Some vs Most Arrows

[kristinaroz93]

I have noticed in the lr bible that for symbolizing relationships that have the term "some" we use double arrows.

i.e. "Some Ws are not Zs"
some
w<-------->not z

But for symbolizing relationships which have the term "most", we use a single arrow.

i.e. "Most Ws are not Zs"
Most
w------->not z

Why is this the case? Is this relationship significant or it does not really matter?

Thanks!

[Dave Killoran]

Hi Kristina,

Yes, it does make a difference and the two representations are meant to convey different possibilites. On page 388, I talk about the Rules of Reversibility which involves the issue you are looking at here. "Some" is a reversible term; "some As are Bs" means that "some As are Bs" and that "some Bs are As." "Most As are Bs" is not reversible, hence the arrow goes in only a single direction. In "Most As are Bs," "Most As are Bs" is true, but "Most Bs are As" is not true. That's a huge difference.

Pretty much everything you see in the LSAT Bibles and our courses has been done for a specific purpose, so when you encounter a difference like this, try first to find the explanation within the text—usually there will be one. It's a great approach because that moment of self-illumination is the most powerful learning moment there is!

Thanks!

[kristinaroz93]

Hi Dave,

thanks for responding! Even though I am not quite done with 13 yet, I haven't come across that being stated (or maybe I missed it). While I can kind of abstractly understand why one is reversible and the other is not, how can this concept be better understood. Why is it that some A's are B's can be reversed to some B's are A's, but Most A's are B's does not equate to most B's are A's?

And another question along similar lines of reasoning:

Why is All X's are Y's a single arrow: X-->Y
But No X's are Y's a double not arrow: x<--/--->Y

Is it like all people in college have loans, but doesn't mean everyone who has loans is in college. The pool of people with loans may be much bigger as loans can be used for mortgages, car payments, etc? (Is this a good analogy for the first question of x-->y).
And the double not arrow is used because if no college people have loans, then no one who has loans goes to college?


Thanks!!

[Emily Haney-Caron]

Hi Kristina,

Good follow up question! The reason that "some As are Bs" is reversible is because some tells you nothing about quantity; "some" could be 1 out of 10 million or it could be 99% or more. If even a single A is a B, then we know at least a single B is an A (that same one). It is possible that 90% of As are Bs but only 1% of Bs are As, but it doesn't matter with "some," because it doesn't specify anything more than "at least one."

"Most" is different; it tells you it has to be more than 50%. Just because at least 51% of As are Bs, that does not mean at least 51% of Bs are As. It could be that there are only 10 As, and 6 of them are Bs, but there are 10,000 Bs, and only 6 of them are As (which would not be most).

I hope that helps!

[kristinaroz93]

Thank you Emily!

I get it now =)

I also revised my last posted question that you answered to add some more stuff to it! Please let me know if my analogies are correct!

-Kristina

[Dave Killoran]

Hi Kristina,

Yes, those analogies work

Also, in response to your diagram question, keep in mind that the double-not arrow is a "super" statement that encompasses both the original statement and it's contrapositive. the original statement for each is the same form:

• All X's are Y's: X Y
  No X's are Y's: X Y

So, they are the same underneath.

Thanks!

[kristinaroz93]

Thanks so much! And I see now that there is a reversibility section, that I just haven't gotten to, I am sure it will be very clear to me now. Doing the drills before seeing that section I guess is what brought the confusion. Thanks again!

-Best

Kristina

[Jon Denning]

Hey Kristina (and all),

I happened across this thread and it reminded me so much of a conversation I had with a tutoring student earlier that I felt compelled to add, very briefly, to it

Basically the discussion I had with him centered in part on how beneficial it can be to give yourself some time with your questions before others step in and answer, so that your growing knowledge has time to sink in and you have the opportunity to answer for yourself! The truth is that answers that are self-supplied (really self-discovered) tend to resonate more and be much more powerful than those that are simply handed out. That kind of self-sufficiency is at the heart of LSAT success! The problem for a lot of test takers, my tutoring student among them, is that they don't give themselves time to find that answer on their own, asking for help immediately instead and suffering somewhat as an unexpected result.

Here I noticed the questions about some/most and single/double arrows and then saw that the relevant section simply hadn't been reached when the questions were posed, and immediately thought, "man, that would have been a great feeling and experience to have considered those questions privately and then answered them independently just a short time later." A lot of what feels initially confusing is temporary and will be completely clarified with just a tad more work, and the benefits of that process are too crucial to ignore.

Again, I don't think it's the end of the world or anything, and we always want people to ask questions when they're unable to work them out privately...but I can't recommend enough how valuable it is to hold off for 3-4 days, think a little longer, learn a little more, and see if the answer can be determined on your own rather than provided immediately. So I hope you, my tutoring student, and anyone else who happens to read this will keep that in mind as you all keep preparing!

[kristinaroz93]

Hi Jon,

I could not agree with you more, I do know what self-discovery is like and it is an amazing feeling, when it does happen. However, by nature I can't seem to move on from what I am doing unless everything on that page makes sense to me, and then I am stuck in this standstill. I guess I should have skimmed ahead, but my ultimate dilemma I would say is not wanting to feeling stuck in one place for too long=/ As I did the drills, I could not understand why the arrows changed for most/some because the explanation came after (but I did not foresee that, because usually explanations come before and then we attempt the practice drills). So I spent a half hour trying to figure out why this could be (not having moved on of course) before leaving the post. So that was what happened, had I known the explanation would come after I wouldn't have left the post! Maybe if the explanation came before I would have been like aha! And then drill would have made much more sense to me.

Sorry for the long post,

Kristina