Thursday, October 7, 2010
Week 7 - Post 3: Contrapositives, Necessary & Sufficient Conditions
When Epstein discussed compound claims in chapter six, I found the topic of contrapositives to be interesting. A contrapositive was defined by Epstein as, “The contrapositive of If A, then B is If not B, then not A.” For instance, if the claim in an example was, “The student will do well in her Critical Thinking class because she studies,” then the contrapositive of the claim would be, “The student will not do well in her Critical Thinking class because she does not study.” Because the first part of the original claim was true, the second part of the original claim was true. In other words, the first claim was a sufficient condition because the truth of B was reliant on the truth of A. Furthermore, because the first part of the second claim was false, the second part of the second claim was false as well. Thus, the second claim was a necessary condition because the falsehood of B was reliant on the falsehood of A.
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I thought you did a really good job explaining contrapositives, especially using the example of the student in a critical thinking class so it is easy for us to relate to. It made it clear that the second part of the argument (B) is truly reliant on the first part (A). This makes B the dependent statement inside of a contrapositives. It puts a lot of weight on the first part (A) and it is important to make sure that when decided if A is true or not to really look into it because it can change the whole argument so much.
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