Fallacies: Denying the antecedent

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Fallacies: Denying the antecedent발음듣기

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(intro music) Hello, I'm Matthew Harris.발음듣기

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I'm a philosophy graduate student at Duke University, and today I'll be discussing the formal fallacy of denying the antecedent.발음듣기

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Denying the antecedent is a formal fallacy, meaning that the argument has a flaw contained in its logical form.발음듣기

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This is important because whenever this pattern of argument occurs, regardless of topic or content, the argument will always be invalid.발음듣기

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So how can we tell when the fallacy of denying the antecedent occurs?발음듣기

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Well, it happens when we mistake the direction of a conditional, or confuse it for a biconditional.발음듣기

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And it starts with the denial of the conditional statement's antecedent, then concludes the denial of its consequent.발음듣기

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The logical form of arguments that commit the fallacy of denying the antecedent look like this: "If P, then Q.발음듣기

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Not P. Therefore, not Q. Now, let's take a look at this conditional: "If you are a ski instructor, then you have a job."발음듣기

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The antecedent statement of this conditional is "you are a ski instructor," and the consequent is "you have a job."발음듣기

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But suppose someone made an argument with this conditional as its first premise.발음듣기

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Premise (1): If you are a ski instructor, then you have a job.발음듣기

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Premise (2): But you are not a ski instructor.발음듣기

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Conclusion: Therefore, you do not have a job.발음듣기

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Here, the second premise is a denial of the antecedent.발음듣기

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This premise does not tell us that only ski instructors have jobs.발음듣기

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So, even if the conditional statement is true (that ski instructors have jobs), it cannot be inferred that if you are not a ski instructor, then you are unemployed.발음듣기

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A conditional could validly be used to argue for the truth of this consequent by affirming the antecedent.발음듣기

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We find this in the arguments of a form called "modus ponens."발음듣기

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It is also valid to argue from the denial of a consequent to a denial of the antecedent.발음듣기

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But it is never, ever valid to deny the antecedent to reject its consequent.발음듣기

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Let's try another example: "If you are a property owner, then you are a human.발음듣기

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But you are not a property owner.발음듣기

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Therefore, you are not a human.발음듣기

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The antecedent, that you are a property owner, is being denied.발음듣기

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Even though you need to be a human to own property, this has no bearing on humans who do not own property at all.발음듣기

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For example, graduate students. Let's consider one last example: "If anyone is watching this video, "then they are on the internet.발음듣기

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Some people are not watching this video.발음듣기

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Therefore, they are not on the internet.발음듣기

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Again, denying the antecedent by pointing out that not everyone is currently watching this video does not validly demonstrate the denial of the consequent, that they're not on the internet at all.발음듣기

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These have been a few cases that I hope will come in handy in avoiding this formal fallacy in your own arguments.발음듣기

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For more related to the fallacy of denying the antecedent, I recommend that you take a look at the other related videos on informal and formal fallacies, the fallacy of affirming the consequent, and conditionals.발음듣기

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