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The example where the employer threatens to fire the employee is very widespread for explaining this fallacy, but this doesn't feel quite right to me. The cases in which the scary factor is independent of the argument maker (who commits the fallacy), like this one (taken from wikipedia):

  • General: "If we accept capitulation, the enemy will take the chance to slaughter us all."
  • Colonel: "So far they have treated captives adequately."
  • General: "This time they won't. And you better believe me if you don't want to find yourself rotting in a mass grave."

...seem to deserve the fallacy title, because the logic "jump" is made by "contaminating" the reasoning with an emotional response, leading to a conclusion that something is true, which might actually be false. On the other hand, when the threatening force is under the direct control of the argument maker, the result seems to be directly in the plane of concrete decision-making rather than judging the truth value of something as in the previous case. If we take it to the extreme:

  • Alice: "The money or your life!" (points gun)
  • Bob: "Okay :(" (hands money over)

...where's the logic error here? would you really call this a fallacy? Bob, facing two possible simple outcomes, chose an action that would very clearly bring about the least undesirable one. The only belief that changed for him is "I should give Alice all my money" to true, the same way his belief "I should stop my car now" would change to true when faced with a red streetlight.

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Fallacies are logical flaws in reasoning. If there is no reasoning, there is no fallacy (there may be other things, even worse than fallacies).

In your Alice x Bob example, there is a reasoning by Bob:

  1. If I don't give my money to Alice, Alice will kill me.
  2. I don't want to die.
  3. (from 1. and 2.) I will give my money to Alice.

And it is a valid reasoning.

But there is no reasoning by Alice; she is not making a statement about the state of affairs of the worlds, she is giving Bob a command, so rules of logic don't apply. What she is doing is a crime, not a fallacy, and it is a problem of ethics, not of logic.

Your other example, concerning the general, goes like this:

  1. The enemy is going to slaughter us if we surrender.
  2. We don't want to be slaughtered.
  3. (from 1. and 2.) We should not surrender.

Up to now, this is a valid reasoning. What is questionable is premise 1. So the objection is:

  1. The enemy has not slaughtered our troops up to now when they surrendered.

~1. (from 0) The enemy is not going to slaughter us if we surrender.

Then the general retorts:

  1. You have to believe 1. because if you don't, you will be slaughtered.

Which is basically begging the question: "1. is true because 1. is true." Which is a different fallacy.

The general could however have answered:

  1. You have to believe 1. because if you don't, I will have you arrested.

Which is the ad baculum fallacy.

How is this different from Alice's utterance to Bob? In that Alice is not asking Bob to believe anything, while the general wants his staff to believe that the enemy will slaughter them, and argues that it must be so, because otherwise they will be arrested.

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    Yes, petitio principii, good old fashioned begging the question, is clear in the General's final statement. Best - GT – Geoffrey Thomas Feb 12 '18 at 8:54
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Bob is not legitimately facing this choice. Once he has given the money, she can still kill him. The choice does not take away her option. Taking the choice seriously assumes that someone willing to threaten your life has a sense of honor, which is insane.

There is never any logic in choosing either option, since the threatener can clearly always just have both. There is in fact no reason to act at all. So the action has no logical motivation.

By letting her frame this as a choice, he is removing the only real choices he has, which are to attempt to disarm her, or to call her bluff. In the end, she either is or is not willing to kill him, and if she were, why not kill him first and then take the money?

The money is going to do him no good when he is dead, so her preferred option is not too bad a call. But the threat itself is hiding his other options.

The same is true when someone invents an external threat without a causal link. It is meant to foreclose the possible solutions by creating urgency, and the best response is to ask what option it is trying to keep you from considering.

As noted by @Luis, the fallacy in the first example is committed in the first line, not in the dismissal of the rebuttal, which is actually just begging the question.

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