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# Overlooked possibilities from A->B

Alum Member
edited June 2016 in General 40 karma
It all concerns the basic form of:
A->B (if you have a rocket, you can kill a cockroach)

Immediately, based on this form, I can think of potential OPs.
It is a mistake to assume that there are no other ways to kill a cockroach. So an argument like the one below would be an error because even though A->B, it could be that C->B as well, or Z->B.

"if you have a rocket, you can kill a cockroach.
Therefore, since you want to kill a cockroach, you must use a rocket"
[A->B, therefore B->A [mistaken reversal)]. This overlooks the possibility that you can use other sufficient means to kill a rocket, and that a rocket is not necessarily necessary to kill a cockroach. It could be, but doesn't have to.

Then there another form of OP derived from the same A->B idea
And that is
A->B ; not A-> not B [mistaken negation]
"if you have a rocket, you can kill a cockroach
Since you don't have a rocket, therefore you can't kill a cockroach."
This overlooks the possibility that without a rocket, you can still do other things. Like kill terrorists. But that is out of the scope relative to the conclusion. But moreover, it is not necessarily necessary that you need a rocket to kill a cockroach, for "A->B; not A->not B" = "A->B; B->A".

In other words, it seems like the overlooked possibilities derived from the A->B form are the same.
(And that is assuming that there are no other sufficient conditions. Conclusions that follow a premise of A->B and concludes in the form of not A -> not B and B->A are making the same flaw and that is missing OPs.

What are your thoughts on this?
What are some implications that I have missed?
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