Help with answering the choices in 421.

[ericjmyuan]

Hello,

In page 421, you have narrowed down the choices for question number 1 into A and B, how was it that choice A was a valid reasoning as opposed to an invalid one? Would this not be a part of error of division as well?

Personally, how would one really identify the validity of an argument, because as of now, I usually use the question stem to indicate if it is valid or not. Are there any sort of a more comprehensive way to do it? For example, I know if conditional reasoning or causation is misapplied, it is then wrong, but for question like the one in page 421, how would I go on and check the validity of the answer choices given?

Another problem I have while doing the questions are my shakiness in Conditional Reasoning. I understood the indicator words and also how the concept applies in terms of identifying a good reasoning. However, I felt very lost when there is a lack of indicator words that can give me the hint of whether it is sufficient/necessary. For example in page 407, choice B, I'm not sure how to apply and identify the components in the statement "Jenny will have lots of balloons at her birthday party." I'm not sure if there's a more rigorous way of identifying the components other than "feel" or "temporal relationships" that some people attribute to.

Thanks for helping.

[Dave Killoran]

Hey Eric,

In answer choice (A) on question 1 on page 421, they are using conditional reasoning, so let's look at that first, starting with diagramming the two premises:

• Premise1: Student at this school take mathematics
  
  Premise 2: Student at this schoolMiguel

If you take those two premises, you enact the Repeat form of conditionality: Miguel meets the sufficient condition for Premise 1, so Miguel then meets the necessary condition. Thus, we can conclude that:

• Conclusion: take mathematicsMiguel

Which is exactly what (A) concludes.

The difference here is that an error of division talks about a characteristic of the whole ("That is a cool company") and then wrongly infers that every element of that whole has that same characteristic ("Thus, every employee at that company is cool"). There is a fundamental difference between the whole (which is its own entity) and the individual parts (which are separate entities).

Now, in the example above, I see where you are thinking it is the same kind of thing, but note how the language is different: the premise says that students at this school take mathematics (and not that the school itself takes mathematics). Since Miguel qualifies as a student, we then know he must have the characteristic of taking math. Answer (A) references the school, but the characteristic it talks about refers to the students therein, and not the school itself. This is one way this can be distinguished from a divisional error.

With respect to validity, there are definitely a set of argument types that are known to be valid and invalid. The Repeat form is valid, and obviously Errors of Division are flawed. Knowing the errors alone (See the Flaw chapter) will help you recognize bad arguments, but it will also help you recognize good arguments. The nice thing is that you tend to see more flawed arguments than good arguments on the test, but validity is really just a measure of logical soundness--does what the author says actually make sense, or are there gaps present? It's actually a topic that can be explored in a great deal of depth, and there really isn't a concise answer (namely because logic is so sprawling). We are always ready to talk about arguments, though, and discuss various ways to understand why something is valid or invalid, so feel free to ask us about the questions that bother you.

I'll also post more about conditional reasoning in general a bit later today, but in the meantime, check out this answer I posted to a question about conditionality earlier: http://forum.powerscore.com/lsat/viewto ... 6166#p6166. That answer references indicators, and when I post again later I'll talk about situations where it is not as clearly indicated. There's definitely more to it than feel or temporality (which really isn't part of it, actually--that's causality)!

Thanks!

[ericjmyuan]

Thank you David,

What you said about the validity of the question for Parallel Reasoning question set make sense. I just have a question, when you refer to the repeat reasoning, I have thought that student body = student in itself, but from what you said, essentially student body is really an entity of itself, separate from that of student, so when can we really equate the terms as being the same? Or should I realize that when LSAT question introduces a term or concept, they will repeat the usage of the terms and concepts specifically and they won't use synonyms to confuse me?

I look forward to your explanation on conditionality, thank you so much.

[Dave Killoran]

I just have a question, when you refer to the repeat reasoning, I have thought that student body = student in itself, but from what you said, essentially student body is really an entity of itself, separate from that of student, so when can we really equate the terms as being the same? Or should I realize that when LSAT question introduces a term or concept, they will repeat the usage of the terms and concepts specifically and they won't use synonyms to confuse me?

Let's start with the first part of your question, as to when we can equate the two. The answer is that the language used by the test makers will tell us when the two are the same. In this case, they reference "students at this school," which in fact means the student body. Miguel is a member of the student body, and since they all have the same characteristic, it applies to him as well.

Applying that idea to the second question you ask, this means you have to track what they reference to very carefully as you read. Sometimes it will be clear that the two are different, but there are instances where they use complex language to see if you can differentiate between elements that sounds similar but are different.

Thanks!

[Dave Killoran]

Let's now return to this part of your original question:

Another problem I have while doing the questions are my shakiness in Conditional Reasoning. I understood the indicator words and also how the concept applies in terms of identifying a good reasoning. However, I felt very lost when there is a lack of indicator words that can give me the hint of whether it is sufficient/necessary. For example in page 407, choice B, I'm not sure how to apply and identify the components in the statement "Jenny will have lots of balloons at her birthday party." I'm not sure if there's a more rigorous way of identifying the components other than "feel" or "temporal relationships" that some people attribute to.

Indicators are an easy way to break down conditional sentences. In a sense, they allow you to go on autopilot and just diagram (when needed) without thinking. But, in a number of situations there isn't a clear or obvious indicator hanging around, so what do you do then? It's at this point that you really need to understand what conditionality is all about, and use that knowledge to parse the sentence.

The first thing to realize is that almost any sentence can be turned into a conditional diagram, but that in most cases you don't want to waste time diagramming the sentence. The cases that you do diagram (or at least see in clear conditional terms) are usually the ones where absolutes are involved. When considering conditionality, one of the easiest ways to see it is that the sufficient condition applies to an entire group or entity (which is one reason "all" and "every" are sufficient condition indicators). A sentence like "Every employee at RiteCo has worked here for at least 5 years," means that if you are an employee at Riteco, we immediately know you have worked there at least 5 years. thus, when we diagram that, "employee at Riteco" becomes the sufficient condition, and we can then follow the arrow to the necessary:

employee at Riteco worked here for at least 5 years

If it said "some" instead of "every," for example, then the absolute meaning of the sentence would be removed, and it wouldn't be diagrammed as above.

The sentence above uses and indicator, but the point I'm focusing on is the absolute aspect of the sufficient condition, because this can help when working with sentences without such a clear indicator. For example, consider this sentence: "City policy dictates that homeowners must carry flood insurance."

First, note that absolute nature of "must"--it's something that has to occur. In this sense, it reflects the same degree of certainty as "all" or "every," etc. Second, note that the argument is restricted to homeowners in the city. But, if you fall into that group, what do we know about you? That every one of you must carry flood insurance (I'll avoid the issue of whether everyone follows the law; the point of the sentence is that the rule says you must carry insurance). So, in considering which condition is which, if I see that someone carries flood insurance, does that mean they are a city homeowner? No--they could live in another city, state, or country. But, what if I see a homeowner from this city? What do I know about them? That they must carry flood insurance, and thus "city homeowner" becomes our sufficient condition:

City homeowner carry flood insurance

When you see a group that all has the same characteristic, that will be the sufficient condition. This also explains the rationale behind power indicators such as "people who" (this described attribute applies to all those people), "if" (it applies to any element that meets the "if" description), and so forth.

In a sense, this absolute reference to a certain group is the "feel" element you mention. It feels conditional because every item in a certain group has the same characteristic.

A temporal relationship is not inherent in a conditional statement, and by this I mean that without any outside information, the sufficient can happen before the necessary, at the same time as the necessary, or after the necessary. All the conditional relationship indicates is that when the sufficient happens, the necessary must happen at some point. Of course, there are certain situations where from commonsense or other information we can determine that one of the conditions happens first; that's not an issue, but that's a result of this other info, not of the conditional relationship itself (Example: "To get to Dublin, you must take a plane." Here, the necessary condition of taking a plane would have to occur prior to you arriving in Dublin ).

That's a start, so please let me know if that helps. Thanks!

[Dave Killoran]

Finally, let's go back to this part of your question:

For example in page 407, choice B, I'm not sure how to apply and identify the components in the statement "Jenny will have lots of balloons at her birthday party."

The first thing I'd say is that I wouldn't diagram this physically during the test (meaning I wouldn't write it out; I'd see the conditional idea because the stimulus used conditionality, but you'd want to be able to recognize the contrapositive as it occurred without spending time actually diagramming).

Ok, all that aside, how would we diagram it if we wanted to?

First, the "group" in question here is really just an event involving one person, Jenny. What do we know about Jenny's birthday, meaning, what always occurs? In this instance, that she will have lots of balloons at her birthday party. Thus, we get this diagram:

Jenny's birthday lots of balloons

But, the next premise states that there are no balloons:

lots of balloons

Thus, the author concludes via a contrapositive that it is not Jenny's birthday, or:

Jenny's birthday

There's some looseness here ("yet"), but more or less they are using a contrapositive structure to make this argument, and either way, that is demonstrably different from the structure of the argument in the stimulus.

In summary, the key to this one is seeing that absolute element ("will") and then understanding what follows from that. However, note that when viewed from this angle, you will see conditionality everywhere! That's why I made my initial comment about diagramming only when you think it will help, and not diagramming every conditional statement (which would drive you crazy and be incredibly time-consuming and counterproductive).

Let me know if that helps. Thanks!

[ericjmyuan]

Hello David,

Thank you so much on your reply and your explanation on sufficient and necessary condition. Just a review, for the Jenny's birthday conditional, since "Jenny's birthday is an entity, henceforth it is a sufficient condition.

When you mentioned that the sufficient condition applies to an entire group or an entity, how does it work with, say, two actions within the conditional statements. For your example, "To get to Dublin, you must take a plane," based on the indicator word, I understand that "must take a plane" is a necessary condition, and "To get to Dublin" is a sufficient condition. But from that example, I couldn't be sure to say that "take a plane" is necessary an entity or a group.

Another example would be from page 466 of the book, question number 2.

I understand that "Good students" is an entity, and therefore a sufficient condition, but what I can't wrap my head around is the fact that in page 467,

LM DP

I would have not been able to deduce such conditionality, I would have just say that:

GS LM

GS DP

So how would you explain the relationship between LM and DP?

[Dave Killoran]

Hi Eric,

Thanks for the reply. In conditionality, it doesn't have to be an entity or group, it can be an action or idea too. The reason I referenced entities and groups in my discussion was because your original question discussed errors of division (which are errors involving part/all of groups). So, my commentary was framed against that background. As you note in a sentence like the Dublin one, taking the plane isn't really a traditional "group" but more an action.

As for page 467, in light of my explanation here, does that relationship now make a bit more sense? The key to deriving LM DP is the language (and not the groups or actions): the second sentence uses "requires," which indicates necessity, and thus DP becomes the necessary. The sufficient is then "this," which refers to the LM idea from the first sentence.

Think of the necessary condition as something that always must occur, and think of the sufficient thing that, when it occurs, tells you something else has occurred.

Please let me know if that helps. Thanks!

[ericjmyuan]

Hello David,

Thank you so much for your discussion on conditionality, so in sum, when I encounter a statement without indicator words, I could do either steps:

1) Look for an entity/group in the phrase and that usually should be Sufficient Condition.

2) Should there be no clear entity or groupings, I would then look at the wordings around the two elements in a statement, and by seeing the wording modifying the two elements (ie. "must," necessary," "will," and other words that indicates the necessity of one element), determine which one is the Necessary Condition, and thereby through deduction, the other element would be Sufficient Condition.

And for the most part, this sort of thinking should be rigorous enough should I encounter counditional statements in general? If it does, it also makes the indicator words provided in your book a lot more understandable as to why they are used as such.

[Dave Killoran]

Hey Eric,

Ok, we're off track with point 1), so let's look at this again. First, I don't really try to think of it in terms of entities or groups being a certain condition. What dictates conditions to me is what I said in my last post:

Think of the necessary condition as something that always must occur, and think of the sufficient thing that, when it occurs, tells you something else has occurred.

For example, here's a counterexample to the principle you propose in point #1:

If you can count to balance on one leg, then you must be a gymnast.

Both conditions technically contain groups (people who can balance on one leg, and gymnasts) so neither helps determine which is sufficient and which is necessary. Instead, it is the "if...then" structure that does all the work. Go back into the Conditional Reasoning chapter and really work on knowing those indicators. Those, and the points I made earlier in this post, determine what is sufficient or necessary, not membership in a group (again, I framed the discussion in those terms because your original question dealt with errors involving groups, and I wanted to highlight how it was actually working).

So, in short, discard your point 1), and use your point 2)

And, regarding indicator words: they are an easy tool to get good at conditionality fast. But no list can ever contain every indicator word, so after that, you have to rely on truly understanding how each condition operates.

Please let me know if that helps. Thanks!