samples, pluralistic quantifiers like "few" and "many" don't have a use).

If you are interested in it, there is intersting work done on these quantifiers by a logician whose last name is "Altham." You can check out his book on this, which is called Logic of Plurality. If you do, however, keep in mind that splitting hairs on quantifiers like this would only be for personal edification, and that it will not get you anywhere on the LSAT (in fact, it might make you do worse because over thinking about things like this will slow you down)

* On the LSAT, any quantifier that means "more than zero" is functionally equivalent to "some" (e.g. "many," "often," "generally," "several," etc) ... The only exception to this is "almost all," which is the inverse of "some" ("some" means at least one is and "almost all" means at least one is not)

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autarkh
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Re: "Some" vs "Many"

Postby autarkh » Fri Mar 19, 2010 11:44 pm

Mattalones wrote:I studied way too much formal logic ...

Warning: Sorry for the slapdash organization of my post, but it should answer your question pretty well if you read through it.

Here is what you need to know:
1) The distinction doesn't matter for the LSAT
2) There is only a small difference in that "many" means "not few" and "few" stands for only an insignificant upper limit of a sample, so "few" has no existential commitment and could be zero (for small samples, pluralistic quantifiers like "few" and "many" don't have a use).

If you are interested in it, there is intersting work done on these quantifiers by a logician whose last name is "Altham." You can check out his book on this, which is called Logic of Plurality. If you do, however, keep in mind that splitting hairs on quantifiers like this would only be for personal edification, and that it will not get you anywhere on the LSAT (in fact, it might make you do worse because over thinking about things like this will slow you down)

* On the LSAT, any quantifier that means "more than zero" is functionally equivalent to "some" (e.g. "many," "often," "generally," "several," etc) ... The only exception to this is "almost all," which is the inverse of "some" ("some" means at least one is and "almost all" means at least one is not)



+1 Good post. One minor quibble: while I agree that "several," "often," and "many" are the functional equivalents of "some," doesn't "generally" mean "most"?
Last edited by autarkh on Fri Mar 19, 2010 11:50 pm, edited 3 times in total.

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Fri Mar 19, 2010 11:45 pm

autarkh wrote:
Mattalones wrote:I studied way too much formal logic ...

Warning: Sorry for the slapdash organization of my post, but it should answer your question pretty well if you read through it.

Here is what you need to know:
1) The distinction doesn't matter for the LSAT
2) There is only a small difference in that "many" means "not few" and "few" stands for only an insignificant upper limit of a sample, so "few" has no existential commitment and could be zero (for small samples, pluralistic quantifiers like "few" and "many" don't have a use).

If you are interested in it, there is intersting work done on these quantifiers by a logician whose last name is "Altham." You can check out his book on this, which is called Logic of Plurality. If you do, however, keep in mind that splitting hairs on quantifiers like this would only be for personal edification, and that it will not get you anywhere on the LSAT (in fact, it might make you do worse because over thinking about things like this will slow you down)

* On the LSAT, any quantifier that means "more than zero" is functionally equivalent to "some" (e.g. "many," "often," "generally," "several," etc) ... The only exception to this is "almost all," which is the inverse of "some" ("some" means at least one is and "almost all" means at least one is not)



+1 Good post. One minor quibble: while I agree that "often" is the functional equivalent of "some," doesn't "generally" mean "most"?

+1 ... Good catch. I haven't had much sleep :lol:

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Re: "Some" vs "Many"

Postby Near » Sat Mar 20, 2010 2:44 am

sirhitch wrote:op, to make you feel confident- i took a lot of pt's up til about 2003. i scored constantly in the 170's. i have never ever ever ever thought twice about the difference between some and many on the lsat. the points i lost on the lsat were not due to some or many mistakes. for test purposes, they are the same thing. period.

So the points you lost on the lsat were due to no mistakes?

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Re: "Some" vs "Many"

Postby PDaddy » Sat Mar 20, 2010 2:52 am

Mattalones wrote:
* On the LSAT, any quantifier that means "more than zero" is functionally equivalent to "some" (e.g. "many," "often," "generally," "several," etc) ... The only exception to this is "almost all," which is the inverse of "some" ("some" means at least one is and "almost all" means at least one is not)


Agreed. And OP need not bother with "many", "most", or "almost all".

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Sat Mar 20, 2010 3:41 am

PDaddy wrote:
Mattalones wrote:
* On the LSAT, any quantifier that means "more than zero" is functionally equivalent to "some" (e.g. "many," "often," "generally," "several," etc) ... The only exception to this is "almost all," which is the inverse of "some" ("some" means at least one is and "almost all" means at least one is not)


Agreed. And OP need not bother with "many", "most", or "almost all".

I agree with you about "Many," but "Most" and "Almost All" are still important.

Example for "most" (sorry if it's morbid, but this is what came to mind): If most over weight people eat to suppress their feelings, and most of them also eat too much, then some people who eat too much do so to supress their feelings ... This requires that the quantifier be at least more than 50%. Otherwise, it won't work.

I know there is an example that rquires "almost all" but I can't think of one this late ... I have seen them on the LSAT. "Trust me" isn't the most convincing argument, but it is all that I've got right now :lol:

Excuse lat night typos ...
Last edited by Mattalones on Sat Mar 20, 2010 3:01 pm, edited 1 time in total.

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Re: "Some" vs "Many"

Postby JasonR » Sat Mar 20, 2010 5:10 am

PDaddy wrote:And OP need not bother with "many", "most", or "almost all".


Wrong.

Just think, maybe you could have been a "175+ scorer with no social skills" if only you had bothered to master some of the really basic formal logic on the test. :lol:

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Gemini
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Re: "Some" vs "Many"

Postby Gemini » Mon Mar 22, 2010 10:38 pm

Some of us on this thread are breathing.

Also, many of us on this thread are breathing.

You can't leave out that Some/Many can also imply ALL.

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Mon Mar 22, 2010 11:30 pm

Gemini Hopeful wrote:Some of us on this thread are breathing.

Also, many of us on this thread are breathing.

You can't leave out that Some/Many can also imply ALL.


Neither of those words imply "all" ... Some guys have slept with three girls in one day, so all guys have pulled it off ... Um, no! You can't even do the converse and say that, if all people on this thread are breathing, then some or many of us on this thread are breathing; we can all conspire to hold our breath!

In order for you to get anything in terms of a relationship between "all" and "some/many," you need to already know that there are "some," watch:

Example of BAD

Premises
-"Everyone on this thread is breathing."
-There is no one on the thread (obviously not true if you're reading this, but immagine one of the many times this thread has been empty)

Invalid conclusion
-"Some people on this thread are breathing" (b/c we already stipulated that there is no one currently on this read)

Even less valid conclusion
-"Many people on this thread are breathing" (remember our stipulation about no one being on the thread)

Example of GOOD

Premises
-"Everyone on this thread is breathing."
-There are currently people on this thread (obviously true b/c you're reading this)

Valid conclusion (even though it isn't that exciting)
-"Some people on this thread are breathing"

Example of BAD

Premises
-"Everyone on this thread is breathing."
-There are currently people on this thread (again, obviously true b/c you're reading this)

Invalid conclusion
-"Many people on this thread are breathing" (um ... not if you're the only one on this thread b/c you're not many people)

Final example of GOOD

Premises
-"Everyone on this thread is breathing."
-You look to the bottom of the page and see a long list of people currently on this thread

Valid conclusion (even this one isn't that exciting either)
-"Many people on this thread are breathing"

Moral of the story:
Because how many things to which an "all" statement applies can vary a great deal, "all" statements alone can never imply "some." The only time when such a statement can imply "many" is when you have an "all" AND and "some" statement that both have the same subject, and you know that there are a good number of things to which both statements apply.

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Gemini
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Re: "Some" vs "Many"

Postby Gemini » Tue Mar 23, 2010 12:10 am

I'm saying "some" CAN imply all, not that it DOES. Which is true because some people on this thread ARE breathing. And I'm not adding any premise to this sentence. It was just that sentence. You added an extra stipulation here.

For sake of brevity, we can change it to SOME LIVING PEOPLE IN THIS WORLD ARE BREATHING. Whatever. The point is the same: some CAN be all. I NEVER said always, but that it CAN.

It also happens to be that all the people on this thread are breathing (when they're on the thread).

But I DO agree with you on the MANY thing. That was my oopsie.

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autarkh
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Re: "Some" vs "Many"

Postby autarkh » Tue Mar 23, 2010 12:41 am

"Some" does not exclude "all," but it never implies "all."

In other words: knowing that some things possess a certain quality does not mean that all of those same things cannot possess the quality, but it would not justify any conclusion about all of those things.

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Re: "Some" vs "Many"

Postby Gemini » Tue Mar 23, 2010 12:50 am

Oh jeez. This is too late at night for me to be doing this lol.

I suppose I should've said it may include ALL. Is that better?

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Tue Mar 23, 2010 2:07 am

Gemini Hopeful wrote:Oh jeez. This is too late at night for me to be doing this lol.

I suppose I should've said it may include ALL. Is that better?

I just think that you are saying it wrong. It is that "some" and "all" can be compatible, but they never imply each other.

It is just the whole talk about implication that is messing up the discussion.

Anyway, the point isn't that important :-)

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Re: "Some" vs "Many"

Postby dakatz » Tue Mar 23, 2010 2:14 am

Mattalones wrote:
Gemini Hopeful wrote:Oh jeez. This is too late at night for me to be doing this lol.

I suppose I should've said it may include ALL. Is that better?

I just think that you are saying it wrong. It is that "some" and "all" can be compatible, but they never imply each other.

It is just the whole talk about implication that is messing up the discussion.

Anyway, the point isn't that important :-)




"they never imply each other"

While some doesn't imply anything except for "at least one", "all" always implies "some". For example, in order for every book in the library to be fiction, there must be at least one book in the library that is fiction. Sounds weird written out, but completely true.
Last edited by dakatz on Tue Mar 23, 2010 2:16 am, edited 1 time in total.

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Re: "Some" vs "Many"

Postby MysticalWheel » Tue Mar 23, 2010 2:16 am

Mattalones wrote:I studied way too much formal logic ...
2) There is only a small difference in that "many" means "not few" and "few" stands for only an insignificant upper limit of a sample, so "few" has no existential commitment and could be zero (for small samples, pluralistic quantifiers like "few" and "many" don't have a use).
[/b])


Perhaps you did not study formal logic enough since there appears to be a contradiction in the statement above. If few has no "existential commitment," then its application should not depend upon relative quantity, no? It should only depend on the existence of some concept of real quantity (0-infinity) of something that is quantifiable. Hence, speaking in strictly formal logic terms, even for small samples, "pluralistic quantifiers" like few and many can and do have a use. How long did you study for again?

-MW

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Tue Mar 23, 2010 2:24 am

dakatz wrote:
Mattalones wrote:
Gemini Hopeful wrote:Oh jeez. This is too late at night for me to be doing this lol.

I suppose I should've said it may include ALL. Is that better?

I just think that you are saying it wrong. It is that "some" and "all" can be compatible, but they never imply each other.

It is just the whole talk about implication that is messing up the discussion.

Anyway, the point isn't that important :-)




"they never imply each other"

While some doesn't imply anything except for "at least one", "all" always implies "some". For example, in order for every book in the library to be fiction, there must be at least one book in the library that is fiction. Sounds weird written out, but completely true.

False!

All Mohekans wear nose rings ... There are no more Mohekans

Dodo birds have curvy beaks ... Dodos are extinct

Every king of France since 1900 has been bald ... France has had only presidents since 1789

Do any of these imply "some?" nope!

You have to know that there are "some" first ... "all" NEVER implies "some."

Your example: "In order for every book in the library to be fiction, there must be at least one book in the library that is fiction." - This depends on there being books in the library in the first place ... I guess if your way of saying that the library is empty is that the books are "fiction," then you are more clever than me, though ... 10pts to you, and none to me, if that is what you meant ;-)

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Re: "Some" vs "Many"

Postby MysticalWheel » Tue Mar 23, 2010 2:29 am

Mattalones wrote:
dakatz wrote:
Mattalones wrote:
Gemini Hopeful wrote:Oh jeez. This is too late at night for me to be doing this lol.

I suppose I should've said it may include ALL. Is that better?

I just think that you are saying it wrong. It is that "some" and "all" can be compatible, but they never imply each other.

It is just the whole talk about implication that is messing up the discussion.

Anyway, the point isn't that important :-)




"they never imply each other"

While some doesn't imply anything except for "at least one", "all" always implies "some". For example, in order for every book in the library to be fiction, there must be at least one book in the library that is fiction. Sounds weird written out, but completely true.

False!

All Mohekans wear nose rings ... There are no more Mohekans

Dodo birds have curvy beaks ... Dodos are extinct

Every king of France since 1900 has been bald ... France has had only presidents since 1789

Do any of these imply "some?" nope!

You have to know that there are "some" first ... "all" NEVER implies "some."

Your example: "In order for every book in the library to be fiction, there must be at least one book in the library that is fiction." - This depends on there being books in the library in the first place ... I guess if your way of saying that the library is empty is that the books are "fiction," then you are more clever than me, though ... 10pts to you, and none to me, if that is what you meant ;-)



To state "All Mohekans wear nose rings" in the present necessitates an application to an extant, quantifiable thing (tangible or not). If this is not the case, then the statement loses logical validity and cannot be made to begin with.

Ditto for the rest of your examples.

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Re: "Some" vs "Many"

Postby dakatz » Tue Mar 23, 2010 2:31 am

Mattalones wrote:
dakatz wrote:
Mattalones wrote:
Gemini Hopeful wrote:Oh jeez. This is too late at night for me to be doing this lol.

I suppose I should've said it may include ALL. Is that better?

I just think that you are saying it wrong. It is that "some" and "all" can be compatible, but they never imply each other.

It is just the whole talk about implication that is messing up the discussion.

Anyway, the point isn't that important :-)




"they never imply each other"

While some doesn't imply anything except for "at least one", "all" always implies "some". For example, in order for every book in the library to be fiction, there must be at least one book in the library that is fiction. Sounds weird written out, but completely true.

False!

All Mohekans wear nose rings ... There are no more Mohekans

Dodo birds have curvy beaks ... Dodos are extinct

Every king of France since 1900 has been bald ... France has had only presidents since 1789

Do any of these imply "some?" nope!

You have to know that there are "some" first ... "all" NEVER implies "some."

Your example: "In order for every book in the library to be fiction, there must be at least one book in the library that is fiction." - This depends on there being books in the library in the first place ... I guess if your way of saying that the library is empty is that the books are "fiction," then you are more clever than me, though ... 10pts to you, and none to me, if that is what you meant ;-)


You do realize that, for the purposes of the test, what I described is the exact logic your supposed to use, right? And the examples you use don't hold up. You can't say that all mohekans wear nose rings if none exist, nor can you say that all dodo birds have curvy beaks if none exist. There are no mohekans so absolutely zero wear nose rings, and there are zero dodos so none have curved beaks. If you are told that some phenomenon is currently happening at a rate of 100%, then you can say with full certainty that there is at least one occurrence of that phenomenon.

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Re: "Some" vs "Many"

Postby MysticalWheel » Tue Mar 23, 2010 2:32 am

dakatz wrote:
You do realize that, for the purposes of the test, what I described is the exact logic your supposed to use, right? And the examples you use don't hold up. You can't say that all mohekans wear nose rings if none exist, nor can you say that all dodo birds have curvy beaks if none exist. There are no mohekans so absolutely zero wear nose rings, and there are zero dodos so none have curved beaks. If you are told that some phenomenon is currently happening at a rate of 100%, then you can say with full certainty that there is at least one occurrence of that phenomenon.


Correct, and precisely what I wrote in my above post, dakatz. Mattalones, you need rest my friend.

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Tue Mar 23, 2010 2:58 am

dakatz wrote:You do realize that, for the purposes of the test, what I described is the exact logic your supposed to use, right? And the examples you use don't hold up. You can't say that all mohekans wear nose rings if none exist, nor can you say that all dodo birds have curvy beaks if none exist. There are no mohekans so absolutely zero wear nose rings, and there are zero dodos so none have curved beaks. If you are told that some phenomenon is currently happening at a rate of 100%, then you can say with full certainty that there is at least one occurrence of that phenomenon.

What you are saying is 100% correct, but it doesn't change what I am trying to say. After reading your post, I realize that there is a distinction that depends on tense. The things that you are saying are in the present tense. What I had in mind mostly applies to things in the subjunctive sense, like rules and such.

Ex.

Rule: "Anyone caught with multiple wives will be prosecuted."
Just because this rule is in place does not mean that there will all of a sudden be someone caught with multiple wives.

Now, for what you say, which is also right, but different: "some phenomenon is currently happening at a rate of 100%"
When you say that it is happening in the present-progressive tense like that, then it will imply "some."

The difference is tense.

Anyway, good discussion even though it turned out that we were arguing different topics. :lol:

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Re: "Some" vs "Many"

Postby MysticalWheel » Wed Mar 24, 2010 2:22 am

Arguments based on semantics are usually the last refuge for the incorrect.

-MW

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Sun Mar 28, 2010 8:17 pm

MysticalWheel wrote:Arguments based on semantics are usually the last refuge for the incorrect.

-MW

I admitted what I said was wrong for some uses ...

Pointing out different contexts isn't a refuge. Either way, it wasn't even on the original point. So, it doesn't matter that much.

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yoni45
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Re: "Some" vs "Many"

Postby yoni45 » Mon Mar 29, 2010 12:19 am

Two points:

Regarding some vs. many (I think this was mentioned in passing before, but to clarify), these are not logically equivalent.

While you can derive 'some' from 'many' (in fact, that's all you can safely derive), you cannot derive 'many' from 'some'.

So as an example, if you know that "some people are going bowling", you cannot derive that "many people are going bowling".

If you know that "many people are going bowling", then you can derive that at least "some" are doing so.

Some means at least 1. Many means at least X, where X is a subjective number or proportion that could be anywhere from 1 to all. Both 'some' and 'many' can mean all.

------

Regarding the possibility of no instances in a set given a statement such as:

"All Mohekans wear nose rings ... There are no more Mohekans"

While it's arguable as to whether logically speaking, Mohekans must exist by the given statement, as far as LSAC is concerned however, it seems that you safely assume that Mohekans do exist (it rarely seems to be an issue, however).

As an example, take PT41, S3, Q25.

All the statements in the stimulus are relative quantifiers -- "most S are H, most S are G, all G are O". Arguably speaking, it's possible that there are no students in any of these groups, yet the correct answer uses an absolute quantifier that states that "Some H are O".

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Mattalones
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Re: "Some" vs "Many"

Postby Mattalones » Mon Mar 29, 2010 2:58 am

yoni45 wrote:Two points:

Regarding some vs. many (I think this was mentioned in passing before, but to clarify), these are not logically equivalent.

While you can derive 'some' from 'many' (in fact, that's all you can safely derive), you cannot derive 'many' from 'some'.

So as an example, if you know that "some people are going bowling", you cannot derive that "many people are going bowling".

If you know that "many people are going bowling", then you can derive that at least "some" are doing so.

Some means at least 1. Many means at least X, where X is a subjective number or proportion that could be anywhere from 1 to all. Both 'some' and 'many' can mean all.

------

Regarding the possibility of no instances in a set given a statement such as:

"All Mohekans wear nose rings ... There are no more Mohekans"

While it's arguable as to whether logically speaking, Mohekans must exist by the given statement, as far as LSAC is concerned however, it seems that you safely assume that Mohekans do exist (it rarely seems to be an issue, however).

As an example, take PT41, S3, Q25.

All the statements in the stimulus are relative quantifiers -- "most S are H, most S are G, all G are O". Arguably speaking, it's possible that there are no students in any of these groups, yet the correct answer uses an absolute quantifier that states that "Some H are O".

+1

All my banter was not LSAT based. Sorry to cause mixups. It was just an interest of mine. The example you provide is particularly helpful at illustrating the limits on how strict you should be about logical assumptions on the LSAT.




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