- Fri Dec 09, 2016 9:50 pm
#31358
Complete Question Explanation
This Assumption question is chock full of conditional reasoning, which can be broken down this way:
First sentence - pay attention to the common sufficient condition indicator "if":
Fall Below $1mil
Repay Loan
Next sentence, continuing from where the first left off:
Repay Loan Declare Bankruptcy
String those together and we get:
Fall Below $1mil Repay Loan Declare Bankruptcy
The third sentence isn't conditional, but tells us that the company had reported that they did not meet the first sufficient condition (they did not fall below $1mil). The last sentence tells us that the report was not accurate (it was overstated), and then concludes that Acme must declare bankruptcy (our final necessary condition).
What's missing? One or both of our sufficient conditions. "Overstating the earnings" is not part of our chain, so our author must have assumed either that the earnings actually did fall below $1mil or that, for some other reason, Acme will have to repay the loan. Either of those occurrences would be sufficient to show that the conclusion is correct.
I know what you're saying to yourself now - "but Adam, this is an Assumption question, not a Justify the Conclusion question, so why are we concerned with proving the conclusion to be true? Shouldn't it be just the opposite?" You have a good point! Typically we are not looking to prove the conclusion is true in an Assumption question, but vice versa. Something's fishy here - the conclusion, a necessary condition, shouldn't be used to prove anything, because it is merely necessary, not sufficient. Still, the author concluded that the necessary condition must happen. He has no evidence to support that claim other than his sufficient conditions. The argument rests solely on those and nothing else. So, if he is convinced, on this evidence alone, that the necessary condition will occur, he can only have done so based on the assumption that a sufficient condition for it must have occurred. It's not strictly "if the conclusion is true, the assumption must be true", but rather "if the conclusion is based on sound reasoning, it can only be because the assumption is true." A minor variation from our standard approach, but a crucial one in this case.
That's a lot of complexity for what is really an easy 2nd question of the section. Your analysis need not be, and should not be, so deep as all this. Just in case you went down that rabbit hole, I wanted to be sure I could pull you back out.
Answer A: This is the correct answer. This answer says that our first sufficient condition has occurred, so everything that follows in the chain - repaying the loan and declaring bankruptcy - must follow. If we negate this answer and say that the company's earnings, while overstated, were not below $1mil, then there is no evidence to support the conclusion that the company must declare bankruptcy. That's what we want to see happen when we negate the correct answer.
Answer B: Other debts are irrelevant - it's only the one loan being repaid that is sufficient for our conclusion.
Answer C: Other years are not relevant - the only issue is whether the company will now have to declare bankruptcy.
Answer D: There's no need to assume anything about this year. It could be a banner year with earnings in the billions! Still, the conditional rule has been triggered - if earnings ever fall below $1mil for any year, the loan must be repaid and the company will need to declare bankruptcy. Whatever happens this year is too late to stop that train.
Answer E: This is a mistaken negation of a portion of our chain, which would be diagrammed this way: Repay Loan Declare Bankruptcy. Mistaken Negations and Mistaken Reversals, while they could be true, are never assumed by an author making a conditional claim. Only the contrapositive is assumed.
This Assumption question is chock full of conditional reasoning, which can be broken down this way:
First sentence - pay attention to the common sufficient condition indicator "if":
Fall Below $1mil
Repay LoanNext sentence, continuing from where the first left off:
Repay Loan
Declare BankruptcyString those together and we get:
Fall Below $1mil
Repay Loan Declare BankruptcyThe third sentence isn't conditional, but tells us that the company had reported that they did not meet the first sufficient condition (they did not fall below $1mil). The last sentence tells us that the report was not accurate (it was overstated), and then concludes that Acme must declare bankruptcy (our final necessary condition).
What's missing? One or both of our sufficient conditions. "Overstating the earnings" is not part of our chain, so our author must have assumed either that the earnings actually did fall below $1mil or that, for some other reason, Acme will have to repay the loan. Either of those occurrences would be sufficient to show that the conclusion is correct.
I know what you're saying to yourself now - "but Adam, this is an Assumption question, not a Justify the Conclusion question, so why are we concerned with proving the conclusion to be true? Shouldn't it be just the opposite?" You have a good point! Typically we are not looking to prove the conclusion is true in an Assumption question, but vice versa. Something's fishy here - the conclusion, a necessary condition, shouldn't be used to prove anything, because it is merely necessary, not sufficient. Still, the author concluded that the necessary condition must happen. He has no evidence to support that claim other than his sufficient conditions. The argument rests solely on those and nothing else. So, if he is convinced, on this evidence alone, that the necessary condition will occur, he can only have done so based on the assumption that a sufficient condition for it must have occurred. It's not strictly "if the conclusion is true, the assumption must be true", but rather "if the conclusion is based on sound reasoning, it can only be because the assumption is true." A minor variation from our standard approach, but a crucial one in this case.
That's a lot of complexity for what is really an easy 2nd question of the section. Your analysis need not be, and should not be, so deep as all this. Just in case you went down that rabbit hole, I wanted to be sure I could pull you back out.
Answer A: This is the correct answer. This answer says that our first sufficient condition has occurred, so everything that follows in the chain - repaying the loan and declaring bankruptcy - must follow. If we negate this answer and say that the company's earnings, while overstated, were not below $1mil, then there is no evidence to support the conclusion that the company must declare bankruptcy. That's what we want to see happen when we negate the correct answer.
Answer B: Other debts are irrelevant - it's only the one loan being repaid that is sufficient for our conclusion.
Answer C: Other years are not relevant - the only issue is whether the company will now have to declare bankruptcy.
Answer D: There's no need to assume anything about this year. It could be a banner year with earnings in the billions! Still, the conditional rule has been triggered - if earnings ever fall below $1mil for any year, the loan must be repaid and the company will need to declare bankruptcy. Whatever happens this year is too late to stop that train.
Answer E: This is a mistaken negation of a portion of our chain, which would be diagrammed this way: Repay Loan
Declare Bankruptcy. Mistaken Negations and Mistaken Reversals, while they could be true, are never assumed by an author making a conditional claim. Only the contrapositive is assumed.
