LGB Grouping Diagram Clarification

[hunterama1]

Two points of confusion for me:

1. pg 218: W X
J W
K X thus J W X thus J X OK

but then K X W does NOT = K W even though it follows but at the same time violates the conditional rule J W. However the J X inference is used to create K X J and thus K J. Please explain how K W is not inferrable. Also it's a little confusing to me to use a double line arrow because it 'appears' as though both variables are not notted even though they really are re: W X really is W X. Any hints or suggestions for thinking with clarity on this visual symboliziation?

2. pg 224 (and generally): N R
N S

is N R, N R
and N S, N S

Thus R N and S N in terms of sufficient conditions have "similar needs" (N) so it appears that R S could be inferred. Is this correct? Even if it is I'm a little confused as to linking different sufficent conditions to like necessary conditions. The closest hint I could find in LGB was from pg 211: "When a necessary condition does not occur, all of the sufficient conditions also can not occur" which leans me toward my hypothesis of R S. Please shine a little light on this for me kindly.

[Steve Stein]

Hey hunterama,

I like the double not arrow, because it concisely shows that two variables do not get along. But you might have an easier time if you just spell out both sides of that relationship; in other words, if W X, we've got to keep them separated--so, we know that:

W NO X,

and we know the contrapositive, that X NO W

Try that and let me know whether you have an easier time creating the conditional chains that you asked about--thanks!

~Steve

[Dave Killoran]

Hi Hunter,

Thanks for the questions. Please let me try to help you out here:

Page 218

K W is inferable--look at the third diagram down on page 219. That shows that exact inference.

The way to view this symbol is as a not equals sign; that slash in the middle of the double arrow always has to go on one of the two variables (and possibly both). So, it's just a matter of understanding that the negativity is there, it's just shown in the middle since either variable could have it.

As far as its utility, the symbol is incredibly powerful for drawing inferences in games and formal logic LR questions. Once you've used it for a while, I think you'll get used to it and the meaning will become second nature.

Page 224

This part is not correct, unfortunately Think about this relationship as R and S having a mutual enemy (N). Does that necessarily mean that R and S hate each other? No, and that's why you cannot infer R S.

Another way to consider this is to initially diagram that statement as:

R
+ N
S

This isn't the diagram we used in the LGB because separating it out reveals the true scope and power of the rule. However, this representation shows how the absence of N allows both R and S to coexist peacefully.

A question: do you have the LSAT Logical Reasoning Bible? If so, I'd suggest you take a look at the chapters on Conditional Reasoning and Formal Logic. Those two will probably clear up a lot of the concerns you have about sufficient and necessary conditions.

Please let me know if that helps. Thanks!

[hunterama1]

Mr. Stein and Mr. Killoran,

I must have spaced on missing that inference on pg 219. It's only written twice! Missing the forest for the trees.

The points of analogy re: enemies and the plus sign diagram clarified things for me.

I do have the Logical Reasoning Bible but confess I haven't gotten to it yet-been focusing on Logic Games.

I have purchased however the Powerscore Lsat Online Course (36hr), as well the deconstructed series, the set up encyclopedias, and LR/ RC/ and LG question type training books. I'm a big Powerscore fan(atic)!

As a point of note it may have been a little clearer to have perhaps used a slash in the middle of the double arrow which follows more clearly the negation of both sides as contrasted to the upright line which implies balance traditionally.

But I'm getting the hang of it.

Perhaps a chart of inferences would be of some help showing all the different ways one can infer esp. from negative sufficient chains and spotting 'internal' inferences from biconditionals so as to tie in to negative sufficient conditionals.

Negative sufficient condition inferences through chains and/or bi-conditionals I am not clear on at this stage of the game. Hopefully with practice they will become clearer to me. If you have any suggestions for a 'map' showing all the possibilities of conditional inferencing this would be useful. In the meantime I will look into the LR Bible as suggested.

Again and as always- my sincere thanks.

[Dave Killoran]

Hi Hunter,

You really are a big fan—thanks very much for that!

There is a chart of all inferences involving arrows—you can find it in the Formal Logic chapter of the LRB (chapter 11), on page 333. That table shows all relationships between none, some, most, and all relationships.

Negative sufficient conditions are tricky, because they revolve around the idea of something not occurring being sufficient. In Games they can be devastating because most people do not understand what a relationship like A B actually means (it means that A or B is always absent, and possibly both are absent). The more work you get with those, the better you will become

Please let me know if this helps, and keep asking questions about anything that is not clear. Thanks!