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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?

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  • You can push the question back one step, using possible world semantics, and say that some state of affairs is absurd if it is not possible which means it does not obtain in any possible world. The question then becomes "is a lack of the ability to imagine this state of affairs obtaining in a possible world proof that there is no possible world in which it obtains?" There is discussion of this in the metaphysics/modal logic literature but I apologize that I cannot remember the name of the specific paper I'm thinking of. It's something like "Is imagination good enough for ___" or something. – Not_Here May 2 '18 at 13:38
  • You are interpreting the words Wrong. Reductio ad absurdum refers or expresses an argument that has a blatantly problematic conclusion. So the method of arguing like this leads to absurdity referring to the method of argument. The absurdity of the argument, if proven, will be the reason to reject the argument conclusion. That is the truth will be the falsity of said conclusion. So if my conclusion is p then the rejection of p being a blatant false proposition must mean that NOT P IS TRUE. This method works outside of mathematical logic. Classical logic uses this method as well. – Logikal May 2 '18 at 14:10
  • Logical fallacies express that the conclusion does not logically follow from the premises. The fact someone can't understand how x could happen is not a logical factor but a personal issue. The reductio ad absurdum form of argument forces the conclusion & shows that the given conclusion is inconsistent -- that is the conclusion has false instances--- & this is why the given conclusion value must be reversed. – Logikal May 2 '18 at 14:21
  • It does not matter whether there is reductio-ad-absurdum involved, considering anything proved relies upon a lack of imagination (or, more properly, accepting that a given level of imagination is mere whimsy and no longer relevant). If you applied more imagination, you could contrive more sophisticated counterexamples and edge cases, and hunt down more suppressed premises, whether or not there is any negation or contradiction involved. The two concepts are not really related in any way. – jobermark May 2 '18 at 20:04
  • I assume "lack of imagination" refers to false dichotomy. Similar concern can be raised about any informal inference, they are all strictly speaking invalid. But absurd and unimaginable are still two different things: the former means one can present plausible arguments for the exhaustiveness of alternatives, not just appeal to imagination. How plausible, how convincing? Well, in the end informal reasoning always rests on judgment calls. – Conifold May 2 '18 at 22:39
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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

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