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Fallacies: Denying the Antecedent

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(intro music) Hello, I'm Matthew Harris. I'm a philosophy graduate[br]student at Duke University, and today I'll be discussing the formal fallacy of[br]denying the antecedent. Denying the antecedent[br]is a formal fallacy, meaning that the argument has a flaw contained in its logical form. This is important because whenever this pattern of argument occurs, regardless of topic or content, the argument will always be invalid. So how can we tell when the fallacy of denying[br]the antecedent occurs? Well, it happens when we mistake the direction of a conditional, or confuse it for a biconditional. And it starts with the denial of the conditional statement's antecedent, then concludes the[br]denial of its consequent. The logical form of arguments that commit the fallacy of denying the[br]antecedent look like this: "If P, then Q. "Not P. Therefore, not Q." Now, let's take a look[br]at this conditional: "If you are a ski instructor,[br]then you have a job." The antecedent statement[br]of this conditional is "you are a ski instructor," and the consequent is "you have a job." But suppose someone made an argument with this conditional[br]as its first premise. Premise (1): If you are a ski[br]instructor, then you have a job. Premise (2): But you are[br]not a ski instructor. Conclusion: Therefore,[br]you do not have a job. Here, the second premise is[br]a denial of the antecedent. This premise does not tell us that only ski instructors have jobs. So, even if the conditional[br]statement is true (that ski instructors have jobs), it cannot be inferred that if[br]you are not a ski instructor, then you are unemployed. A conditional could validly be used to argue for the[br]truth of this consequent by affirming the antecedent. We find this in the arguments of a form called "modus ponens." It is also valid to argue from[br]the denial of a consequent to a denial of the antecedent. But it is never, ever valid[br]to deny the antecedent to reject its consequent. Let's try another example: "If you are a property[br]owner, then you are a human. "But you are not a property owner. "Therefore, you are not a human." The antecedent, that you are a property owner, is being denied. Even though you need to be[br]a human to own property, this has no bearing on humans who do not own property at all. For example, graduate students. Let's consider one last example: "If anyone is watching this video, "then they are on the internet. "Some people are not watching this video. "Therefore, they are not on the internet." Again, denying the antecedent by pointing out that not everyone is currently watching this video does not validly demonstrate[br]the denial of the consequent, that they're not on the internet at all. These have been a few cases[br]that I hope will come in handy in avoiding this formal[br]fallacy in your own arguments. For more related to the fallacy[br]of denying the antecedent, I recommend that you take a[br]look at the other related videos on informal and formal fallacies, the fallacy of affirming the[br]consequent, and conditionals. Subtitles by the Amara.org community