Either.. or.

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Fianna13
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Either.. or.

Postby Fianna13 » Tue Apr 17, 2012 2:23 pm

How do you negate that? Neither.. nor?

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fashiongirl
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Re: Either.. or.

Postby fashiongirl » Tue Apr 17, 2012 3:27 pm

[either A or B] would be negated as [not A and not B]

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flem
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Re: Either.. or.

Postby flem » Tue Apr 17, 2012 3:33 pm

fashiongirl wrote:[either A or B] would be negated as [not A and not B]


Yup, always remember that "or" becomes "and" and vice versa in contrapositives.

bp shinners
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Re: Either.. or.

Postby bp shinners » Tue Apr 17, 2012 4:50 pm

fashiongirl wrote:[either A or B] would be negated as [not A and not B]


Which is neither nor.

Though it's much better to think about it in fashiongirl's terminology.

NYCLSATTutor
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Re: Either.. or.

Postby NYCLSATTutor » Tue Apr 17, 2012 5:03 pm

Actually the negation of "either A or B" would be "(Not A & Not B) OR (A & B)" [all at once]

This is assuming you are intending "either A or B" to mean "A or B, but not both"

I don't think most companies have symbolism for "either or" and I don't believe the LSAT has either necessitated that one negate an either or statement, so the point is a bit moot.

The posters above me have negated an "or" statement not an "either or" statement. They are correct as far as or statements go.

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Re: Either.. or.

Postby bp shinners » Fri Apr 20, 2012 2:14 pm

NYCLSATTutor wrote:Actually the negation of "either A or B" would be "(Not A & Not B) OR (A & B)" [all at once]

This is assuming you are intending "either A or B" to mean "A or B, but not both"


Which the LSAT doesn't assume. So this is bad advice.

If you see "either A or B" on the LSAT, it means A; B; or A and B. If it says "either A or B, but not both" then it means "but not both", i.e. A; or B.

I don't think most companies have symbolism for "either or" and I don't believe the LSAT has either necessitated that one negate an either or statement, so the point is a bit moot.


I think every LSAT company has a symbol for "either or" - we call it "or". And you most certainly have had to negate those statements on the LSAT. As far as "either or, but not both", I am sure at least we at BP teach how to symbolize it, and the LSAT definitely has used it several times (especially in Logic Games).

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suspicious android
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Re: Either.. or.

Postby suspicious android » Fri Apr 20, 2012 5:42 pm

Always enjoy threads like this.

skip james
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Re: Either.. or.

Postby skip james » Fri Apr 20, 2012 8:02 pm

NYCLSATTutor wrote:Actually the negation of "either A or B" would be "(Not A & Not B) OR (A & B)" [all at once]

you really shouldn't say shit like this, you're gonna confuse people. it's just downright unfriendly, imo.

_____________

OP, I think it may be helpful to have a single, memorable example which you can remember and reason through in order to figure out the logical relationship of the 'or' statement.

The one I like to use this this:

I'd be happy on Christmas if I had gotten either a puppy or a million bucks.

P or $$ -> H

NOT H -> NO Puppy and NO $$
So if on Christmas I'm unhappy, then I couldn't have gotten a puppy and I also couldn't have gotten a million bucks.

NYCLsattutor (wouldn't pay this person a dime, personally) is saying that one could possibly mean

NOT H -> (NO puppy and NO money) OR (Puppy and $$)

..which doesn't really make sense.

bp shinners wrote:This is assuming you are intending "either A or B" to mean "A or B, but not both"


+1

and that's why one would have to include the phrase 'not both' to actually mean that.

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suspicious android
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Re: Either.. or.

Postby suspicious android » Fri Apr 20, 2012 8:10 pm

skip james wrote:
NYCLsattutor (wouldn't pay this person a dime, personally) is saying that one could possibly mean


Awwww, no need to be so harsh. He probably just got mixed up for a minute, happens to everyone. Good example though.

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Richie Tenenbaum
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Re: Either.. or.

Postby Richie Tenenbaum » Fri Apr 20, 2012 8:31 pm

Wow, y'all are harsh. NYCLSATTutor really shouldn't have brought in formal logic that isn't tested on the LSAT, but he is technically right. "Either...or" is typically used to indicate an exclusive or, and his definition matches up with this. See http://en.wikipedia.org/wiki/Exclusive_or .

But yeah, I agree with BP shinners that this is bad advice since the rules of LSAT world are what matter.

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Re: Either.. or.

Postby skip james » Fri Apr 20, 2012 8:35 pm

suspicious android wrote:
skip james wrote:
NYCLsattutor (wouldn't pay this person a dime, personally) is saying that one could possibly mean


Awwww, no need to be so harsh. He probably just got mixed up for a minute, happens to everyone. Good example though.


:? you're right.. that was childish of me. I apologize for being immature, NYCLsattutor.

Richie Tenenbaum wrote:Wow, y'all are harsh. NYCLSATTutor really shouldn't have brought in formal logic that isn't tested on the LSAT, but he is technically right. "Either...or" is typically used to indicate an exclusive or, and his definition matches up with this. See http://en.wikipedia.org/wiki/Exclusive_or .

But yeah, I agree with BP shinners that this is bad advice since the rules of LSAT world are what matter.

i looked at the article, but it doesn't seem to say that is, in fact, what 'either' means but what is seems to imply..

directly from the article:

In English, the construct "either ... or" is usually* used to indicate exclusive or and "or" generally used for inclusive


*emphasis mine

I dunno, I think 'or' is inclusive unless explicitly stated, and I think it's the LSAC's opinion (the only one that really matters) too..

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Richie Tenenbaum
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Re: Either.. or.

Postby Richie Tenenbaum » Fri Apr 20, 2012 8:47 pm

skip james wrote:i looked at the article, but it doesn't seem to say that is, in fact, what 'either' means but what is seems to imply..

directly from the article:

In English, the construct "either ... or" is usually* used to indicate exclusive or and "or" generally used for inclusive


*emphasis mine

I dunno, I think 'or' is inclusive unless explicitly stated, and I think it's the LSAC's opinion (the only one that really matters) too..


Human language is imperfect, but there is a reason that there are two different ways to state "or."

Or= inclusive-or. Example: A or B= A or B or both AB
Either...oR= exclusive-or. Example: Either A or B= A or B (but not both)

It might very well be the case that using "either...or" to mean an exclusive-or has fallen out of use among a lot of people, but I've always known the two constructs to mean two different things. (And I believe dictionaries still define "either...or" as an exclusive-or.*) If English was more precise, there would just be two different words for the two different meanings.

ETA
*http://dictionary.reference.com/browse/either-or
http://www.merriam-webster.com/dictionary/either-or
--LinkRemoved--

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Re: Either.. or.

Postby skip james » Fri Apr 20, 2012 9:41 pm

human language is definitely ambiguous, i agree, and i don't deny the fact that one 'could' mean exclusivity when saying 'either.. or' but one could also mean no such thing. just because those two definitions endorse one meaning of a phrase, does not indicate that there is only one meaning to that phrase.

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Ded Precedent
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Re: Either.. or.

Postby Ded Precedent » Fri Apr 20, 2012 9:48 pm

Way to confuse OP, either/or on the LSAT is equal to "At least one of the two, POSSIBLY BOTH". No need for further discussion.

NYCLSATTutor
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Re: Either.. or.

Postby NYCLSATTutor » Sat Apr 21, 2012 10:05 am

A little clarification.

Either or, but not both IS tested on the LSAT and generally (not always) when the test-makers say "either or" they follow it by "but not both". As I said, I was assuming that is what the OP meant, since it is significantly more common.

The test does treat "either or" (without not both) and "or" as identical statements. If the test has either, or, but not both, I doubt (and have never seen) they would ask you to do the contrapositive.

That being said, I don't subscribe to the theory of "don't teach anything thats not included on the test directly, that will just confuse people". The greater understanding someone has of the ins and outs of logic, the better one can apply the specific logical principles required by the test. Knowing the contrapositive of "either or but not both" may not be directly tested, but knowing what "either or but not both" means may become more clear by understanding what the contrapositive is.

My original post was unclear and for that, I apologize. But I did mean to be referring too "either or, but not both".

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Re: Either.. or.

Postby bp shinners » Sat Apr 21, 2012 5:08 pm

NYCLSATTutor wrote:My original post was unclear and for that, I apologize. But I did mean to be referring too "either or, but not both".


Re-reading my response, it sounded more harsh than I intended. I mainly wanted to make it absolutely clear that, for the purposes of the LSAT, "either or", by itself, is inclusive. With so many people lurking, I didn't want anyone to read that and get confused.

So I apologize for that.

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suspicious android
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Re: Either.. or.

Postby suspicious android » Sat Apr 21, 2012 7:42 pm

This has been such a positive, respectful discussion. We should all hug.

But seriously, "Either . . . or" is inclusive in real life, not just the LSAT. The dictionary links above are referring to the idiomatic expression "either/or", as in "it's an either/or situation". That really is exclusive, but not the construction "either X or Y", which by itself is inclusive but becomes exclusive either through the addition of some phrase like "not both" or by context.

Just like to point these things out, because I'm a strong believer that by and large, there is no "LSAT world", where words have different meanings than in real life.

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Richie Tenenbaum
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Re: Either.. or.

Postby Richie Tenenbaum » Sun Apr 22, 2012 12:43 am

PSA: Ignore this post if you are currently studying for the LSAT. It holds only confusion for you.

suspicious android wrote:This has been such a positive, respectful discussion. We should all hug.

But seriously, "Either . . . or" is inclusive in real life, not just the LSAT. The dictionary links above are referring to the idiomatic expression "either/or", as in "it's an either/or situation". That really is exclusive, but not the construction "either X or Y", which by itself is inclusive but becomes exclusive either through the addition of some phrase like "not both" or by context.

Just like to point these things out, because I'm a strong believer that by and large, there is no "LSAT world", where words have different meanings than in real life.


I respectfully disagree :lol:

While I think that common usage is sloppy when it comes to "or" and "either...or"--and such sloppiness might have started to affect the definitions of each, I think that at some point in time it was more clear that "or"=inclusive-or and "either...or"=exclusive-or.

From the wiki article I linked earlier:
The Oxford English Dictionary explains "either ... or" as follows:

The primary function of either, etc., is to emphasize the indifference of the two (or more) things or courses ... but a secondary function is to emphasize the mutual exclusiveness, = either of the two, but not both.


The exclusive-or explicitly states "one or the other, but not neither nor both."


From random google seach site: http://robin.hubpages.com/hub/Grammar_M ... _Either-Or
"Either" and "Or"

"Either" is also a singular adjective. It means one or the other, but not both. "Either" expresses one noun/pronoun doing one thing and the other noun/pronoun doing another; in this way it is a "positive" word because what is occurring is true. "Either" can be paired with "or", but not "nor".

She wanted to paint either a landscape or a self-portrait. (She wanted to paint one or the other, but not both.)

I can't remember if either Georgia or Julia wanted a doll for Christmas. (One of the girls wanted a doll, but not both.)



I don't claim that there is a consensus about that is what the terms mean now, I'm just sticking by my claim (w/o proof) that the distinction was more clear in the past. (Or maybe it's just more of a formal logic type thing and common usage was always confused between the terms.) In any case, the main reason why I wish we could have a clear distinction between the two is so we can forever get rid of the "and/or" term. It's ugly and repetitive, but lots of people still feel the need to use it because some people won't recognize "or" to be inclusive on its own.

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suspicious android
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Re: Either.. or.

Postby suspicious android » Sun Apr 22, 2012 2:20 am

The dictionary quote suggested that there are English sentences in which 'or' is exclusive, and others, less commonly, in which 'or' is inclusive. This is probably true, the OED doesn't mess around. But that quote isn't suggesting what you seem to me to be inferring from it, as the rest of the section just points out that there are conflicting views on the idea. The "myth of the exclusive or" paper mentioned is not something I have ever read, but seems to jibe with what I think I remember from my logic classes: in English, an "or" statement's exclusivity is determined by context or by phrases such as "not both". Maybe "either" is one of those phrases and my brain just isn't working right, but it doesn't seem to do it for me. As for an actual argument to support all this, like you, I'm not gonna kill myself over this, but:

Either X or Y

With no context, this could be inclusive (the most popular students are always either pretty or smart. Obviously a smart and pretty student wouldn't be an outcast based on that sentence), or it could be exclusive (You can have either coffee or tea after dinner. Probably you cannot have both).

Since there's no way to determine whether it's inclusive or exclusive, it must be context or helping phrases that make it one or the other. So you cannot safely infer exclusivity from "or" by itself, you need to lean on something outside the term to get that. It just so happens that in most situations in which we use "or" we mean it exclusively, so we kind of assume that to be the default meaning, when actually the word by itself just gives us the A v B part, not the ~(A & B) part.

But if you're some kind of pinko descriptivist, I guess you could just say "or" is exclusive because that's what people usually mean, I guess you'd have a point. But that's anarchy, man.
Last edited by suspicious android on Sun Apr 22, 2012 4:57 am, edited 1 time in total.

skip james
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Re: Either.. or.

Postby skip james » Sun Apr 22, 2012 4:26 am

group hug?

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Re: Either.. or.

Postby foggynotion » Sun Apr 22, 2012 5:44 am

I'm not sure why some of you feel that "either...or" means something different than "or". Maybe conversationally "either" might be used to emphasize exclusivity, but logically it doesn't make a difference--you're still saying "or". I agree that "or" might sometimes be used in conversation to indicate "one or both" in some situations, and other times it might be used to indicate "either but not both" in another situation--but that kind of ambiguity is precisely why you have to treat it as inclusive.

NYCLSATTutor wrote:If the test has either, or, but not both, I doubt (and have never seen) they would ask you to do the contrapositive.


I wasn't sure what you meant by this exactly. Are you saying they wouldn't have statements like this: "either A or B but not both" in a situation where you'd typically want to do a contrapositive? If so, they have had statements like that in games, and you might very well want to do a contrapositive (I apologize in advance if I've misunderstood you).

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Re: Either.. or.

Postby NYCLSATTutor » Sun Apr 22, 2012 10:50 am

foggynotion wrote:I'm not sure why some of you feel that "either...or" means something different than "or". Maybe conversationally "either" might be used to emphasize exclusivity, but logically it doesn't make a difference--you're still saying "or". I agree that "or" might sometimes be used in conversation to indicate "one or both" in some situations, and other times it might be used to indicate "either but not both" in another situation--but that kind of ambiguity is precisely why you have to treat it as inclusive.

NYCLSATTutor wrote:If the test has either, or, but not both, I doubt (and have never seen) they would ask you to do the contrapositive.


I wasn't sure what you meant by this exactly. Are you saying they wouldn't have statements like this: "either A or B but not both" in a situation where you'd typically want to do a contrapositive? If so, they have had statements like that in games, and you might very well want to do a contrapositive (I apologize in advance if I've misunderstood you).


I've never seen a question where the contrapositive of the "but not both" part of an "either or but not both" is actually helpful. You are correct that these show up in games where the contrapositive is used a lot, but I think that contrapositive is not one they expect you to know.

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totgafk180
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Re: Either.. or.

Postby totgafk180 » Sun Sep 09, 2012 8:58 pm

PT 35.1.17

I think in this particular question, "either ... or ..." refers to "either A or B, but not both." That interpretation would make the answer a solid fit.

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Re: Either.. or.

Postby foggynotion » Mon Sep 10, 2012 5:07 am

totgafk180 wrote:PT 35.1.17

I think in this particular question, "either ... or ..." refers to "either A or B, but not both." That interpretation would make the answer a solid fit.


If you mean the part that says "either severe climatic warming or volcanic activity...", I don't think it means "but not both". There's nothing about what the author says there that would imply both circumstances couldn't have happened. In other words, if it turned out that there was severe climatic warming and volcanic activity, that wouldn't conflict with what the author is saying. The author is just giving two possible conditions, each of which could have led to the ice sheet melting, but I don't believe one automatically excludes the other. When answer choice E says "...is treated as though only one resolution is possible", it's not referring to the climatic warming or volcanic activity (I thought maybe that's why you were saying that "but not both" would clinch that answer choice, my apologies if I misunderstood). The "one possible resolution" is the melting of the ice sheet (there could be other explanations for the fossil).

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totgafk180
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Re: Either.. or.

Postby totgafk180 » Mon Sep 10, 2012 12:04 pm

The first time I did this problem I also went with that explanation.

"[T]he Antarctic sheet temporarily melting" is actually an effect that stems from a cause. The stimulus gives two possible causes which could include either "severe climatic warming" or "volcanic activity." As a set of information, the combination of cause/causes and the effect could be considered as the only resolution put forward by the argument.

If another resolution were to be proposed, the effect would remain constant; however, the resolution would contain a new cause (or new causes). Other possible causes could include fluctuations in the Earth's orbit around the sun (which thereby led to the melting of the ice). In any case, for this problem, the resolution seems to be more dependent on interpretations of the cause (or causes) as opposed to just the effect (the effect is not a resolution in itself).

I thought interpreting "either... or" as (not both) made this argument tighter. I know that, for this argument to follow, "either... or" does not have to be interpreted in that way. Looking at the argument this way is probably overkill and I'm not trying to advocate that "either...or" is definitely on the test.




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