Conditional & Causal Reasoning

[alta]

Hi PowerScore,
I am having some difficulty with Causal & Conditional issues and I would appreciate your help.
Thank you for your help.

1. How does “Contribute to” function as a Causal Indicator? Partial Cause

How does “Contributes to” function as a Conditional Indicator? Necessary Indicator



2. If the Premise is [SD does not cause P in People who do not have X: [SD -> P], and the Conclusion is [SD could not lead to P in People who have X] (SD=Spinal Deformations, P=Pain), then:

2A. Can the Conclusion be represented in the following way: NOT [SD -> P][/
1) Would the Conclusion be inconsistent with the statement that [SD -> P] ?
2) Would it be consistent with the statement that P can occur with or without SD?
3) Would it be correct to say this does not disprove the Causal Relationship [SD -> P]?
4) How can this Causal Relationship Disprove the Conclusion?
5) How can this Causal Relationship Prove the Conclusion?


2B. How would you represent this relationship Conditionally?
1) [ SD is not necessary for P = IF you have P, you may or may not have SD.


1. Is this representation correct? [P ->SD and P-> SD] OR [not (P->SD]
2) How can this Conditional Relationship Disprove the Conclusion?

3) How can this Conditional Relationship Prove the Conclusion?


2C. When it is said that the Necessary Condition can occur without the Sufficient Condition, does it mean:
  A-> B, then [A->B][/

[Jeremy Press]

Hi Alta,

It would help me out a little if you could shed some light on where you got the language for your example in your question 2, as I don't find it in any disclosed LSAT questions or our Logical Reasoning bible. Without additional context, I may not be able to effectively address some of those questions.

Regarding your question number (1), you're correct that the phrase "contributes to" is an indicator that something is a partial cause. That's because the phrase has as one of its common meanings "to play a significant part in bringing about an end or result." Since we only know from that phrase that the thing plays a significant part, there might be other things that also play a part in bringing about the result (hence the accuracy of the "partial cause" label). However, you should not interpret "contributes to" as a necessary condition indicator. The phrase "contributes to" by itself does not imply there is any conditional relationship between two things.

Regarding question 2, it's hard for me to know what X is, so that makes it a little rougher to interpret some of your questions. I'm also having a little trouble seeing the premise-conclusion relationship as you've laid it out. It would be helpful to have the argument laid out fully without abbreviations.

The conclusion in that argument seems to be a conditional statement with a causal necessary condition. It should be diagrammed: X SD could not lead to P (meaning, if someone has X, then spinal deformation could not lead to pain). I'm not sure whether you intend the diagram in 2A1 to represent a conditional or causal relationship, and that matters for how someone would answer your question. If you mean it as a pure conditional (if you have a spinal deformation, then you do not experience pain), then it's consistent with the conclusion.

I need to know what "it" is in questions 2A2 and 2A3 before I can answer them. Is "it" the Conclusion of your stated argument, or the conditional relationship in 2A1?

I also need to know what the "causal relationship" is that you're talking about in questions 2A4 and 2A5 before I can answer those questions.

Regarding question 2B, we generally do not represent statements that something is not necessary as conditional statements. A conditional relationship only exists where one thing actually IS necessary for another thing. So there's no need to diagram such a statement. If spinal deformation is not necessary for pain to occur, this means pain could occur with or without a spinal deformation. Such a relationship is helpful for (but doesn't prove) the conclusion you've stated, because it means it would be possible for a spinal deformation to exist without pain (consistent with the statement that a spinal deformation might not lead to pain).

Regarding question 2C, when we say a necessary condition can occur without its sufficient condition, that means there is some possible circumstance where that necessary condition happens without the sufficient condition. We do not diagram that relationship as A B, because we don't know that it's always true that when A doesn't occur, B occurs. We merely know there are some possible situations where A doesn't occur and B still occurs.

I hope this helps!

Jeremy

[alta]

Hi Jeremy,
Thank you for the prompt response!

I was referencing LR62B, Q19.
SD=bulging/slipped discs
P=Pain
X= People experiencing Pain

2A Questions were Causal

2B Questions were Conditional

The "it" referred to in 2A refers to the Conclusion.

I hope this will help clarify my questions.

Thank You.

[alta]

Hi Jeremy,

Can you give me some examples where the necessary condition can occur without its sufficient condition and in what context/Q-type it usually appears?

What are some examples of when a sufficient occurs without a necessary condition and in what situations/Q-type?

Thanks.

[cmorris32]

Hi Alta! I figured I could give an example from my notes of the things you asked for.

Necessary conditions can occur without the sufficient condition because the necessary condition is what is REQUIRED for the sufficient condition to occur.
EXAMPLE: If you are a dog, then you love cookies.
dog love cookies
This means that EVERY SINGLE dog loves cookies, because in order to be a dog, it is required that you love cookies. However, I also love cookies, and I am a human, not a dog. Maybe horses love cookies, maybe cats love cookies.

I've seen this relationship/rule tested in a variety of question types, including Must Be True, Parallel Reasoning, etc. Its important to know for any question that involves conditional reasoning, which can show up in basically any type of Logical Reasoning question! Maybe take a look at LR question from December 2006 Section 3 #20.

Also this idea is EXTREMELY EXTREMELY important for logic games
EXAMPLE: If A is in spot one, B is in spot two.
A in spot 1 B in spot 2
This means that in order for A to be in spot one, it is required that B is in spot two. However, B can be in spot 2 without A being in spot one. B could be in spot 2 and A could be in spot 3.
Maybe a good game to look at for some basic practice with this would be the December 2008 Parks & Trees Game. Then maybe for more advanced practice look at the 10 CDs game from the June 2000 test.

Sufficient conditions CANNOT occur without the necessary condition.
Example (classic PowerScore example): In order to get an A+ on the test, you must study.
A+ study
This means that if someone gets an A+ on the test, we know that they definitely studied. You cannot get an A+ without studying.
This is an important idea for Cannot Be True questions, which are a small question type on the LSAT. A good/correct answer for a Cannot Be True question with this example would be "She got an A+ but did not study." According to the relationship above, that CANNOT BE TRUE, because we know that getting an A+ REQUIRES studying.

All these notes came from my notebook, which combined notes from a bunch of different PowerScore resources! I hope this helps

[Jeremy Press]

Hi alta,

Cmorris's post does a nice job of identifying examples of a necessary condition occurring without a sufficient condition. Literally any conditional relationship allows for this.

A couple more examples: "If you go to law school, then you must have a college degree." The necessary condition here is having a college degree. One can have a college degree without going to law school. That's a real world example so it probably makes a lot of sense to you. But we don't just have to think real world examples for these. Take an interesting example from the December 2007 test (LR1, question 21): "The trees always blossom in May if April rainfall exceeds 5 centimeters." Here, the necessary condition is "trees blossom in May." It could occur whether or not April rainfall exceeded 5 centimeters. There's a mistake in reasoning in that stimulus in which the author assumes that the failure of April rainfall to exceed 5 centimeters must automatically mean the trees did not blossom in May. Not so (because the necessary can happen without the sufficient)!

A sufficient condition can never occur without its necessary condition (that's what it means to be a sufficient condition). The occurrence of a sufficient condition is dependent on its necessary condition. If you can show that a sufficient condition occurs without an alleged necessary condition, then you've disproved the conditional relationship. Take this example: "If you go to law school, then you must have taken the LSAT." If you show me an instance of a person going to law school without taking the LSAT (say, your friend is in law school, and they took the GRE but not the LSAT), you've disproved the conditional relationship. You've shown that the condition of going to law school is not sufficient to determine that someone has definitely taken the LSAT.

I hope this helps!

[alta]

Thank you cmorris for your thorough and well thought-out response. I very much appreciate your having taken the time to clear up these very critical and fundamental issues!

[alta]

Thank you Jeremy for suggesting these example Questions. I just finished going through them and they proved most helpful for solidifying these concepts.

[ajsadeghi]

Hello Powerscore and everyone!

This is a question of concept I have been struggling with for some time, I apologize if I become repetitive and for this long explanation. I understand the idea and identification of conditional reasoning as well as the clear cases in which "if" modifies the sufficient and "then" modifies the necessary, but a problem I have had is when it comes to the tense or chronological order of some sentences. What I mean is, in the example used above: "The trees always blossom in May if April rainfall exceeds 5 centimeters." You say that the Necessary condition is "trees blossom in May" and the Sufficient is "In April rainfall exceeds 5 cm". I can initially see that because of where "if" is. But when I read it closer I do not understand how logically it makes sense for the necessary condition to be the occurrence that occurs AFTER the sufficient. In the popular examples, "if you get an A+, then you must have studied" and "if you have a driver's license, then you know you are 16+". But in each of those the necessary condition is always met before the sufficient occurs, "If x happens, then you know the condition of y must have been satisfied before". I understand that well. Yet in this case and in this sentence, we are saying the necessary condition of "trees blossoming in May" must be fulfilled for us to know that it rained over 5cm in the previous month April? It is not the order presented (i.e. the sufficient condition/"if" coming after the necessary condition) to me that confuses me, it is the fact that a later occurrence in May is necessary for there to have been over 5 cm of rainfall in April. When I initially read that sentence it clearly sounds like "for the trees to blossom in May, rainfall in April must exceed 5 cm/ the occurrence in May will happen, on the required condition that it rained over 5 cm in the previous month" where the necessary condition is the rainfall in April. Even if you phrase it in the style of assuming the rainfall is sufficient as you did (Sufficient-->Necessary): "If the rainfall in April exceeds 5cm, then we know the trees will always blossom in May" I do not understand how we can then call the blossoming in May a Necessary condition for the rainfall in April to occur, it sounds more like a guaranteed prediction based on what already occurred (the rainfall) or similarly that the exceeding rainfall sounds like what is necessary to occur for the trees to blossom in May. If it was a Necessary condition that means it can happen with or without the rainfall and I understand how it could, but the sufficient (the rainfall in April) can only happen if the trees blossom a month later in May? That does not make logical sense to me. The sentence makes it seem like the rainfall is what must happen to cause/causes the blossoming. Is it not saying if it rains this much, with that necessary occurrence we can then guarantee that the future blossoming occurrence in May will occur which could not happen without the exceeding rainfall?

Another similar confusing example is in the On Demand coursebook Lesson 2 pg 9, the first example says "If it rains on Tuesday, then we will go see a movie". I get that because of the "if" and "then" placements, movie is the necessary condition. But I do not understand how logically for it to rain, it is necessary for us to go see a movie i.e. us going to a movie MUST occur for it to rain. Does us watching a movie allow for the rain to occur and that it cannot rain on Tuesday without us satisfying the condition of going to see a movie? It sounds as if the rain happens first, and then the movie because of the tense of "then we will go", if this happens, then (indicating the next event follows) we will go to see a movie. I would understand if like the studying example it said "If it rains on Tuesday, then we WOULD HAVE/WENT to see a movie, indicating the necessary already occurred and was satisfied. But that is not how the sentence is worded.

What I generally mean is sometimes the use of "if" and/or the chronological tense of the events, sounds like the sentence modified by "if" is the necessary i.e. "x will happen if y happens" is the same as "x will happen on the condition that y happens" where y sounds like the necessary condition that must occur for x to occur even though it is modified by "if".

I apologize if what I said was confusing and too long, I would be happy to clarify it in any way. Any help with this would be greatly appreciated! Thank you!

[Paul Marsh]

Hey ajsadeghi - no worries on the long writeup! It seems like you are doing a job of identifying the sufficient and necessary conditions, but are confused about what it means the sufficient condition occurs chronologically prior to the necessary condition.

I think maybe some of the confusion is the way you're thinking about necessary conditions. You seem to be thinking about a necessary condition as though it's saying something like, "In order for A to occur, it's necessary for B to occur first". I think this is potentially misleading. It would be more helpful to think about a necessary condition as saying, "it necessarily follows that...". As in the example you gave, "If A+, then you must have studied example", we can restate that to say, "If you get an A+, it necessarily follows that you must have studied".

For example, let's say I have the following conditional, "Every time I have 6 beers, I sleep through my alarm the following morning". Having 6 beers is the sufficient condition, and sleeping through my alarm is the necessary condition. I could re-state that to say, "If I have 6 beers, it necessarily follows that I will sleep through my alarm the following morning". Sleeping in will necessarily result (It's just science!). Every time my sufficient condition occurs, my necessary condition will always follow.

Here's another one: "Every time I drop an egg off my roof, it breaks". Dropping an egg off my roof is ALWAYS sufficient to say that breaking of the egg will necessary follow.

Practice some conditionals, framing the necessary condition with the language "it necessarily follows that...". See if that helps!