A reductio ad absurdum is a correct way to argue. An argument by lack of imagination is an informal fallacy.
But if a reductio ad absurdum is applied outside of a highly formalized setting like mathematics, how do we distinguish it from an argument by lack of imagination?
Isn't stating that something is absurd the same as stating that you can't imagine it to be true?
Reductio ad Absurdum is simply showing that an argument results in a false conclusion.
In mathematics, that's a formally proven false conclusion.
In an "informal" setting, all that is required is that both parties agree that the conclusion is false. The purpose isn't to show that something is false merely because it is absurd, but to show that an argument, when its premises are followed through, results in an absurd (and patently false) conclusion, thereby demonstrating that the original argument was a bad one.
Simply, put, if there is a premise, and I show that it results in an absurd conclusion (that we both agree is a false conclusion), then we also must both agree that the premise is false.
Now, on the other hand if there's a dispute about whether the "absurd" conclusion is actually false, and you say it isn't, and I say that it is, purely because it's absurd, in that case I'm just making an argument from a lack of imagination. But that's not the point of an "informal" reducto ad absurdum, the point is to show that we arrive at a point of mutually agreed falsehood
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super informally:
valid:
person 1 : I think A is true because B is true
person 2 : but if B is true then C is true. And if C were true, then D would be true.
person 1 : But D is clearly absurd (and false)!
person 2: Exactly, and if D is false, then B must also be false (and therefore is not a valid supporting argument for A)
As opposed to:
not valid:
person 1: A is true
person 2: but if A were true, then B would be true, and if B were true, then C would be true, and C is clearly absurd!
person 1: B and C are also true, and if you would allow be to finish, I can demonstrate why
person 2: but they're absuuuuuuuuuurd
person 1: you may feel that way, but I think if you consider the...
person 2: absuuuuuuuuuuuuuuuuuuuuuuuuuurd
