full group (ALL), "there are no...neither...nor," translated

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theZeigs
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full group (ALL), "there are no...neither...nor," translated

Postby theZeigs » Thu Mar 04, 2010 11:19 pm

I need help translating/understanding these type of statements [Edit: maybe I don't, I just spent about an hour and a half writing this out and thinking about this, but I could still use your discussion!] :

From Superprep C.3, #15, answer choice (c):

"There are no sources for historical understanding that are neither considered best by historians nor neglected by them."

Is this the same as saying:

"All sources of historical understanding are either considered best by historians or neglected by them."

It seems to me to be true, after typing all of this out.

It doesn't seem like "logical negation" or any other similar rules from LR bible apply when the statement is in it's negative form. It also doesn't seem to lend itself immediately to diagramming like the positive form would:

"a source of historical understanding is either considered best by historians or neglected by them"

source of historical understanding --> considered best by historians OR neglected by historians

So let me make up some other examples:

"there are no lightbulbs which are neither fully bright nor totally off."
= "all lightbulbs are either fully bright or totally off."

"there are no knives which are neither razor sharp nor completely dull."
= "all knives which are either razor sharp or completely dull."

So, when it's:
"no" something is "neither" blah "nor" bleh
the negatives all become the logical opposite
"all" somethings are "either" blah "or" bleh

Does this work in reverse? Seems so.

"every student is either smart or a dullard."
= "there is no student which is neither smart nor a dullard"

"all cars drive fast or drive slowly"
= "there are no cars which neither drive fast nor drive slowly"

Note that these diagram well positively, but the "negative version" of these do not diagram well:
student --> smart OR dullard (contra = "-smart AND -dullard --> -student"),
but the negative version of this?

So, when it says:
"all/every/each" something is "either" blah "or" bleh
the equivalent is
"no" something is "neither" blah "nor" bleh

I suppose, then, that this doesn't work when we are not talking about the entire set, i.e. ALL, of a given group:

"most athletes are either fast or strong"
=? "there are no athletes that are neither fast nor strong" (NOT true because there could be some athletes that are neither fast nor strong initially, meaning that second statement is not valid.)

this leads to:

"there are some athletes which are neither fast nor strong"
--> "there are no athletes which are either fast or strong" (NOT true, same as above)

What if I have a "no" but not a "neither"

"no eggs contain lactose"
=? "eggs contain no lactose"

but when I have a "not" but two things

"no eggs contain lactose or sugar"
= "eggs contain no lactose nor sugar"

So when I have a:
"no/none/none of" something is (or another verb) blah or is(or another verb) bleh
this becomes
"all/every" something is(or another verb) "not" blah "nor" bleh

"no student is smart or a dullard"
= "all students are neither smart nor a dullard"

"no A is neither a B nor a C"
= "A is either B or C"

"there exist no people who are neither tall nor short"
= "all people are either tall or short"

What about a combination:

"no cheese contains vegetables nor no lactose"
= "all cheese contain lactose and no vegetables"

how important is nor?
"There are no sources for historical understanding that are neither considered best by historians or which are neglected by them."
= "all sources of historical understanding are considered best by historians and not neglected by them"
Here, you can't have the "neither" without "nor", it seems, based on the English language.
This should be:
"There are no sources for historical understanding that are considered best by historians or which are neglected by them."
= "all sources for historical understanding are not considered best by historians and are not neglected" (see below, this is so complex. But this actually happens to turn out to be the same as our original statement, i.e. "neither considered best nor neglected" = "not considered best and are not neglected" ..."Neither...Nor" means "not...and not" !)

To end with the most basic statements:

"A is B"
= "no A is not B" and these are logically equivalent

"A is B and C"
= "no A is neither B nor C" [EDIT: THIS IS INCORRECT. "Neither...nor" means "not one AND ALSO not the other". As written here, this could mean that "no A both not B and not C, but A could possibly be not B or not C, independent of each other." In fact, what "A is B and C" means is that "no A can be either not B and/or not C." This is correctly written, immediately below.]
= "no A is not B or not C"
= "no A is not B and furthermore no A is not C"


"A is B or C" = "A is either B or C"
= "no A is not B and not C"
= "no A is neither B nor C" (this seems OK, two statements are equivalent)

"A is not B"
= "no A is B"

"A is not B and it is C" = "A is C and not B"
= "no A is B or not C"
= "no A is not C or B" (here is where things get a little tricky: this seems to imply that "no A is not C or not B" but this is not the case, it becomes more clear when you write it out so that any "not" is written second, as above).

"A is not B and not C"
= "no A is B or C"

"A is not B or not C" ---> (this seems distinct from "A is neither B nor C"; in the first casting, A is not B or A is not C, but it could also be not be both (or not), but in the second casting, A is certainly not B in addition to not being C)
= "no A is B and C"
(distinct!) vs. "no A is either B or C"

Then, for all of these "basic" types, you can extend from B, C, etc. to D, E, F...ad nauseum. You also have the negative version of all of these, starting with "No A is not B" --> = "A is B" but these are already done.

I guess, now that I type/think all of this out, it makes a lot more sense to me, except the point about "neither" always being paired with "nor" last point. Just to make sure, is "nor" the equivalent of when you have an "and" joining two "neithers" ? Man I'm going nuts. It seems like flashcards going back and forth here would be of a lot of help for the LR of the LSAT, there would only be 9 different flashcards though. (three different variables, each being "yes/no" "on/off" etc.; 2^3 = 8 plus the one last inconsistency discussed above. Could also split up the "A is C and not B" as discussed).

I was wondering if there is any diagramming/shortcuts/established theories that would make this more easy and faster rather than having to get used to it [Edit: or having spent an hour and a half thinking through this, though maybe this is best!!!]. Is there a way to categorize this kind of statement?

I also hope that, in this mental exercise, someone else find this useful.

Any help, useful links, discussion, or corrections are very appreciated! Thank you!
Last edited by theZeigs on Mon Mar 08, 2010 3:13 pm, edited 1 time in total.

Shrimps
Posts: 271
Joined: Sun Feb 14, 2010 10:04 pm

Re: full group (ALL), "there are no...neither...nor," translated

Postby Shrimps » Thu Mar 04, 2010 11:54 pm

logic chains are useful for conditional (i.e. hypothetical) situations, usually marked by words "if", "when" and such.

For general statements involving words like 'all', 'none', 'neither' and so on, picturing a Venn or an Euler/Leibniz diagram in your head is, in my experience, both quicker and more useful, especially for LR questions.

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autarkh
Posts: 314
Joined: Sat Sep 26, 2009 9:05 pm

Re: full group (ALL), "there are no...neither...nor," translated

Postby autarkh » Fri Mar 05, 2010 12:11 am

"There are no sources for historical understanding that are neither considered best by historians nor neglected by them."

Shorthand:

SHU = sources of historical understanding
CBH = considered best by historians
NBH = neglected by historians

“Neither… nor” just means “not one and not the other”
“No” means negate the necessary condition.

Combining both, we get:

1. SHU --> not(not CBH & not NBH)
The “not” distributes:
2. SHU --> not not CBH (or) not not NBH
Simplified:
3. SHU --> CBH (or) NBH

In plain English:

"Every source of historical understanding either is considered best by historians or is neglected by them."

ly2010
Posts: 104
Joined: Sat Aug 07, 2010 8:30 pm

Re: full group (ALL), "there are no...neither...nor," translated

Postby ly2010 » Tue Aug 17, 2010 5:33 pm

theZeigs wrote:I need help translating/understanding these type of statements [Edit: maybe I don't, I just spent about an hour and a half writing this out and thinking about this, but I could still use your discussion!] :


"A is B"
= "no A is not B" and these are logically equivalent

"A is B and C"
= "no A is neither B nor C" [EDIT: THIS IS INCORRECT. "Neither...nor" means "not one AND ALSO not the other". As written here, this could mean that "no A both not B and not C, but A could possibly be not B or not C, independent of each other." In fact, what "A is B and C" means is that "no A can be either not B and/or not C." This is correctly written, immediately below.]
= "no A is not B or not C"
= "no A is not B and furthermore no A is not C"


"A is B or C" = "A is either B or C"
= "no A is not B and not C"
= "no A is neither B nor C" (this seems OK, two statements are equivalent)

"A is not B"
= "no A is B"

"A is not B and it is C" = "A is C and not B"
= "no A is B or not C"
= "no A is not C or B" (here is where things get a little tricky: this seems to imply that "no A is not C or not B" but this is not the case, it becomes more clear when you write it out so that any "not" is written second, as above).

"A is not B and not C"
= "no A is B or C"

"A is not B or not C" ---> (this seems distinct from "A is neither B nor C"; in the first casting, A is not B or A is not C, but it could also be not be both (or not), but in the second casting, A is certainly not B in addition to not being C)
= "no A is B and C"
(distinct!) vs. "no A is either B or C"

Then, for all of these "basic" types, you can extend from B, C, etc. to D, E, F...ad nauseum. You also have the negative version of all of these, starting with "No A is not B" --> = "A is B" but these are already done.

I guess, now that I type/think all of this out, it makes a lot more sense to me, except the point about "neither" always being paired with "nor" last point. Just to make sure, is "nor" the equivalent of when you have an "and" joining two "neithers" ? Man I'm going nuts. It seems like flashcards going back and forth here would be of a lot of help for the LR of the LSAT, there would only be 9 different flashcards though. (three different variables, each being "yes/no" "on/off" etc.; 2^3 = 8 plus the one last inconsistency discussed above. Could also split up the "A is C and not B" as discussed).

I was wondering if there is any diagramming/shortcuts/established theories that would make this more easy and faster rather than having to get used to it [Edit: or having spent an hour and a half thinking through this, though maybe this is best!!!]. Is there a way to categorize this kind of statement?

I also hope that, in this mental exercise, someone else find this useful.

Any help, useful links, discussion, or corrections are very appreciated! Thank you!


I was searching for a "no" vs. "not" thread and found this. This is really helpful! Thanks a lot!




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