Diagramming conditional statements with subscript

[sarahg]

Hi,

I'm interested in understanding what the principles are that govern the use of subscript when diagramming conditional statements. In the Logical Reasoning Bible, 2012 edition, p. 162, practice test queston #2, the explanation answer on p. 165 indicates lots of subscript use, and the last sentence in the stimulus is of course diagrammed with a subscript but also in a sort of compacted way that seems odd, meaning that it was done in a way not discussed when diagramming was talked about in the book. This question is from PT29, October 1999, Section 4, #12.

So for instance, the last sentence of that stimulus reads, "Unfortunately, it is almost always impossible to make drivers with a large number of demerit points more responsible drivers" and is diagrammed as R with a slash through it and a subscript d, where R = likely to be made more responsible drivers, sub D = drivers with a large number of demerit points, etc and slash meaning "not." I however saw the sentence as being diagrammed more like, DLD ------>~DLMR, where DLD = drivers with a large number of demerit points, etc and DLMR = driver likely more responsible and "~" = "not."

Now, I got the correct answer, but I noticed that doing it my way was cumbersome and laborious, not to mention time consuming. Under the contraint of time and various pressures, I could see that making a mistake with all that conbining would be more likely. The subscript and the compact nature of the diagramming in the answer explanation is excellent, but I am not clear on how to know when and when not to diagram in this compacted, subscripted way.

It would be great to get some specific clarification on that issue because I would very much like to better understand this type of diagramming. I'm particularly interested in any principles, rules of thumb, etc., that may guide such diagramming.

Ok, thanks.

Sarah

[Dave Killoran]

Hi Sarah,

Thanks for the very good question. Let me make a few points about diagramming that might help a bit:

1. I want to start by addressing the point you make in the third paragraph of your question. The good news here is that as you continue in your studies, these moments of uncertainty and possible mistake-making will start to disappear. The more variations on the theme that you see, the more confident you will feel in making certain decisions about diagramming. And, as you are already seeing, there are a lot of decisions to make in certain situations.

Considered as a whole, diagramming statements is a sprawling area, and at times things get a bit messy. Thus, it's extremely hard (well, impossible) to cover every eventuality in the early stages of the book. That's why you will sometimes see elements later that weren't specifically discussed earlier. The process you are going through right now--asking questions and determining why certain things are happening--is a great sign that you are getting the foundation in place correctly.

2. Ok, that said, let's move on to why subscripts were used and when to use them.

The general answer of when to use subscripts is: when you think it will clarify the diagramming. But, while that makes sense, it's not very helpful in a specific sense. So, let's look at some examples of when I think subscripts clarify the diagramming:

• A. When a specific element meets the requirements of a broader condition in the argument.
  
  That sounds pretty confusing, but what I mean but that is when a player in the stimulus is actually stated to have met or be included in a condition. For example:
  
  • All honors students at this school have received merit-based scholarships. Maria is an honors student at this school, therefore Maria has received a merit-based scholarship.
  In this case, "Maria" is the specific element, and she meets the criterion of the broader condition (being an honors students at this school. Thus, "Maria" isn't a separate condition, but a sub-component of the condition. The diagram then ends up appearing as:
  
  • Premise: HSS MBS
    Premise: HSSM
    
    Conclusion: MBSM
  B. When a group or portion meets the requirements of a broader condition in the argument.
  
  This is similar to the first example, but here, instead of a specific individual, it's a group of elements, or an indistinct portion (notably, this is what is occurring on page 165). Here's an example:
  
  • All honors students at this school have received merit-based scholarships. My friends are honors student at this school, therefore my friends have received a merit-based scholarship.
  In this case, "my friends" is the group element, and they meet the criterion of the broader condition (being an honors students at this school. Thus, "my friends" isn't a separate condition, but a sub-component of the condition. The diagram then ends up appearing as:
  
  • Premise: HSS MBS
    Premise: HSSmf
    
    Conclusion: MBSmf

Referring this back to the question explained on page 165, the drivers with the large number of demerit points and serious driving offenses are referenced within the context of two other larger groups, leading me to use that group as a subscript. That said, this is a tough problem (which, of course, is why we are looking at it in the book!) so seeing this takes a bit of work.

Hopefully, this gets you thinking more deeply about the issue, and based on the way you asked the question, I feel pretty confident this is the type of problem that you will be able to largely resolve soon.

Please let me know if that helps, or if I can clarify further. Thanks!

[sarahg]

Hi Dave,

Thank you for that nice response--and for getting back so quickly! I appreciate it. What you've written does shed some light on this issue. However, while I can certainly appreciate the vastness of the diagramming circumstances one might encounter on the LSAT, I would have guessed that what ever particular models are tested on in the text would also have been covered in the text, so I was slightly taken off guard by that subscript method. Up to that point in the LRB, we've primarily been exposed to the "ABC -------> ~DEF" kind of construct, yet the answer explanations were in an unfamiliar diagramming language.

Ok, well, again, thanks for the information. I do enjoy this stuff, and I very much appreciate any helpful information.

In the meantime, I'm going to study the information you've provided a bit closer, and if I find that I need more clarification, I will be sure to write back

Sarah

[Dave Killoran]

Hi Sarah,

Thanks for the nice reply!

There is actually prior discussion of the diagramming subscript idea in the book. For example, pages 118 and 119 reference subscripts, as does page 142, and page 146. Thus, by the time I arrived at page 165, I didn't reference the concept further, mainly because the examples on earlier pages introduced the idea (and in an easier form than the one on page 165). However, as that book is being updated again very soon, I'll add a more detailed section on handling subscripts

Thanks!

[sarahg]

Hi Dave,

Thank you for that information. It was very helpful--in fact, a lot helpful You're absolutely right that subscripting was referenced on those pages. I remember reading through those sections and not only finding the treatment of subscripting interesting, but I found myself wanting more...

The problem is it's only touched on in one very simple instance and no priciples, examples, variations nor real-life stimulus stituations are used to hit home the underlying ideas governing the use of subscripting in different situations. So while pp. 118-119 demostrate the use of subscripting where a single individual is experiencing a single condition, the answer explanation on p. 165 for pratice test question #2 on p. 162 uses subscripting to decode an actual stimulus where individuals are epxeriencing a host of individual elements that make up a condition; so, because no real subscripting workout is offered to make clear and to familiarize students with this fantastic concept and all of its vicissitudes, it was not clear that subscripting was indicated in that particualr stimulus, unfortunately.

In any case, your referring me back to pp. 118-119, 142, 146 was enormously helpful. It would be wonderful however if the book dedicated a section to subscripting and treated it as thoroughly and brilliantly as it has done with every issue tackled in the book up to this point.

Ok, well, thanks again, and if I have any further questions, I'm sure I'll be bothering you folks again

Sarah

[Dave Killoran]

Hi Sarah,

I agree, and fortuitously, the Logical Reasoning Bible is coming up for revisions in about 6 weeks. So, at that time, I'll add several pages on subscripts and how they work, and include multiple examples. In the meantime, hopefully my first post will suffice to lay the groundwork. If not, please feel free to ask more questions about the concept

Thanks again!

[sarahg]

Hi Dave,

Yes, your first post has lain the goundwork very nicely. It definitely made a possitive difference.

Those revisions you mentoned sound very exciting. I was wondering if there's a way one could purchase those revisions somewhere? That would be fantastic!

Ok, well, thank you so much for taking the time to answer my questions. I appreciate it a lot. And I will be sure to run my coffee cup aross the bars when bewilderment catches up to me!

Sarah

[Dave Killoran]

Hi Sarah,

That's a really good idea to sell the updates! Unfortunately, because of how they are made to the text, it would be very difficult to sell them. Typically, instead of just adding new sections, I'll do that, but I'll also expand pre-existing sections. So, instead of a document that would be, say, 50 wholly new pages, you end up with hundreds of changed pages.

However, I'll make you a deal. When I get to the subscript section, I'll send you a copy of that so you can see what it looks like. It will be longer than six weeks from now though, because although that's when the updates start, I won't get to that section for a while after that.

Thanks again!

[sarahg]

Hi Dave,

Oh, that would be great! I'd love to get my hands on that lol. And I totally understand the idea of specific expansions of one concept-in-need along with various tweeks and developments to the whole publication in general. But it's still an exciting idea to get a copy of the revisied edition!!

Ok, well, again, thanks so much for all the great information. It's been a big help.

Have a great Sunday!

Sarah

[est15]

Hi,

I have a question about this same problem, so I thought I would post it here. The premise in the stimulus refers to the drivers (sub-D) as those with (1) a large number of demerit points and (2) who have been convicted of a serious driving-related offense. However, the last sentence in the stimulus only refers to the drivers as those with demerit points. Why is the conditional relationship representing the last sentence as ~R_D still valid? Additionally, answers B and E do not say that the drivers have been convicted for a serious driving-related offense, so is there a reason why I can still use the conditional relationship given that it was formed for drivers with demerit points AND serious driving-related offenses? I'm wondering when I have to be careful about the wording and how to determine whether the subscript applies to a conditional relationship or not.

Thanks.