"The greater the X, the more the Y"

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WaltGrace83
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"The greater the X, the more the Y"

Postby WaltGrace83 » Sat Jan 17, 2015 2:02 pm

Whenever we get something like this in a question: "The greater the X, the more the Y," is it okay to assume that "The LESS the X, the LESS the Y?" My gut tells me yes but this is a pretty weird logical construction so I just wanted to make sure.

For example, 23.3.10 (the "walk rather than drive" question) has the following phrase: "the greater the congestion is, the more nonmoving running vehicles there are." This would probably also mean, "the less the congestion is, the less nonmoving running vehicles there are," right?

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Dr. Nefario
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Re: "The greater the X, the more the Y"

Postby Dr. Nefario » Sat Jan 17, 2015 2:12 pm

X
Last edited by Dr. Nefario on Sat Jan 17, 2015 3:35 pm, edited 2 times in total.

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Clearly
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Re: "The greater the X, the more the Y"

Postby Clearly » Sat Jan 17, 2015 2:16 pm

Not necessarily. I'm not looking at this particular question, and it sounds like a reasonable inference in this case, but not strictly because of that phrasing. I'd view the phrase itself as a conditional to be safe.

The greater ones cholesterol, the greater ones risk of heart attack.
If more cholesterol -> more heart attack
Less or equal chance of heart attack-> ~ more cholesterol

But you couldn't infer that less cholesterol means less heart attack, because their risk of heart attack could be higher for other reasons, or perhaps in place of cholesterol, they consume something that causes even higher risk of heart attack etc.

kcdc1
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Re: "The greater the X, the more the Y"

Postby kcdc1 » Sat Jan 17, 2015 2:17 pm

In most cases, yes. Depends on how literally they mean "as X goes up, Y goes up." For your traffic example, there could be a lower bound where the relationship falls apart. Maybe if the road isn't too crowded, there are no stopped cars. But past a certain point, the more congestion you add, the more cars are stopped. So the y=f(x) relation holds at the top end, but not at the bottom. But unless context suggests otherwise, you should interpret premises given by the LSAT as strictly true.

In response to the above comment, this is not a contrapositive situation. It's not an if-then statement; it's a statement that informs you about a correlation between two quantities.

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Dr. Nefario
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Re: "The greater the X, the more the Y"

Postby Dr. Nefario » Sat Jan 17, 2015 2:39 pm

X
Last edited by Dr. Nefario on Sat Jan 17, 2015 3:34 pm, edited 1 time in total.

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Clearly
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Re: "The greater the X, the more the Y"

Postby Clearly » Sat Jan 17, 2015 2:51 pm

kcdc1 wrote:In most cases, yes. Depends on how literally they mean "as X goes up, Y goes up." For your traffic example, there could be a lower bound where the relationship falls apart. Maybe if the road isn't too crowded, there are no stopped cars. But past a certain point, the more congestion you add, the more cars are stopped. So the y=f(x) relation holds at the top end, but not at the bottom. But unless context suggests otherwise, you should interpret premises given by the LSAT as strictly true.

In response to the above comment, this is not a contrapositive situation. It's not an if-then statement; it's a statement that informs you about a correlation between two quantities.


You can choose to interpret it however you'd like, but it is certainly appropriate to translate this phrase into formal logic. Look at my analogous example, are you implying that less cholesterol guarantees a lower risk of heart attack?

I don't understand why you would want to take a statement and process it into anything that's not guaranteed to be true. Perhaps treating it as a correlation makes sense intuitively, but in your own explanation you had to qualify it as "in most cases" and with "perhaps at a lower bounds it falls apart". If you treat it conditionally, you leave behind everything that doesn't have to follow logically, and figure out all of the things that absolutely have to be true based on what you know.

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WaltGrace83
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Re: "The greater the X, the more the Y"

Postby WaltGrace83 » Sat Jan 17, 2015 3:04 pm

In the question I mention, it seems like you HAVE TO take this logical leap that less X = less Y. Otherwise, the correct answer wouldn't make sense. That is why I am asking.

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Clearly
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Re: "The greater the X, the more the Y"

Postby Clearly » Sat Jan 17, 2015 3:08 pm

WaltGrace83 wrote:In the question I mention, it seems like you HAVE TO take this logical leap that less X = less Y. Otherwise, the correct answer wouldn't make sense. That is why I am asking.


Like I said, I'm not looking at the question, and it's prob a safe jump to make in this question, not because of the wording of the phrase, but rather because it's a common sense inference about the nature of traffic. There are other questions that hinge on this language exclusively, and that inference doesn't always follow from it.

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PeanutsNJam
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Re: "The greater the X, the more the Y"

Postby PeanutsNJam » Sun Jan 18, 2015 1:33 am

Clearly wrote:
WaltGrace83 wrote:In the question I mention, it seems like you HAVE TO take this logical leap that less X = less Y. Otherwise, the correct answer wouldn't make sense. That is why I am asking.


Like I said, I'm not looking at the question, and it's prob a safe jump to make in this question, not because of the wording of the phrase, but rather because it's a common sense inference about the nature of traffic. There are other questions that hinge on this language exclusively, and that inference doesn't always follow from it.


This. On the LSAT, you're allowed to make super-obvious-common-sense assumptions. Assuming that less congestions = less stopped cars is one of these assumptions. Clearly is on point, but here's another example.

What if I said:

"The more books I read, the smarter I am"?

That doesn't mean if I read less books than I otherwise would, or if I didn't read books at all, I'd be dumber. Maybe I'm learning a language instead. Or practicing some other skill.

You can translate it into formal logic:

If I read books -> I get smarter

You can't say that if I'm not reading books, I get dumber.

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Jeffort
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Re: "The greater the X, the more the Y"

Postby Jeffort » Sun Jan 18, 2015 11:29 pm

The 'greater congestion, the more non-moving vehicles' part of the CR is an example of a semi-rare type of statement on the LSAT in that it's a correlation, a conditional relationship and a causal premise all in one short phrase due to the full context and subject matter of the question!

It being a cause and effect relationship under which we can infer that less of the cause will likely produce less of the effect is, as described above, a warranted/justified assumption/inference that is supported by common sense real world knowledge about the substance/subject matter elements involved in the stated relationship. Recognizing the causality is critical in order to fully understand/recognize how/why the CR does logically strengthen this argument via the valid inference that less congestion is likely to cause there to be fewer non-moving vehicles on the road.

Clearly's analysis is on point regarding viewing that language structure (regardless of the subject matter) as a conditional statement, but you can and should also view it as a correlation in this question since it is one. Viewing it as a correlation is helpful to arrive at the common sense warranted assumption/inference that more congestion CAUSES more non-moving cars since a true cause and effect relationship cannot exist between elements that don't correlate with each other.

Once we have a known/established cause and effect relationship, it's logical to infer that less of (when it's a sliding scale causal relationship like this one) or absence of the cause is likely to result in less or none of the effect and vice versa with (more) cause ---> (more) effect.

This is partly why a common type of CR logically works for strengthen Qs with a causal argument/conclusion when it gives an example of no-cause-no-effect, since that's just a negative correlation between the elements. When you have a positive correlation between two elements (typically presented as a premise in the argument), it shows that there MIGHT be cause and effect but it isn't sufficient to guarantee it. By adding in an additional negative correlation between the elements (a no-cause-no-effect answer choice), it increases the probability that there is indeed a cause and effect relationship between the elements rather than the correlation more likely being due to coincidence or a third factor that caused the two things that correlate (showing they're likely both effects of a third thing that is the cause for the correlation), hence why no-cause-no-effect negative correlation answer choices are correct and do logically strengthen (make the conclusion more LIKELY to be true) a causal argument/conclusion.

That wouldn't be valid logic with a conditional relationship that doesn't also entail a cause and effect relationship between the elements where the cause is the sufficient condition of the conditional relationship and the effect is the necessary condition since that would simply be a mistaken/incorrect/invalid negation/flawed logical use of a non-causal conditional statement/relationship

Although conditional logic and cause and effect logic work differently in several ways and conditional statements do not necessarily involve causation/cause and effect, there is some overlap between the two areas of logic such as being able to validly treat a true cause and effect relationship also as a conditional relationship with the cause being the sufficient condition and the effect the necessary condition. This question is a great example of a situation where correlation, cause and effect and conditional logic are all involved/overlap and where identifying and viewing it from both conditional and correlation/causation perspectives can be helpful for understanding and solving the question correctly with valid logical reasons.

Hopefully this helps rather than makes things more confusing! I went deep in this post for you WaltGrace since you're now at the point in prep where you're reviewing and making sure you understand the underlying logic and things involved in high difficulty level logically complex/tricky questions. Please ask for clarification or any further questions if this is confusing or if you want to continue discussion of this higher level more complex type of stuff that the test writers like to use to construct some high level difficulty questions.




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