Avoiding Fallacious Reasoning: Lesson 5

The necessary and sufficient conditions are discussed in Hurley’s Intro to Logic.

"A is said to be a sufficient condition for B whenever the occurrence of A is all that is needed for the occurrence of B. B is said to be a necessary condition for A whenever A cannot occur without the occurrence of B" (23).

Translate this: Which of the following is a sufficient condition for getting a speeding ticket?(A)Driving a vehicle,(B) driving on a road,(C) driving 30 over the speed limit in the presence of a cop
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Ask yourself, if this condition holds, then does the event have to happen? Must the event happen if the condition holds?

So when asking if it’s a sufficient condition, ask yourself the key question, "If this condition holds, must the event occur?"

The following are some examples from Hurley’s chapter 1:

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If you have a racket, must the event occur? Of course not, as you could merely be holding onto a racket for someone else. Or, you could be a collector of tennis rackets.

When asking if it’s a necessary condition, remind yourself the key phrase, "The event cannot occur if the condition doesn’t hold."

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Ask yourself, "if this condition holds(paying attention), then does the event have to happen? Must it happen? Of course not, the student paying attention might simply not be bright enough to understand the lecture.

If the condition doesn’t hold(not paying attention), then the event cannot occur.

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Ask yourself, "if this condition holds(opening the door), then does the event have to happen? No, one can open the door, and just stand there or run away.

If the condition doesn’t occur(not opening the door), then the even cannot occur(crossing the threshold). I found this problem a little confusing because I can imagine someone bursting through(not opening the door) the door and crossing the threshold.

I suppose common sense is needed for some of these practice problems.

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