Some are not/Not all question

ioannisk
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Some are not/Not all question

Postby ioannisk » Fri Aug 02, 2013 3:08 pm

Am I understanding the equivilance of some are not/not all correctly?
Some As are not B: This is stating 0 to 99 percent are A=B, adn 1 to 100 percent could be A is not B

Not All means the same thing.

Am I correct?

sasquatchsam
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Re: Some are not/Not all question

Postby sasquatchsam » Fri Aug 02, 2013 3:34 pm

If I am understanding correctly you are asking if the terms "some A are not B" and "not all A are B" are equivalent. The short answer is they are not logically equivalent statements.

"Some A are not B" means that there is at least one A that is not a B.

"Not all A are B" means that IF there is such a thing as an A there must exist at least one A that is not also B.

I want to add that you are mostly correct in your assertion that they are equivalent statements but that you should not assume (especially if you run into this scenario in a LG) that "Not all A are B" guarantees the existence of an A.

ioannisk
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Re: Some are not/Not all question

Postby ioannisk » Fri Aug 02, 2013 3:49 pm

sasquatchsam wrote:If I am understanding correctly you are asking if the terms "some A are not B" and "not all A are B" are equivalent. The short answer is they are not logically equivalent statements.

"Some A are not B" means that there is at least one A that is not a B.

"Not all A are B" means that IF there is such a thing as an A there must exist at least one A that is not also B.

I want to add that you are mostly correct in your assertion that they are equivalent statements but that you should not assume (especially if you run into this scenario in a LG) that "Not all A are B" guarantees the existence of an A.

I understand Not all A are Bs does not gurantee the existence of an A=B
I meant to imply that Not all As are Bs implies atleast one A is not B

and for Some As are not Bs, that implies atleast one A is not B and implies it does not gurantee an A=B
which is why I said they're equivilant, Am I correct?

sasquatchsam
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Re: Some are not/Not all question

Postby sasquatchsam » Fri Aug 02, 2013 4:00 pm

Sorry I will clarify. The statement "Some A are not B" means that their has to be at least one A. The statement "Not all A are B" does NOT mean that there has to be any A at all. The statement only asserts that if any A exist they cannot all be B.


I can truthfully say that not all great-great-great-great-great-great-great-great-grandparents are less than 1000 years old because none exist in the first place.

I cannot truthfully say that some great-great-great-great-great-great-great-great-grandparents are less than 1000 years old because I am asserting that a great-great-great-great-great-great-great-great-grandparent exists.

ioannisk
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Re: Some are not/Not all question

Postby ioannisk » Fri Aug 02, 2013 4:07 pm

sasquatchsam wrote:Sorry I will clarify. The statement "Some A are not B" means that their has to be at least one A. The statement "Not all A are B" does NOT mean that there has to be any A at all. The statement only asserts that if any A exist they cannot all be B.


I can truthfully say that not all great-great-great-great-great-great-great-great-grandparents are less than 1000 years old because none exist in the first place.

I cannot truthfully say that some great-great-great-great-great-great-great-great-grandparents are less than 1000 years old because I am asserting that a great-great-great-great-great-great-great-great-grandparent exists.


I get what you're saying now, but I'm not sure if you're correct.

This thread:
http://www.top-law-schools.com/forums/v ... 6&t=206295

seems to agree with me

sasquatchsam
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Re: Some are not/Not all question

Postby sasquatchsam » Fri Aug 02, 2013 4:31 pm

To be honest you are making me a little unsure of myself now about how well I remember my formal logic classes haha. I decided to do a little digging and in all honesty it seems there is a little controversy regarding the concept.

The way I was taught is that universal statements (all A are B/No A are B) and their negations do not have existential import but that particular statements and their negations (some A are B/some A are not B) do have existential import. This seems to be the "modern" view proposed by George Boole. You can look up more on wikipedia regarding existential import and the square of opposition.

lalalany
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Re: Some are not/Not all question

Postby lalalany » Sun Aug 04, 2013 11:05 pm

.
Last edited by lalalany on Sat Oct 19, 2013 9:58 am, edited 1 time in total.

sasquatchsam
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Re: Some are not/Not all question

Postby sasquatchsam » Mon Aug 05, 2013 1:29 pm

These links may be useful in resolving any questions regarding this topic. Hope it helps :) If anyone finds something that contradicts these articles please share.

http://cstl-cla.semo.edu/hill/pl120/not ... import.htm

http://www.wwnorton.com/college/phil/lo ... import.htm

http://www.philosophypages.com/lg/e07b.htm

http://en.wikipedia.org/wiki/Square_of_opposition

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Archangel
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Re: Some are not/Not all question

Postby Archangel » Mon Aug 05, 2013 1:40 pm

Some covers a broad range from 1 to all.
Some, but not all covers 0.001 to 99.99%.
Not all could be none to 99.99%.

foggynotion
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Re: Some are not/Not all question

Postby foggynotion » Wed Aug 07, 2013 3:18 am

I didn't follow the links you guys posted, so please forgive me if what I'm about to say was covered in there already. But when I took logic in school, we learned that "some" statements did, in fact, imply the existence of the things they described--the reason seemed to be that this is just what was meant by using the terminology. In other words, in modern symbolic logic, when you say "some A's are B", you're saying "there exists an A such that that A is B". It's not so much that "some" implies this, but that "some" has been defined this way.

"Not all A's are B" is equivalent to "some A's are not B", and they mean the same thing logically, so you can use them interchangeably. If you say "not all A's are B", you're saying that not every single A is B, which means that there must be some A that's not B. And if you say "some A's are not B", that means that, since there is a A that's not B, not all A's can be B. When you say "not all..." it's not the same thing as saying "all.." In other words, you're not saying:

(not-all A's are B)

you're saying:

not (all A's are B)

which translates to (some A's are not B)

In symbolic logic, an "all" statement would be written like this: all x(Ax -->Bx) (except that there would be a specific symbol you'd use instead of "all", and there's another one for "some", but I don't have them on my keyboard), and this would mean literally "for all x, if x is A then x is B. A "some" statement would be written: some x(Ax & Bx), which literally would mean "there exists an x such that x is A and x is B". And the negation of the first sentence "all..." would equate to "some are not..." for pretty much the same reason that a sentence like: ~(A --> B) converts to (A & ~B) (because the only way a conditional can be false is if the first part (the antecedent) is true and the second part (the consequent) is false).

However, I can't recall any questions from the lsat where you needed to know that "all" didn't imply "some"--usually the information they give you does allow you to draw a conclusion like that because they've give you other information also (Example: All parrots can learn to speak, and some Australian parrots have a sweet temper--you can conclude that some sweet-tempered parrots can learn to speak. It's not an issue that there might not be any parrots, because they tell you about the Australian parrots.) So I don't know if I'd even worry about that. I'm not even sure if the idea that "all" does not imply the existence of anything would really be an issue either. I can't recall off the top of my head if there are any questions that deal only with "all" statements and then expect you to draw a "some" conclusion. Usually they mix "all" with "most" or mix "all" with "some" (or "none" with "most"/"some").

TylerJonesMPLS
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Re: Some are not/Not all question

Postby TylerJonesMPLS » Sat Aug 10, 2013 5:01 pm

All/Some/None logic is often called Categorical logic. Aristotle was the originator. The most famous part is Aristotle's Square of Opposition. It is laid out in a diagram of a square. It shows the contradictories (e.g. “every A is B” is the contradictory of “Some A is not B”) and the contraries (e.g. “Every A is B” is the contrary of “No A is B.”)

Two propositions are contradictories if the two cannot both be true, and cannot both be false. Two propositions are contraries if the two cannot both be true, but they can both be false. In ordinary English we use the term “opposite” for both; but it is an important distinction in logic.

Contradictories: House says to Chase and Cameron, “If Chase is right, then Cameron is wrong, and if Cameron is right then Chase is wrong.”

Contraries: House says to Chase and Cameron, “You can’t both be right, but you can both be wrong.”


When modern logicians (modern = late 19th century and afterward) looked at Aristotle’s Square of Opposition, they noticed that Aristotle assumed that all four corners of his square had existing members. But modern logic makes it obvious that Aristotle’s assumption was an unjustified one. So, Aristotle’s square is no longer considered valid.

But, the LSAT makes the same assumption that Aristotle did. When the LSAT says, “Every A is B” the LSAT assumes that at least one A exists and at least one B exists.


and for Some As are not Bs, that implies at least one A is not B and implies it does not guarantee an A=B
which is why I said they're equivalent, Am I correct?

Yes, you are correct.
Not all A’s are B’s implies that Some A’s are not B’s, which implies that Some B’s are not A’s, which implies that Not All B’s are A’s.

There is a good discussion of the Square of Opposition on the Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/square/

Not All means the same thing.

“Not All” could mean “Some,” or could mean “None.”
"All" can mean "Some." This is used as a common trick on the LSAT. The passage/stimulus says, e.g. "All otters can swim." And the correct answer-choice says, "Some otters can swim." If all otters can swim, then some otters can swim. But that is logic- it isn't the usual way we employ those words in our everyday lives. And the LSAC is hoping that we won't remember the logical truth that If All X then Some X.




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