# Fallacies of division

Does the following argument involve a fallacy?

If my kidnappers were planning on killing me, it wouldn’t matter if I knew where they were driving me to. And they did not blindfold me. So they don’t care if I see where we are going. Clearly, then, they intend to kill me.

(a) affirming the consequent (b) ad ignorantiam (appeal to ignorance) (c) the black and white fallacy (d) no fallacy

• Affirming the consequent: "If my kidnappers intend to kill me, then they don’t care if I see where we are going." "But they don’t care; thus they intend to kill me." Commented Sep 4, 2016 at 12:35
• Why is this titled, "fallacy of division"? Commented Sep 4, 2016 at 12:57
• I concur with Mauro. The question in effect says if (kidnappers plan to kill) then (they do not blindfold me). This is one of those conditionals where we have a tendency to assume that it implies the converse also: if (kidnappers do not plan to kill) then (they do blindfold me). But this is not stated in the question, it is just a plausible implicature. Commented Oct 5, 2016 at 20:36
• What if the kidnappers are just thorough. What if the kidnappers are just doing what they've done before? What if the kidnappers intend to take you to a secret birthday party and want you to see all participants at once in a big surprise? Or what if you're right!? Commented May 4, 2017 at 13:28

Given the premises, it is an example of affirming the consequent. If we put the argument into statement form, and by a little natural deduction, then it is easy to see!

For,

A=They plan to kill me, B=They care that I see where we are going, C=They blindfold me

1. A ⇒ ¬B (Premise, "If they plan to kill me, then they don't care that I see where we are going)
2. ¬C ⇒ ¬B (Premise, "If they don't blindfold me, then they don't care that I see where we are going")
3. ¬C (Premise, "They don't blindfold me")
4. ¬B (2,3 Modus Ponens, "So, they don't care that I see where we are going")
5. A (1,4 "They plan to kill me" only by Fallacy of Affirming the Consequent)
• If the first premise was changed to ¬A ⇒ B (If they aren't going to kill me, then they would care that I can see where I am going), that would resolve the issue, right? (logic: ¬A ⇒ B implies ¬B ⇒ A, which is enough to prove 5). Commented May 4, 2017 at 17:56
• @CortAmmon, Yes it would! But ¬A ⇒ B was not given in the informal argument as a premise. Commented May 5, 2017 at 19:15
• I'm kind of mixed on this. It's not clear to me that a conditional is the best formulation of the first premise. The use of "if" doesn't determine it since we're looking at an informal argument. Commented May 10, 2017 at 3:05
• It doesn't matter that the argument is informal if the translation to formal form is done correctly. You can see the first premise I give is the first sentence of OP's original argument. Commented May 10, 2017 at 17:04

I do not think there is a fallacy here.

1. If A (they do not blindfold me) then B (they intend to kill me).
2. A (they did not blindfold me).
3. [from 1. and 2.] B (they intend to kill me).

If both premises are true, then the conclusion is also necessarily true.

It can be perhaps argued that 1. is not true; there could be other reasons why kidnappers would not blindfold their victims. Sheer incompetence, or having some kind of power over the victim that will prevent the latter from seeking the police after the fact, come to mind. If so, not the full reasoning, but the major premise may be characterised as a black-and-white, or excluded middle, fallacy.

But if 1. is true (ie, the victim knows that the kidnappers are not incompetent, and cannot think of any reason why s/he won't immediately seek the police to get justice done), I can see no fallacy there.

So, barring any doubts of the kidnappers incompetence or the possibility of an ongoing blackmail after ransom and release, option (d), no fallacy.

(And, in practical life, if you are kidnapped and not blindfolded, yes, fear for your life, and attempt to escape whenever possible. Do not let concerns about the competence of your kidnappers or the possibility of blackmail stop you from trying.)

• It is not so; it is : 1) If A (my kidnappers were planning on killing me) then B (they do not blindfold me). 2) B (they did not blindfold me). Then: 3) A (they are planning to kill me). Commented Sep 4, 2016 at 14:47
• I think you're right.. I think there is no fallacy as such, unless you count 'false premises' as a fallacy. Commented May 4, 2017 at 13:25

Assume the kidnappers are in possession of a drug that erases your memory of all events of the last week completely. And look at the statements made in the light of this assumption. But the question looks too much like homework to me to go further into it.

(Many alternatives: Maybe they are just very inexperienced kidnappers? Maybe they take you to a neighbourhood with thousand houses, all looking exactly alike? )

That said, you should be worried. Just because an argument is fallacious doesn't mean the conclusion must be wrong. It's actually a fallacy to assume that a fallacious argument implies the conclusion is wrong. The fallacy here was confusing A->B and B->A (with A and B being "they will kill me", and "they don't blindfold me"). A->B and B->A are different whenever one is true but the other isn't. The two situations are (1) they blindfold me, but still are going to kill me. (2) they don't blindfold me, and they are not going to kill me. The more rare that second case is, the more you should be worried.