- Sat Jan 22, 2011 12:00 am
#36671
Complete Question Explanation
Flaw in the Reasoning, SN. The correct answer choice is (A)
The scientist begins this dialogue by describing a study of experimental medications involving two
groups of people with athlete’s foot. One of the groups of athlete’s foot sufferers was given only
medication M, and the other was given only medication N. The only people to be cured had been
given medication M. In other words, if any given study participant was cured, that person was on
medication M. This conditional statement can be diagrammed as follows:
the scientist’s statement. The reporter’s invalid conclusion is that anyone who was not cured was not
on medication M. This is actually a Mistaken Negation of the scientist’s statement, which can be
diagrammed as follows:
Mistaken Negation: Cured On medication M
This is not a valid conclusion because all we know from the scientist’s statements is that anyone who
was cured was on medication M. This could mean that just one person was cured from a large group
of participants that had been on medication M. So it is not valid to conclude, as the reporter does,
that everyone on M had been cured.
Thus, we know the flaw in the reasoning of the reporter is conditional in nature, and in seeking the
correct answer choice, we need an answer that describes the conditional error (preferably using
conditional terms such as “necessary” or “sufficient,” although that is not a requirement).
Answer choice (A): This is the correct answer choice. The reporter considers the premise that M
can possibly cure athlete’s foot (perhaps even in just one person), and incorrectly concludes that M
always cures athlete’s foot. This answer is tricky because it actually describes the contrapositive of
the Mistaken Negation above:
Contrapositive of Mistaken Negation: On medication M Cured
(a.k.a. the Mistaken Reversal)
The contrapositive of a Mistaken Negation is the Mistaken Reversal of the original statement
(remember, the Mistaken Negation and the Mistaken Reversal of the same original statement are
contrapositives of each other). Thus, because this answer choice describes a relationship that is
functionally identical to error in the reporter’s statement, it is correct.
Answer choice (B): The reporter’s error is not in drawing invalidly broad conclusions based on a
small sample, but rather in misunderstanding the conditional statement provided by the scientist.
Answer choice (C): The reporter’s statement only concerns people involved in the study, reflecting
no mistaken presumptions about those who were not involved in the study.
Answer choice (D): The reporter’s response deals only with study participants, so there is no reason
to consider the circumstances of those who may be cured without either of the two medications
studied.
Answer choice (E): This potentially confusing incorrect answer choice provides a fairly convoluted
conditional point—that the reporter wrongly presumes that there are not many people who can be
cured only by avoiding medication M. But the reporter’s actual conclusion regards those who took
medication M, and the reporter’s mistake is in presuming that all of those participants were cured.
Flaw in the Reasoning, SN. The correct answer choice is (A)
The scientist begins this dialogue by describing a study of experimental medications involving two
groups of people with athlete’s foot. One of the groups of athlete’s foot sufferers was given only
medication M, and the other was given only medication N. The only people to be cured had been
given medication M. In other words, if any given study participant was cured, that person was on
medication M. This conditional statement can be diagrammed as follows:
- Cured On medication M
the scientist’s statement. The reporter’s invalid conclusion is that anyone who was not cured was not
on medication M. This is actually a Mistaken Negation of the scientist’s statement, which can be
diagrammed as follows:
Mistaken Negation: Cured On medication M
This is not a valid conclusion because all we know from the scientist’s statements is that anyone who
was cured was on medication M. This could mean that just one person was cured from a large group
of participants that had been on medication M. So it is not valid to conclude, as the reporter does,
that everyone on M had been cured.
Thus, we know the flaw in the reasoning of the reporter is conditional in nature, and in seeking the
correct answer choice, we need an answer that describes the conditional error (preferably using
conditional terms such as “necessary” or “sufficient,” although that is not a requirement).
Answer choice (A): This is the correct answer choice. The reporter considers the premise that M
can possibly cure athlete’s foot (perhaps even in just one person), and incorrectly concludes that M
always cures athlete’s foot. This answer is tricky because it actually describes the contrapositive of
the Mistaken Negation above:
Contrapositive of Mistaken Negation: On medication M Cured
(a.k.a. the Mistaken Reversal)
The contrapositive of a Mistaken Negation is the Mistaken Reversal of the original statement
(remember, the Mistaken Negation and the Mistaken Reversal of the same original statement are
contrapositives of each other). Thus, because this answer choice describes a relationship that is
functionally identical to error in the reporter’s statement, it is correct.
Answer choice (B): The reporter’s error is not in drawing invalidly broad conclusions based on a
small sample, but rather in misunderstanding the conditional statement provided by the scientist.
Answer choice (C): The reporter’s statement only concerns people involved in the study, reflecting
no mistaken presumptions about those who were not involved in the study.
Answer choice (D): The reporter’s response deals only with study participants, so there is no reason
to consider the circumstances of those who may be cured without either of the two medications
studied.
Answer choice (E): This potentially confusing incorrect answer choice provides a fairly convoluted
conditional point—that the reporter wrongly presumes that there are not many people who can be
cured only by avoiding medication M. But the reporter’s actual conclusion regards those who took
medication M, and the reporter’s mistake is in presuming that all of those participants were cured.