Relative Statements

CREATION
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Relative Statements

Postby CREATION » Mon Apr 16, 2012 11:23 pm

If I say that as A increases, B increases.

And I know that B has increased and A exists.

I cannot infer that A has increased, correct?

I believe I can infer that A decreasing will lead to B decreasing. But then again, why couldn't A decrease while B still increases?

Does anyone have a grasp on these relative statements?
Last edited by CREATION on Mon Apr 16, 2012 11:48 pm, edited 1 time in total.

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Clearly
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Re: Issue of Relative Statements

Postby Clearly » Mon Apr 16, 2012 11:29 pm

CREATION wrote:If I say that as A increases, B increases.

And I know that B has increased and A exists.

I cannot infer that A has increased, correct?

I believe I can infer that A decreasing will lead to B decreasing. But then again, why couldn't A decrease while B still increases?

Does anyone have a grasp on these relative statements?


I don't believe your inference that a decreasing will lead to b decreasing to be valid

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LSAT Blog
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Re: Issue of Relative Statements

Postby LSAT Blog » Mon Apr 16, 2012 11:33 pm

Clearlynotstefan wrote:
CREATION wrote:If I say that as A increases, B increases.

And I know that B has increased and A exists.

I cannot infer that A has increased, correct?

I believe I can infer that A decreasing will lead to B decreasing. But then again, why couldn't A decrease while B still increases?

Does anyone have a grasp on these relative statements?


I don't believe your inference that a decreasing will lead to b decreasing to be valid


(I'm going to use "up" and "not up" to make things even simpler than "increase" and "decrease.")

A up -> B up

Therefore, "B not up, A not up"

That's all you can infer.

You cannot infer "B up -> A up"

Nor can you infer "A not up -> B not up"

"A not up" doesn't tell you anything about what B's doing.

"A up" is the only info that tells you what B's doing.

CREATION
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Re: Issue of Relative Statements

Postby CREATION » Mon Apr 16, 2012 11:41 pm

What about:

The lower my blood pressure, the lower my risk of a heart attack.

It would seem that the higher my blood pressure, the higher my risk of heart attack. That seems to be valid? Why isnt my first example

dkb17xzx
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Re: Relative Statements

Postby dkb17xzx » Mon Apr 16, 2012 11:56 pm

I think you are confusing correlations and conditional statements.

CREATION
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Re: Relative Statements

Postby CREATION » Tue Apr 17, 2012 12:11 am

So do you or do you not agree with the idea that the prior post of blood pressure is valid

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Clearly
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Re: Relative Statements

Postby Clearly » Tue Apr 17, 2012 12:25 am

CREATION wrote:So do you or do you not agree with the idea that the prior post of blood pressure is valid


Logically, it's invalid as far as the LSAT goes. Correlation is one thing, a valid principle. But conditional logic (lsat wise) doesn't account for this. For example, write a paradox question with that same stimulus.

Blood pressure goes up then heart attack goes up, but blood pressure going low, doesn't reduce the chance of heart attack
Which of the following resolves the apparent paradox:

As blood pressure falls too low, the heart works harder to move blood, and initiates a heart attack
As blood pressure falls, veins constrict causing heart attack
etc.

If you could see this principle in this form, you might see what I'm saying.


As far as conditional logic goes, you can't chart anything but the contrapositive of one rule. If the rule or a contrapositive of a rule should tie in with another rule, then you might be able to expand on the concept...but with what you gave, the only thing to be said is

A up -> B up
~B up -> ~A up

CREATION
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Re: Relative Statements

Postby CREATION » Tue Apr 17, 2012 12:31 am

Are you really saying that:

The lower my blood pressure, the lower my risk of a heart attack.

...Would not allow us to infer that the higher my blood pressure, the higher my risk?

That just seems to be a valid inference.

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shifty_eyed
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Re: Relative Statements

Postby shifty_eyed » Tue Apr 17, 2012 11:06 am

CREATION wrote:Are you really saying that:

The lower my blood pressure, the lower my risk of a heart attack.

...Would not allow us to infer that the higher my blood pressure, the higher my risk?

That just seems to be a valid inference.


No. It may seem like a common sense fact, but it doesn't logically follow simply from that statement alone.

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ben4847
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Re: Relative Statements

Postby ben4847 » Tue Apr 17, 2012 11:13 am

As this thread gets longer with incorrect responses, I find it more amusing.

This does not mean that if I found it more amusing, it would be longer.

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flem
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Re: Relative Statements

Postby flem » Tue Apr 17, 2012 2:08 pm

shifty_eyed wrote:
CREATION wrote:Are you really saying that:

The lower my blood pressure, the lower my risk of a heart attack.

...Would not allow us to infer that the higher my blood pressure, the higher my risk?

That just seems to be a valid inference.


No. It may seem like a common sense fact, but it doesn't logically follow simply from that statement alone.


Yup

Correct

One thing could happen without the other. Couldn't you have a heart attack without having low blood pressure?

If your blood pressure is low, your risk of high attack is low.

BP ----> LR

The correct contrapositive would be:

~LR ---> ~BP

If your risk of heart attack is not low, your blood pressure is not low.

Incorrect

To assume what you're saying would be:

~BP ---> ~LR

Which, in LSAT terms, is a mistaken negation. You're forgetting to flip the necessary and sufficient conditions.

I realize this makes no sense from a common sense standpoint, but it's purely logic.

CREATION
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Re: Relative Statements

Postby CREATION » Tue Apr 17, 2012 2:12 pm

You guys are so caught up on contrapositives when it is not at issue here. It seems to be a math thing.


But the example of the lower the BP, the lower the risk of heart attack.....

Can't I say that the higher the BP, the higher the risk of heart attack?


I mean if I had:

X3 Y3

X2 Y2

X1 Y1


It seems that the BP going down the X column would also show that from where it came from (higher) implies a higher Y point.

Example: If X3 goes down to X1, we know that Y goes from Y3 to Y1, yet I can see that from where I came from (X3) that this is a higher point of blood pressure, and its risk of heart attack is higher at Y3.

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flem
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Re: Relative Statements

Postby flem » Tue Apr 17, 2012 2:14 pm

CREATION wrote:You guys are so caught up on contrapositives when it is not at issue here. It seems to be a math thing.


But the example of the lower the BP, the lower the risk of heart attack.....

Can't I say that the higher the BP, the higher the risk of heart attack?


I mean if I had:

X3 Y3

X2 Y2

X1 Y1


It seems that the BP going down the X column would also show that from where it came from (higher) implies a higher Y point.

Example: If X3 goes down to X1, we know that Y goes from Y3 to Y1, yet I can see that from where I came from (X3) that this is a higher point of blood pressure, and its risk of heart attack is higher at Y3.


In the LSAT realm, ignore all common sense and outside knowledge. In this scenario, you simply don't know enough info to make that inference.

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suspicious android
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Re: Relative Statements

Postby suspicious android » Tue Apr 17, 2012 4:14 pm

In your original example, the language was not enough to show a correlation between A and B, so it was possible, as LSAT blog noted, that A and B move independently.

In your second example, if you really know that lower blood pressure means lower risk of heart attack, then that is enough to establish a correlation. As such, higher blood pressure would mean higher risk of heart attack.

It comes down to the language used to connect the two ideas. "If low A, then low B" doesn't guarantee a correlation, because it only provides half of the needed relationship. "LowER A then lowER B" tells us that for any particular value of A, there is a corresponding B value that could be at least partially determined by finding A. So if the correlation were perfect, knowing Bs value would give you As value.

CREATION
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Re: Relative Statements

Postby CREATION » Wed Apr 18, 2012 2:10 pm

The lower bp is, the lower the risk of HA

Is that a perfect correlation?

I thought my first example is the same idea as the one above.

As bp goes down, risk of HA goes down.

Is that not the same thing?

I see that you are saying lowER and lowER give us justification for inferring higher and higher but why not more and more.....less and less.

Both of these examples are correlations and I'm not sure what a perfect correlation is.




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