Argumentum ad baculum
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Argumentum ad baculum (Latin for argument to the cudgel or appeal to the stick), also known as appeal to force, is an argument where force, coercion, or the threat of force, is given as a justification. It is a specific case of the negative form of an argument to the consequences.
As a logical argument 
A fallacious argument based on argumentum ad baculum generally proceeds as follows:
- If x accepts P as true, then Q.
- Q is a punishment on x.
- Therefore, P is not true.
This form of argument is an informal fallacy, because the attack Q may not necessarily reveal anything about the truth value of the premise P. This fallacy has been identified since the Middle Ages by many philosophers. This is a special case of argumentum ad consequentiam, or "appeal to consequences".
- Employee: I do not think the company should invest its money into this project.
- Employer: Be quiet or you will be fired.
- Student: I do not think it is fair that the deadline for our essay is so soon.
- Teacher: Do not argue with me or I will send you to detention.
In both of these examples, the authority figures ended the argument with a threat, but this does not automatically mean they are correct. They did not win the argument because they did not refute the other person's contention.
The Non-fallacious Ad Baculum 
An ad baculum argument is fallacious when the punishment is not meaningfully related to the conclusion being drawn. Many ad baculum arguments are not fallacies. For example:
- If you drive while drunk, you will be put in jail.
- You want to avoid going to jail.
- Therefore you should not drive while drunk.
This is called a non-fallacious ad baculum. The inference is valid because the existence of the punishment is not being used to draw conclusions about the nature of drunk driving itself, but about people for whom the punishment applies. It would become a fallacy if one proceeded from the first premise to argue, for example, that drunk driving is immoral or bad for society. Specifically, the above argument would become a fallacious ad baculum if the conclusion stated:
- Therefore you will not drive while drunk.
if using the form as above:
- If x does P, then Q.
- Q is a punishment on x.
- Therefore, x should not do P.
See also 
- Argument from authority
- In terrorem
- Logical fallacy
- Management by perkele
- Pascal's Wager
- Proof by intimidation
- Woods, John. Irvine, Andrew. Walton, Douglas. Argument, Critical Thinking, Logic and the Fallacies
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