Page 407, Parallel Reasoning #1, answer (B)

[obs23]

Jenny will have lots of balloons at her birthday
party. There are no balloons around yet, so
today is not her birthday.

As per p.408 of the book this is a mistaken contrapositive and I do not understand how. Please show me the correct diagram for this . I have diagrammed the above this way:

JB - Jenny's birthday
LB - lots of balloons

JB -->LB
~LB-->~JB

And I, therefore, thought it was a valid reasoning. Obviously common sense whispered "dude, there is this 'yet' in the equation, and it can't be correct" It did not sound correct, but I was convinced by the diagram I created

Generally, in the above, how do you identify the sufficient and necessary conditions? Since it seems to me this is where the problem rests...

Thanks,
obs

[Dave Killoran]

Hey Obs,

First, take a close look at what is occurring in the stimulus: you have a Mistaken Negation. Then, that is followed by a question stem that asks you to parallel "the flawed pattern of reasoning." So, you are looking for an answer that contains another Mistaken Negation. That means any form of valid reasoning or anything other than a Mistaken Negation will automatically be incorrect in this question. This is where you got tripped up, I think.

Second, when you arrive at (B), it is a contrapositive of sorts that they are driving at (it's not perfect due to the "yet" issue, but the form is certainly heading in the CP direction). This sometimes draws student in and makes them want to select this answer as correct (because, after all, this answer seems to make sense). But, again, you aren't looking for the answer with a contrapositive form, and that is a reason to eliminate this answer as it doesn't parallel what is occurring in the argument

Last, your diagram, for the purposes of killing this answer, is just fine. For most people, diagramming the first sentence is where they run into issues (they reverse the terms), but you got that part right (good job on that!).

To answer your question about diagramming when no obvious indicators are present, what do you do? Look for the term that tells you something else is going to happen (or not happen). The one that tells you something else will be the sufficient condition. In this case, if you know it's Jenny's birthday part, then that tells you there will be lots of balloons. that creates a diagram like the one you created: JBP LB.

Please let me know if that helps. Thanks!

[obs23]

Dave - thanks a lot for your elaborate reply. It is very helpful. One thing to clarify "This answer choice contains a mistaken contrapositive", the explanation directly from the book. Basically, I am confused because in the book it is a mistaken contrapositive while you responded it was a valid contrapositive...

In your response, you confirmed my and the test makers' valid reasoning about the problem (and correct diagramming), correct me if I'm mistaken, that B is incorrect because it contains valid reasoning. In the book, and this is where I am still not clear, you define answer choice B as "mistaken contrapositive" - in the book, did you imply that mistaken contrapositive was "mistaken" relative to the stimulus? Or what did you mean? You have just answered "it is a contrapositive of sorts that they are driving at" and I am not sure I am with you.

And finally, mistaken contrapositive is not the same thing as Mistaken Reversal, right?

So I wanted to get back to basics: Our argument, JBP --> LB; Correct contrapositive, ~LB-->~JBP (There are no balloons around yet, so today is not her birthday); Mistaken negation ~JBP -->~LB; Mistaken Reversal LB-->JBP; so how would you diagram a mistaken contrapositive, ~JPB-->~LB? If so, it does not look like this is what we are having in B, do we? It also looks like it is the only time you have used such wording in the book.

By the way, I did get the question right, I am just not clear about your explanation for the answer B specifically (making sure I am not getting lucky here and eliminating properly... as well as getting a broader perspective on looking at things, such as understanding your explanation ) and I can't quite articulate the point on mistaken contrapositive myself, hence my questions.

Thanks much.
Obs

[Dave Killoran]

Hey Obs,

Hmm, I've got a couple different versions of the book in front of me, and they each say, "This answer choice contains a contrapositive" (with no reference to "mistaken"). Could it be that you are superimposing the "mistaken" that appears in both (A) and (C) with what it says in (B)? I ask this because "mistaken contrapositive" is not a phrase that I would typically use. In any event, it should just state "contrapositive" (and a contrapositive is definitely different from a Mistaken Reversal or Negation).

Thanks!

[obs23]

That makes a lot of sense! Thanks for pointing that out. Actually I bought my books not so long ago...and perhaps I could send you a scanned version of the page, but the idea is that my version has "mistaken contrapositive" so I was hopelessly confused

Thanks again,
Obs

[obs23]

Also, while I am at it, do we have a name for this flawed diagram based on the argument above ~JPB ~LB? Does it exist or did I just come up with it?

Thank you,
Obs

P.S. it looks like I cannot attach anything to a PM, I wonder if there is an email to which I could send you the attachment? Thanks.

[Dave Killoran]

Also, while I am at it, do we have a name for this flawed diagram based on the argument above ~JPB ~LB? Does it exist or did I just come up with it?

Based on an original diagram of JBP LB? That's a Mistaken Negation then. Based on JB LB, that's a third term. So, it depends on the starting point.

I can save you the time of sending the scan--it's in the most recent version according to our publications manager The idea here is that a contrapositive would be mistaken as an answer, because we are looking for a flaw, not valid reasoning. As a contrapositive, it's not a perfect one--it's more in the "form" of a CP rather than a perfect CP (because of the difference between "birthday" and "birthday party."). I'm about to embark on making some additions to that book, so I'll probably expand this answer explanation considerably to address precisely what is occurring here, and eliminate any confusion.

Thanks!

[obs23]

Wonderful, thanks a lot for clarifications and help!

Regards,
Obs