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Need expert help :( (I am a bit confused)

by voodoo_child » Thu Jul 07, 2011 3:50 am
For the link

Cause => Effect ("=>" means *causes * OR Conditional link); It is a known fact that an assumption could be :

a) Effect =/> Cause ("=/>" means *doesnt cause*)
b) ~Cause => ~Effect (i.e. when there is no cause, effect doesnt happen)

However, if we take contrapositive of a) we get, ~Cause =/> ~Effect which is opposite to b). can you please let me know what I am doing wrong ?

Thanks
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by Ashley@VeritasPrep » Thu Jul 07, 2011 5:37 am
voodoo_child wrote:For the link

Cause => Effect ("=>" means *causes * OR Conditional link); It is a known fact that an assumption could be :

a) Effect =/> Cause ("=/>" means *doesnt cause*)
b) ~Cause => ~Effect (i.e. when there is no cause, effect doesnt happen)

However, if we take contrapositive of a) we get, ~Cause =/> ~Effect which is opposite to b). can you please let me know what I am doing wrong ?

Thanks
(I'm not 100% sure I'm understanding your question exactly right, so let me know if this doesn't answer it.)

Given the premise A ---> B,

(1) We CANNOT conclude that B ---> A. (Note, the fact that we can't conclude that doesn't allow us to conclude that B -/-> A; we just can't conclude anything about B ---> or -/-> one way or the other.)

(2) We also CANNOT conclude that ~A ---> ~B. (But, as above, we also can't conclude that ~A -/-> ~B; we just can't conclude anything about ~A ---> or -/-> one way or the other.)

(3) We CAN conclude that ~B ---> ~A (the contrapositive of the original statement). This is the only conclusion we can validly draw from the original statement.


Example that illustrates why (3) is valid and (1) and (2) aren't. Let A = "you are my brother" and let B = "I am related to you."

Conditional: A ---> B : If you are my brother, then I am related to you. (We know this is true in real life.)

Converse: B ---> A : If I am related to you, then you are my brother. (We know this is invalid in real life; note, though, that the fact that it's invalid just means it's not *necessarily* true -- I can't, in other words, use the fact that this is invalid to go all the way to saying it's always false and that if I am related to you, then you are NOT my brother. I just can't draw any conclusions one way or the other about whether or not you're my brother just based on the fact that I'm related to you. This is a careful distinction that needs to be made: to say the converse (B ---> A) is invalid is to say that in fact, "B does not imply A" -- it isn't to say "B implies ~A.")

Inverse: ~A ---> ~B : If you're not my brother, then I am not related to you. (Also clearly invalid in real life -- I might very well be related to you even if you're not my brother; again, though, that the fact that it's invalid just means it's not *necessarily* true -- I can't, in other words, use the fact that this is invalid to go all the way to saying it's always false and that if you're not my brother, then I AM related to you. I just can't draw any conclusions one way or the other about whether or not I'm related to you based solely on the fact that you're not my brother. Again, careful to ditinguish -- it's the "implies" that's being negated: to say the inverse (~A ---> ~B) is invalid is to say that in fact, "~A does not imply ~B" -- it isn't to say "~A implies B.")

Contrapositive: ~B ---> ~A : If I'm not related to you, then you are not my brother. Certainly true/valid.
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by voodoo_child » Thu Jul 07, 2011 8:43 am
Thanks for responding, Ashley. I agree with your post. However, my question is a bit different.

[Let's use the symbol "=/=>" to denote "doesnt cause", and "=>" to denote "causes"]

What I was saying is that if X=> Y

then one of the assumption behind this causality is that Y shouldnt cause X i.e. the effect shouldnt cause "cause" In other words, Y =/=> X....Equation 1

Secondly, another assumption that can be made is that when there is no cause (~X) then effect shouldnt happen (~Y). In other words, ~X => ~Y. ....Equation 2



Now, if we take contrapositive of Equation 1, CONTRAPOSITIVE (Y =/=> X ), we get ~X =/=> ~Y which is completely different from Equation 2 (i.e. ~X => ~Y) ....

Both the equations are assumptions. While one says ~X doesnt cause ~Y, the other one says ~X causes ~Y. I am lost :(
I know that I am being mistaken somewhere. Not sure where.

Can you please help me?

Thanks
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by Ian Stewart » Thu Jul 07, 2011 11:00 am
A few things here:

I don't recommend learning formal logic for the GMAT. It is not explicitly tested, and it can lead to a lot of confusions. Some of the ideas we express in words, like 'smoking causes cancer', need to be rephrased more precisely if you want to express them in formal logic. When we say 'smoking causes cancer', we mean that probabilistically, not deterministically. If you just take the contrapositive, 'not having cancer means you do not (or did not) smoke', you can see that it is not logically correct;

In any case, the second assumption you've identified, that "when there is no cause (~X) then effect shouldnt happen (~Y)", is *not* an assumption at all. If you are assuming this to be true, then you're assuming the *converse* of your argument to be true, and you can never deduce something from its converse. It's much easier to see this using a concrete example. If I say "If I go swimming, I'll get wet", I'm certainly *not* assuming there are no other ways to get wet. It might rain, for example. That is, if I take away the cause, I can still have the effect. To give a mathematical example, it's true that "if x is prime, then x is positive". When you say that, you aren't making an assumption that "if x is not prime, x is not positive"; that's clearly absurd.

So, with your reasoning above, what you've demonstrated is that an argument is not equivalent to its converse; you can't just take "A--->B" and reverse it to get "B--->A". The flaw is in your second assumption.
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by voodoo_child » Thu Jul 07, 2011 11:22 am
Thanks for your inputs, Ian. However, the assumption that I have quoted in my example is from PowerScore Book. I have borrowed the book from my friend. I have also seen the same statement in LSAT book/powerscore.

I am quoting the exact statement :

Section Strengthen and Assumption - PAge 160 C) - Show that "when cause does not occur, the effect doesnt occur"

Any scenario where the cause does not occur and effect not occur supports the conclusion."

Similar statement also appears on page 187 (Assumption) - Show that when the cause does not occur, the effect doesnt occur."

They have also given an example :


Modern navigation systems, which are found in most of today's commercial aircraft, are made with low-power circuitry, which is more susceptible to interference than the vacuum-tube circuitry found in older planes. During landing, navigation systems receive radio signals from the airport to guide the plane to the runway. Recently, one plane with low-power circuitry veered off course during landing, its dials dimming, when a passenger turned on a laptop computer. Clearly, modern aircraft navigation systems are being put at risk by the electronic devices that passengers carry on board, such as cassette players and laptop computers.

Which one of the following, if true, LEAST strengthens the argument above?
(A) After the laptop computer was turned off, the plane regained course and its navigation instruments and dials returned to normal.
(B) When in use all electronic devices emit electromagnetic radiation, which is known to interfere with circuitry.
(C) No problems with navigational equipment or instrument dials have been reported on flights with no passenger-owned electronic devices on board.
(D) Significant electromagnetic radiation from portable electronic devices can travel up to eight meters, and some passenger seats on modern aircraft are located within four meters of the navigation systems.
(E) Planes were first equipped with low-power circuitry at about the same time portable electronic devices became popular.

The correct answer is E. But I am concerned about A) which clearly states/supports the link

Electronic devices -> Interference with low power circuitry.

A is nothing but ~(Elect. devices) -> ~(Interference with ...)

Any thoughts ? I am not sure where is the disconnect :(
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by Ian Stewart » Thu Jul 07, 2011 11:42 am
I find the discussion you're quoting pretty misleading. Modifying the example you quote above, imagine the following dialogue: "If I turn my cell phone on during a flight, that will cause the plane to crash." "How do you know that?" "Because I kept my cell phone off the entire flight, and we landed safely!" That's obviously a ridiculous argument. That is, if I suggest a certain cause (turning on a cell phone) produces a certain effect (the plane will crash), I'm proving absolutely nothing of relevance if I show that when there is no cause (the phone is off) there is no effect (the plane lands fine).

In the question you quote from the book, the reason A is right is *not* because it shows that when the cause is absent, the effect is absent. It's right because it clearly provides a *link* between the two phenomena. In the argument in the question you quote, there's an assumption that turning on the laptop computer was somehow linked to the dimming of the dials - that it wasn't just pure coincidence. Answer A strengthens the argument by providing further evidence that these two phenomena are linked; if the dials light up the instant the computer is turned off, it seems highly unlikely that the two phenomena are unrelated.
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by voodoo_child » Thu Jul 07, 2011 12:52 pm
Ian and Ashley,

I agree with your explanation. However, I am not sure why the book says the following in the explanation : (I will use C and E to denote Cause and Effect. This way, my text will not be "googleable"

"Answer choice (A) - This answer ch strengthens the argument by showing that when the C is absent, the effect does not occur (Type C - {Type C is nothing but what I wrote in my post}) Once the laptop was turned off, the C disappeared, and as per author's beliefs, the E should disappear as well"

It's so confusing. Can you please tell me whether I am missing anything ? I checked the LSAT version of the book and it says the same thing.

What's your suggestion ? Should I ignore this rule?

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by GMATMadeEasy » Thu Jul 07, 2011 1:53 pm
Source of confusion here is mixing up of conditional statements and cause and effect relationship.

1. For cause and effect relationship, no cause - > no effect holds true.

modern aircraft navigation systems are being put at risk by the electronic devices that passengers carry on board, such as cassette players and laptop computers.

2. If X then Y, if NOT X then NOT Y .. this is incorrect.

If I turn my cell phone on during a flight, that will cause the plane to crash.

Ian's example is an example of conditional statement. Whereas the question you have quoted is an example of cause and effect.

Hope this resolves the paradox :)
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goo

by voodoo_child » Thu Jul 07, 2011 3:39 pm
GMATMadeEasy wrote:Source of confusion here is mixing up of conditional statements and cause and effect relationship.

1. For cause and effect relationship, no cause - > no effect holds true.

modern aircraft navigation systems are being put at risk by the electronic devices that passengers carry on board, such as cassette players and laptop computers.

2. If X then Y, if NOT X then NOT Y .. this is incorrect.

If I turn my cell phone on during a flight, that will cause the plane to crash.

Ian's example is an example of conditional statement. Whereas the question you have quoted is an example of cause and effect.

Hope this resolves the paradox :)
GMATMADEEasy - Please peruse the thread. We are NOT saying that "If X then Y, if NOT X then NOT Y .. this is incorrect." The question is about finding the assumptions. I think Ashley has already clarified this in the beginning.

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by Ian Stewart » Thu Jul 07, 2011 5:16 pm
GMATMadeEasy wrote:Source of confusion here is mixing up of conditional statements and cause and effect relationship.
Cause/Effect statements can be rephrased as conditional statements. When I say that "X (always) causes Y", I'm saying that "if X happens, Y happens", or "if X is true, then Y will be true".

Voodoo, I think part of the issue here is that you need to distinguish between *assumptions*, which are things that need to be true for the argument to be true, and simply those facts which strengthen an argument. If you look back at the laptop computer/airplane question, not one of the answer choices is an assumption in the argument. Each (besides the wrong answer) simply demonstrates that it is more likely that the laptop computer has some effect on the airplane's equipment, or explains how that effect might be produced. That is, many of the answers simply help to establish that the first observation (turn laptop on, the controls get messed up) was not coincidental. In that sense, 'no cause means no effect' can sometimes help to strengthen an argument. But it is not an assumption in the argument.
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by voodoo_child » Thu Jul 07, 2011 6:08 pm
Ian Stewart wrote:
GMATMadeEasy wrote:Source of confusion here is mixing up of conditional statements and cause and effect relationship.
Cause/Effect statements can be rephrased as conditional statements. When I say that "X (always) causes Y", I'm saying that "if X happens, Y happens", or "if X is true, then Y will be true".

Voodoo, I think part of the issue here is that you need to distinguish between *assumptions*, which are things that need to be true for the argument to be true, and simply those facts which strengthen an argument. If you look back at the laptop computer/airplane question, not one of the answer choices is an assumption in the argument. Each (besides the wrong answer) simply demonstrates that it is more likely that the laptop computer has some effect on the airplane's equipment, or explains how that effect might be produced. That is, many of the answers simply help to establish that the first observation (turn laptop on, the controls get messed up) was not coincidental. In that sense, 'no cause means no effect' can sometimes help to strengthen an argument. But it is not an assumption in the argument.
Thanks Ian. I see your point. The example that i borrowed was from Strengthen section in the book. I couldn't find an example for the (Not Cause) => (Not Effect) type of assumption under Assumption section. The book states that "similar to Strengthen question, the author assumes that one of the assumption WILL be (Not Cause) => (Not Effect)"

I believe this statement is not correct in the book...What do you think ?

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by voodoo_child » Thu Jul 07, 2011 6:23 pm
Aah....just thought of this example :


If I drive my car to Holland Tunnel, I reach Manhattan.


Here the assumption is that If I dont drive my car to Holland Tunnel, I wouldnt reach Manhattan. Sounds true to me.

I believe that ~X => ~Y Assumption works here ...any thoughts?
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by Ashley@VeritasPrep » Fri Jul 08, 2011 10:34 am
Ashley@VeritasPrep wrote:
voodoo_child wrote:For the link

Cause => Effect ("=>" means *causes * OR Conditional link); It is a known fact that an assumption could be :

a) Effect =/> Cause ("=/>" means *doesnt cause*)
b) ~Cause => ~Effect (i.e. when there is no cause, effect doesnt happen)

However, if we take contrapositive of a) we get, ~Cause =/> ~Effect which is opposite to b). can you please let me know what I am doing wrong ?

Thanks
Well, one important thing is that there's really no such thing as a contrapositive of a "doesn't cause" statement. The very concept of a contrapositive relies one the GUARANTEE made by a formal if-then statement. The ONLY reason it's valid to go from a statement to its contrapositive is that a true if-then statement says IF X, THEN DEFINITELY Y... and it's only that "definitely" that allows you to say that if Y doesn't manifest itself, x can't possibly have happened. We don't have anything of this sort in a "doesn't cause" statement, since a "doesn't cause" statement isn't guaranteeing anything one way or the other -- neither a definite manifestation of Y NOR a definite absence of Y. So it's not an arena to which contrapositives are applicable in the first place -- just like there would be no meaning to (say) "the contrapositive of Ashley."

Another thing (and this may not be helpful) w.r.t. to the question about planes and electronic devices. Choice (A) strengthens the argument, but just by a step... it certainly doesn't go all the way to proving the argument. IF we indeed noticed that as soon as the guy turned off his laptop, the plane regained his course, we might gain more confidence in our theory that the laptop was responsible for sending the plane off course, EVEN THOUGH we still couldn't know for sure. Take this even further. Say that he then turned his laptop back on, and the plane again lost its course. Then we'd have even further reason to suspect that the laptop was the course of the problem. And if he then turned it back off again and the plane regained its course again, we'd have still further reason to suspect that. From an ABSOLUTELY RIGOROUS logical perspective, we could actually never conclude that the laptop caused the veering off course if all we did was run this experiment ad nauseam... because it could, for instance, be the case that just by coincidence some intermittent power outage kept occurring, only by chance in sync with the laptop, and that the laptop was actually totally innocent. But the more times we observed a perfect correlation between laptop state and on/off-courseness, the more confidence we could gain.
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by voodoo_child » Fri Jul 08, 2011 7:42 pm
Thanks Ian and Ashley. It's clear to me now!

thanks
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by XLogic » Sat Jul 09, 2011 12:30 am
Fascinating discussion.

Cause and effect vs. Conditional.

My Thought Process for Both:

1. Causal Reasoning: implies Cause occurred some time before Effect. and Cause connects directly to Effect
Cause --> Effect (C caused E to occur. If C occurs, E must occur afterward)

2. Conditional Reasoning: Sufficient condition guarantees Necessary condition. But Sufficient condition need not precede the Necessary condition, and both conditions need not be directly connected.
Sufficient --> Necessary (S condition=true, guarantees that N condition=true)

Strengthen Cause n Effect: Cause --> Effect

Perform one or more of the following:

- Eliminate Effect --> Cause (reverse)
- Eliminate Cause2 --> Effect (some other cause)
- Eliminate Cause2 --> Cause and Cause2 --> Effect (Other cause leads to both)
- More evidence to support Cause --> Effect

To Weaken Cause n Effect:

- Substitute "Eliminate" above for "Show"
- Any evidence to undermine Cause --> Effect

-----
Source: Paraphrased from Multiple sources (including prep-test books)
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