Critical Reasoning

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

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

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.

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.