Many people are X, and Many people are Y

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Jack Smirks
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Re: Many people are X, and Many people are Y

Postby Jack Smirks » Thu Mar 31, 2011 1:29 am

BrianOz1 wrote:Many = > 50%. there has to be overlap. I don't understand the debate.

Many=/= Most.

Many=Some


hth

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suspicious android
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Re: Many people are X, and Many people are Y

Postby suspicious android » Thu Mar 31, 2011 1:38 am

BrianOz1 wrote:Many = > 50%. there has to be overlap. I don't understand the debate.


Your first statement is false but your second statement is true. Consider:

Many Americans live in California. True.
Most Americans live in California. False.

Many people have been to France. True.
Most people have been to France. False.

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well-hello-there
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Re: Many people are X, and Many people are Y

Postby well-hello-there » Thu Mar 31, 2011 2:19 am

naterj wrote:
BrianOz1 wrote:Many = > 50%. there has to be overlap. I don't understand the debate.

Many=/= Most.

Many=Some


hth

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Easy-E
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Re: Many people are X, and Many people are Y

Postby Easy-E » Thu Mar 31, 2011 2:56 am

BrianOz1 wrote:Many = > 50%. there has to be overlap. I don't understand the debate.


Is this a hard rule that many indicates more than half? I just assumed "many" and "some" were basically interchangable.


EDIT: Didn't see second page, questioned answer.

Curry

Re: Many people are X, and Many people are Y

Postby Curry » Thu Mar 31, 2011 3:12 am

Many has the same logical definition as some. Most = 50%+1
Many and Some just mean 1 or more. They both can mean all, (Some/Many people who read this are also breathing).
The difference between some and many is that many is a "large relative quantity" and some is a "small relative quantity". There does not need to be an overlap "many people currently live in china and many people currently live in the usa." This does not mean that some people who live in china also live in the USA.

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alexonfyre
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Re: Many people are X, and Many people are Y

Postby alexonfyre » Thu Mar 31, 2011 11:49 am

Curry wrote:Many has the same logical definition as some. Most = 50%+1
Many and Some just mean 1 or more. They both can mean all, (Some/Many people who read this are also breathing).
The difference between some and many is that many is a "large relative quantity" and some is a "small relative quantity". There does not need to be an overlap "many people are physically in china and many people currently are physically in the usa." This does not mean that some people who are physically in china are also currently, physically in the USA.


Fixed for objectivity.

(People learning the LSAT may still be at the phase where they reject an argument's validity on the basis of soundness.)

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Easy-E
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Re: Many people are X, and Many people are Y

Postby Easy-E » Thu Mar 31, 2011 12:21 pm

alexonfyre wrote:
Curry wrote:Many has the same logical definition as some. Most = 50%+1
Many and Some just mean 1 or more. They both can mean all, (Some/Many people who read this are also breathing).
The difference between some and many is that many is a "large relative quantity" and some is a "small relative quantity". There does not need to be an overlap "many people are physically in china and many people currently are physically in the usa." This does not mean that some people who are physically in china are also currently, physically in the USA.


Fixed for objectivity.

(People learning the LSAT may still be at the phase where they reject an argument's validity on the basis of soundness.)



But it seems like this specific example (physically being somewhere) eliminates the possibility of cross-over, no? If you said "Many people have dark hair and many people wear glasses". In a case like this, their COULD be people with dark and glasses, but its not necessarily true. Or am I missing the point?

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alexonfyre
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Re: Many people are X, and Many people are Y

Postby alexonfyre » Thu Mar 31, 2011 12:55 pm

emarxnj wrote:
alexonfyre wrote:
Curry wrote:Many has the same logical definition as some. Most = 50%+1
Many and Some just mean 1 or more. They both can mean all, (Some/Many people who read this are also breathing).
The difference between some and many is that many is a "large relative quantity" and some is a "small relative quantity". There does not need to be an overlap "many people are physically in china and many people currently are physically in the usa." This does not mean that some people who are physically in china are also currently, physically in the USA.


Fixed for objectivity.

(People learning the LSAT may still be at the phase where they reject an argument's validity on the basis of soundness.)



But it seems like this specific example (physically being somewhere) eliminates the possibility of cross-over, no? If you said "Many people have dark hair and many people wear glasses". In a case like this, their COULD be people with dark and glasses, but its not necessarily true. Or am I missing the point?


Yeah, I changed his example to a mutually exclusive grouping to illustrate that just because there are many in either group does not mean there are some in both groups.
For comparison saying "Many people are over 6 feet tall" and "Many people are under 6 feet tall" does not mean that "Some people are both over and under 6 feet tall."

When you use non exclusive groupings, then you get something like "Many people have brown hair" and "Many people wear glasses" so it is POSSIBLE that Some have brown hair and wear glasses, but it is by no means necessary. You have to check all outside knowledge at the door when you answer these questions. Just because you or someone you know has brown hair and wears glasses means nothing in the context of the problem. In Logic Land it is possible that 30 percent of people have brown hair and good vision, and 30 percent wear glasses and have blond hair and 40 percent have red hair and good vision, you just don't know.

Curry

Re: Many people are X, and Many people are Y

Postby Curry » Thu Mar 31, 2011 1:01 pm

alexonfyre wrote:
emarxnj wrote:
alexonfyre wrote:
Curry wrote:Many has the same logical definition as some. Most = 50%+1
Many and Some just mean 1 or more. They both can mean all, (Some/Many people who read this are also breathing).
The difference between some and many is that many is a "large relative quantity" and some is a "small relative quantity". There does not need to be an overlap "many people are physically in china and many people currently are physically in the usa." This does not mean that some people who are physically in china are also currently, physically in the USA.


Fixed for objectivity.

(People learning the LSAT may still be at the phase where they reject an argument's validity on the basis of soundness.)



But it seems like this specific example (physically being somewhere) eliminates the possibility of cross-over, no? If you said "Many people have dark hair and many people wear glasses". In a case like this, their COULD be people with dark and glasses, but its not necessarily true. Or am I missing the point?


Yeah, I changed his example to a mutually exclusive grouping to illustrate that just because there are many in either group does not mean there are some in both groups.
For comparison saying "Many people are over 6 feet tall" and "Many people are under 6 feet tall" does not mean that "Some people are both over and under 6 feet tall."

When you use non exclusive groupings, then you get something like "Many people have brown hair" and "Many people wear glasses" so it is POSSIBLE that Some have brown hair and wear glasses, but it is by no means necessary. You have to check all outside knowledge at the door when you answer these questions. Just because you or someone you know has brown hair and wears glasses means nothing in the context of the problem. In Logic Land it is possible that 30 percent of people have brown hair and good vision, and 30 percent wear glasses and have blond hair and 40 percent have red hair and good vision, you just don't know.

I feel like this point was already made.

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alexonfyre
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Re: Many people are X, and Many people are Y

Postby alexonfyre » Thu Mar 31, 2011 1:05 pm

Curry wrote:
alexonfyre wrote:
emarxnj wrote:
alexonfyre wrote:Fixed for objectivity.

(People learning the LSAT may still be at the phase where they reject an argument's validity on the basis of soundness.)



But it seems like this specific example (physically being somewhere) eliminates the possibility of cross-over, no? If you said "Many people have dark hair and many people wear glasses". In a case like this, their COULD be people with dark and glasses, but its not necessarily true. Or am I missing the point?


Yeah, I changed his example to a mutually exclusive grouping to illustrate that just because there are many in either group does not mean there are some in both groups.
For comparison saying "Many people are over 6 feet tall" and "Many people are under 6 feet tall" does not mean that "Some people are both over and under 6 feet tall."

When you use non exclusive groupings, then you get something like "Many people have brown hair" and "Many people wear glasses" so it is POSSIBLE that Some have brown hair and wear glasses, but it is by no means necessary. You have to check all outside knowledge at the door when you answer these questions. Just because you or someone you know has brown hair and wears glasses means nothing in the context of the problem. In Logic Land it is possible that 30 percent of people have brown hair and good vision, and 30 percent wear glasses and have blond hair and 40 percent have red hair and good vision, you just don't know.

I feel like this point was already made.


It was, but emarxnj was still confused to why I said it that way, so I reiterated it.

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Easy-E
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Re: Many people are X, and Many people are Y

Postby Easy-E » Thu Mar 31, 2011 1:14 pm

alexonfyre wrote:
Curry wrote:
alexonfyre wrote:
emarxnj wrote:
But it seems like this specific example (physically being somewhere) eliminates the possibility of cross-over, no? If you said "Many people have dark hair and many people wear glasses". In a case like this, their COULD be people with dark and glasses, but its not necessarily true. Or am I missing the point?


Yeah, I changed his example to a mutually exclusive grouping to illustrate that just because there are many in either group does not mean there are some in both groups.
For comparison saying "Many people are over 6 feet tall" and "Many people are under 6 feet tall" does not mean that "Some people are both over and under 6 feet tall."

When you use non exclusive groupings, then you get something like "Many people have brown hair" and "Many people wear glasses" so it is POSSIBLE that Some have brown hair and wear glasses, but it is by no means necessary. You have to check all outside knowledge at the door when you answer these questions. Just because you or someone you know has brown hair and wears glasses means nothing in the context of the problem. In Logic Land it is possible that 30 percent of people have brown hair and good vision, and 30 percent wear glasses and have blond hair and 40 percent have red hair and good vision, you just don't know.

I feel like this point was already made.


It was, but emarxnj was still confused to why I said it that way, so I reiterated it.



And I appreciate the clarification, thank you.

inmans
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Re: Many people are X, and Many people are Y

Postby inmans » Thu Mar 31, 2011 2:27 pm

...
Last edited by inmans on Thu Jul 28, 2011 4:33 pm, edited 1 time in total.

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mac35352
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Re: Many people are X, and Many people are Y

Postby mac35352 » Thu Mar 31, 2011 2:53 pm

great thread but now I need some clarification.
*Many=some
*two somes can't create an inference, therefore a many and a some can't create an inference. Example: some members have money to invest. No member lives in the city but many work there.
From this statement we infer: * some members who have money to invest do not live in the city.
But not this: *Some members who have money to invest work in the city.
what if we switch the many with a most? could we infer: *some members who have money to invest work in the suburbs.

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alexonfyre
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Re: Many people are X, and Many people are Y

Postby alexonfyre » Thu Mar 31, 2011 3:01 pm

mac35352 wrote:great thread but now I need some clarification.
*Many=some
*two somes can't create an inference, therefore a many and a some can't create an inference. Example: some members have money to invest. No member lives in the city but many work there.
From this statement we infer: * some members who have money to invest do not live in the city.
But not this: *Some members who have money to invest work in the city.
what if we switch the many with a most? could we infer: *some members who have money to invest work in the suburbs.


This post confuses me, but if I understand correctly you mean this

(conditional + conditional = logical probability)

Many/Some/1 + Many/Some/1 = possible
Many/Some/1 + Most = more likely than not
Many/Some/1 + All/None = NECESSARY or NECESSARILY NOT (respectively)
Most + Most = NECESSARY
Most + All/None = NECESSARY or NECESSARILY NOT (respectively)
All/None + All/None = Transitive Inference

Does that help?
Last edited by alexonfyre on Thu Mar 31, 2011 3:02 pm, edited 1 time in total.

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suspicious android
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Re: Many people are X, and Many people are Y

Postby suspicious android » Thu Mar 31, 2011 3:02 pm

inmans wrote:
"Most a are x, most a are y, therefore some x are y"

This is actually incorrect.

What you want to say: Most a are x; most a are y. Therefore, there is at least one (some) a that is both x and y. Gotta be careful with that language.


No, it isn't incorrect. Your formulation is a valid inference, but so is Kurst's.

Most children are short.
Most children are shy.
Therefore, some shy things are short. OR, some children are both shy and short.

Curry

Re: Many people are X, and Many people are Y

Postby Curry » Thu Mar 31, 2011 3:11 pm

suspicious android wrote:
inmans wrote:
"Most a are x, most a are y, therefore some x are y"

This is actually incorrect.

What you want to say: Most a are x; most a are y. Therefore, there is at least one (some) a that is both x and y. Gotta be careful with that language.


No, it isn't incorrect. Your formulation is a valid inference, but so is Kurst's.

Most children are short.
Most children are shy.
Therefore, some shy things are short. OR, some children are both shy and short.


X Most Y
X Most Z

From here you can conclude:
Y some Z
Z some Y
X some Y and Z

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mac35352
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Re: Many people are X, and Many people are Y

Postby mac35352 » Thu Mar 31, 2011 3:13 pm

alexonfyre wrote:
mac35352 wrote:great thread but now I need some clarification.
*Many=some
*two somes can't create an inference, therefore a many and a some can't create an inference. Example: some members have money to invest. No member lives in the city but many work there.
From this statement we infer: * some members who have money to invest do not live in the city.
But not this: *Some members who have money to invest work in the city.
what if we switch the many with a most? could we infer: *some members who have money to invest work in the suburbs.


This post confuses me, but if I understand correctly you mean this

(conditional + conditional = logical probability)

Many/Some/1 + Many/Some/1 = possible
Many/Some/1 + Most = more likely than not
Many/Some/1 + All/None = NECESSARY or NECESSARILY NOT (respectively)
Most + Most = NECESSARY
Most + All/None = NECESSARY or NECESSARILY NOT (respectively)
All/None + All/None = Transitive Inference

Does that help?

My understanding is that some/many + some/many: no inference.

Curry

Re: Many people are X, and Many people are Y

Postby Curry » Thu Mar 31, 2011 3:15 pm

mac35352 wrote:My understanding is that some/many + some/many: no inference.

They are logical equivalents and you can make no inference from a statement with only some and many. You can make a connection between two mosts and an all and some/many/most.

inmans
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Re: Many people are X, and Many people are Y

Postby inmans » Thu Mar 31, 2011 3:27 pm

...
Last edited by inmans on Thu Sep 01, 2011 12:16 pm, edited 1 time in total.

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alexonfyre
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Re: Many people are X, and Many people are Y

Postby alexonfyre » Thu Mar 31, 2011 3:29 pm

mac35352 wrote:
alexonfyre wrote:
mac35352 wrote:great thread but now I need some clarification.
*Many=some
*two somes can't create an inference, therefore a many and a some can't create an inference. Example: some members have money to invest. No member lives in the city but many work there.
From this statement we infer: * some members who have money to invest do not live in the city.
But not this: *Some members who have money to invest work in the city.
what if we switch the many with a most? could we infer: *some members who have money to invest work in the suburbs.


This post confuses me, but if I understand correctly you mean this

(conditional + conditional = logical probability)

Many/Some/1 + Many/Some/1 = possible
Many/Some/1 + Most = more likely than not
Many/Some/1 + All/None = NECESSARY or NECESSARILY NOT (respectively)
Most + Most = NECESSARY
Most + All/None = NECESSARY or NECESSARILY NOT (respectively)
All/None + All/None = Transitive Inference

Does that help?

My understanding is that some/many + some/many: no inference.


I would generally put no inference, however I have seen a rare question with a transitive "Some + Some" "Could be true" answer.

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birdlaw117
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Re: Many people are X, and Many people are Y

Postby birdlaw117 » Thu Mar 31, 2011 3:34 pm

I haven't seen this point made so I'll mention it.

I believe the difference between "some" and "many" is that "some" = 1 to 100 and "many" = 2 to 100.

This doesn't make a difference as far as making inferences goes, just thought I would mention it though.

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Easy-E
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Re: Many people are X, and Many people are Y

Postby Easy-E » Thu Mar 31, 2011 5:08 pm

So the hard rules would be...

Some = 1+
Most = > Half
Many = 2+


Can any of these allow for ALL? If you say "Many X are Y", is it POSSIBLE that in fact "All X are Y", or does it only allow for any amount below 100%

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alexonfyre
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Re: Many people are X, and Many people are Y

Postby alexonfyre » Thu Mar 31, 2011 5:48 pm

emarxnj wrote:So the hard rules would be...

Some = 1+
Most = > Half
Many = 2+


Can any of these allow for ALL? If you say "Many X are Y", is it POSSIBLE that in fact "All X are Y", or does it only allow for any amount below 100%


At this point the discussion is so far removed from pragmatism it doesn't even matter, but yes, all of them are true if "All" is true, but if you know "All" you would just say that.

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well-hello-there
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Re: Many people are X, and Many people are Y

Postby well-hello-there » Thu Mar 31, 2011 5:52 pm

birdlaw117 wrote:I haven't seen this point made so I'll mention it.

I believe the difference between "some" and "many" is that "some" = 1 to 100 and "many" = 2 to 100.

This doesn't make a difference as far as making inferences goes, just thought I would mention it though.

wrong.

many = 1 or more

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nshapkar
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Re: Many people are X, and Many people are Y

Postby nshapkar » Thu Mar 31, 2011 6:01 pm

Curry wrote:Many has the same logical definition as some. Most = 50%+1
Many and Some just mean 1 or more. They both can mean all, (Some/Many people who read this are also breathing).
The difference between some and many is that many is a "large relative quantity" and some is a "small relative quantity". There does not need to be an overlap "many people currently live in china and many people currently live in the usa." This does not mean that some people who live in china also live in the USA.



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