### 3.4 Fallacies in Logic

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• Math Help

Be sure you understand that just because a syllogism is a fallacy does not mean that the conclusion is false. Consider the following fallacy.

 • Premise: When it rains, the ground gets wet. • Premise: The ground is wet. • Conclusion: Therefore, it must have rained.

This is a fallacy because the conclusion does not follow logically from the two premises. And yet, common sense tells you that most of the time, the conclusion would be true. After all, if you woke up in the morning and walked outside and saw that the ground was wet, wouldn't you assume that it had rained during the night?

Deduction of a fallacy is especially important in legal matters. Think about the situation described in Example 1. How would you feel if you were accused of a crime, given a polygraph test in which you truthfully proclaimed your innocence, and then told that the polygraph indicated that you lied?

Do you see why the type of fallacy in Example 1 is called affirming the consequent?

 • Premise: When people lie, their heart rate increases and they sweat. • Premise: This man has an increased heart rate and is sweating. • Conclusion: Therefore, he is lying.

The second part of the first premise is called the consequent. The second premise is affirming that the consequent is true.

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• Checkpoint Solution

To help see that this argument is a fallacy, you can write it as a syllogism.

 • Premise: When a large meteor hits Earth, it forms a large crater. • Premise: The diameter of Crater Lake in Oregon is about 5 miles. • Conclusion: So, Crater Lake must have been formed by a huge meteor.

In this form, you can see that the logic is not correct. This is another example of affirming the consequent. In this particular case, the reasoning is not only incorrect, the conclusion is actually false. Crater Lake was formed about 7700 years ago when an ancient volcano collapsed. It is not the result of a meteor striking Earth.

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Guest   9 years ago |
After examining 57 polygraph studies, the National Academy of Sciences concluded: "In populations of examinees such as those represented in the polygraph research literature, untrained in countermeasures, specific-incident polygraph tests can discriminate lying from truth telling at rates well above chance, though well below perfection." Their analysis of the 30 most recent polygraph data sets showed an overall accuracy of 85%.
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Guest   9 years ago |
Thanks for giving me this explanation of lie detectors. For some time I have thought that a lie detector could be used to convict an innocent person, but I didn't know how to explain my concern. Learning that this is a common type of fallacy that has a name helps me.
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Ron Larson (author)9 years ago |
I like Example 1. I have never had a "lie detector test", but I often wonder if I wouldn't be so nervous that my palms would sweat and my heart would race ... and the result would be that I was lying about my own name.
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Cody (moderator)9 years ago |
To see a fallacy used in the analysis of the space shuttle program, read the article "6 False Lessons of the Space shuttle" at PopularMechanics.com (a link is given below). Note the fallacy mentioned near the end of the article. What do you think of the writer's analysis?