Embedded If-Then Statements
Usually, arguments involve an if-then statement. Unfortunately, the if-then thought is often embedded in other equivalent structures. In this section, we study how to spot these structures.
Example:
John and Ken cannot both go to the party.
At first glance, this sentence does not appear to contain an if-then statement. But it essentially says: if John goes to the party, then Ken does not.
Example:
Danielle will be accepted to graduate school only if she does well on the G
Given this statement, we know that if Danielle is accepted to graduate schoo
l, then she must have done well on the GRE. Note: Students often wrongly interpret this statement to mean:
If Danielle does well on the GRE, then she will be accepted to graduate school.
There is no such guarantee. The only guarantee is that if she does not do we
ll on the GRE, then she will not be accepted to graduate school.
A only if B is logically equivalent to if A, then B.
Affirming the Conclusion Fallacy
AB
B
Therefore, A
Remember that an if-then statement, AB, tells us only two things: If
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