If Miles told Frank: “Copying a DVD is stealing”
And Frank's response to Miles: “if copying a DVD is stealing, then, by that logic, taking a photo of someone is kidnapping”
And Miles Response is: “They are not comparable”
Is Miles right. Or is Frank's argument reasonable by making an opposing argument to contrast how absurd Miles's logic is?
Reductio ad absurdum is not a fallacy. Rather, RAA is correct reasoning that exposes a fallacy. From the Logically Fallacious page for it:
[RAA is a] mode of argumentation or a form of argument in which a proposition is disproven by following its implications logically to an absurd conclusion.... The fallacy is in the argument that could be reduced to absurdity -- so in essence, reductio ad absurdum is a technique to expose the fallacy.
Your example is not a valid case of Reductio ad Absurdum. It's just an example of an absurd argument.
A real example would be:
Miles: "Copying a DVD is stealing"
Frank: "Why?"
Miles: "If someone created a piece of art, they have full rights to allow or prohibit its reproduction"
Frank: "Oh, so when I take a selfie in the city, I need to obtain permission from all the architects?"
Here, Frank RAA'd the second Miles's assertion (though not the original one). This is a perfectly valid counterpoint, and Miles needs to resolve it by, e.g. pointing out the circumstances in which certain rights are granted to the public, then showing how these don't apply to DVDs.
Frank’s argument is not a reductio. It is an argument from analogy, which is not deductive reasoning and needs to be evaluated differently
(Mark’s answer adequately covers the fact that reductio is a valid form of reasoning.)
Reductio ad adsurbum requires that there be a valid chain of reasoning that leads from the initial premise to an impossible or unacceptable conclusion.
Your example is not RAA because Frank's response does not describe an actual consequence of the Miles's statement. There may be some similarity between the two situations in Frank's mind, but Miles argues that this is tenuous.
Since the two situations are not comparable, we can't reasonably say that one leads to the other. Since the conclusion doesn't follow logically from the premise, the absurdity of the conclusion can't be used to refute the premise.
tl;dr– Frank's arrived at an absurd conclusion, which successfully demonstrates that one-or-more of the premises/arguments used to arrive at that conclusion is faulty. However, since Frank hasn't yet demonstrated that all of the other premises/arguments are necessarily solid, it doesn't yet follow that Miles's claim is the faulty premise. Frank's argument-as-stated is a non-sequitur.
Reductio ad absurdum is when a system of logic is applied to arrive at an inconsistency (absurdity). Doing this demonstrates that the system of logic is inconsistent (broken).
Reductio ad absurdum can be used to attack a specific argument when it's done using only that specific argument and well-accepted premises. Then when the overall system is shown to fail, the target argument can be faulted as the other arguments are assumed to be faultless.
For example, consider the argument:
If A and B, then C.
If C and D, then E.
E is contradicts F.
This shows that A, B, D, F, Claim 1, Claim 2, or/and Claim 3 is/are absurd. This can be taken to imply that A is absurd only if all of the others are eliminated as possible sources of error.
In this scenario, Frank has successfully demonstrated that whatever system of logic he used to arrive at his conclusion is broken. However, Frank has failed to demonstrate that Miles's premise is the faulty component; Frank's absurd conclusion may be due to another one of his premises or/and arguments being absurd.
So, as stated, Frank's argument is a non-sequitur, as the conclusion does not follow from the stated premises.
In common practice, there're two ways Miles might respond:
Dismiss Frank's argument as a non-sequitur.
As stated, Frank's argument is a non-sequitur. If Miles doesn't care to help develop it, Miles can just disengage.
Ask for Frank to explicitly lay out his arguments.
As stated, Frank's argument is a non-sequitur and thus invalid – but, this could be fixed if Frank lays out all of his arguments. If he does so, then the new statement of Frank's argument could be assessed.
If Miles can show that one of Frank's other arguments isn't solid, then Miles can demonstrate that the absurdity doesn't demonstrate the inconsistency of Miles's own argument.
If Frank can successfully argue his position using only arguments that Miles agrees with, then presumably Miles ought to accept that Frank has demonstrated an inconsistency in Miles's beliefs.
Since reductio ad absurdum isn't an attack on a specific premise, someone making a reductio ad absurdum is putting forth an attack on the collection of all arguments that they've used in their argument, as this is strictly necessary for their conclusion that the contested premise is faulty to follow.
However, in common social situations, not everyone seems to get this. Folks might put forth a reductio ad absurdum, thinking that they're attacking only the premise that they're arguing against. Then when their other arguments are requested for critical analysis, they may feel personally attacked. This might be described as sealioning.
In such situations where an arguer isn't willing to elaborate or have their argument critically assessed, then it may be socially advisable to disengage them.
I note this here because a good reductio ad absurdum can require a lot of critical analysis to sustain, to such an extent that it's often best to just ignore such arguments.
Many logical arguments have some severability. This is, small defects don't necessarily completely invalidate an argument.
For example:
1 + 1 = 2.
Humans have a left foot and a right foot.
Therefore, humans have 1+1=2 feet.
People walking down a sidewalk wear shoes.
Therefore, people walking down a sidewalk wear 2 shoes.
Premises (2) and (4) aren't necessarily true. Still, this sort of argument is severable in that, while perhaps imperfect, it's a reasonable observation that's generally approximately true.
Now let's say that Frank and Miles are chatting. Frank lays out this argument, then appends:
Look at that guy; they're not wearing any shoes!
Therefore, 1+1=2 is absurd.
While we may've tacitly accepted the earlier arguments in a general context, appreciating that the conclusion in (5) is mostly correct, Frank's argument in (7) is clearly silly.
Point being that, while reductio ad absurdum is a valid mode of argument when done correctly, it's unusually non-severable. Since it's an attack on all arguments, we have to be stricter, attacking claims that, in other modes of reasoning, may've been appreciated as approximately true.
In this particular case, I don't see the comparison as valid
Let's say Alan copies Bob's DVD, then Alan takes a photo of Bob, then Alan kidnaps Bob.
In each situation, look at Alan's gain and Bob's loss and compare
Copying DVD: Bob loses nothing, Alan gains an asset (DVD) equivalent in quality to Bob's asset (DVD) (high value win for Alan, no loss to Bob) Taking a photo: Bob loses nothing, Alan gains an asset (photo) of less value than Bob (Himself) (low value win for Alan, no loss to Bob) Kidnap: Bob loses his freedom, Alan gains an asset (Bob) (high value win for Alan, high value loss to Bob)
If we equate these outcomes to scores, where 0 is unaffected, +1 is a small win, +2 is a big win, -1 is a small loss, -2 is a big loss
| BOB | ALAN |
DVD | +2 | 0 |
PHOTO | +1 | 0 |
KIDNAP | +2 | -2 |
One could argue that a person is not of equal value to a DVD, but I equate them here because the copied DVD is of equal quality to the original, like a person who has been kidnapped, while a photo of something is not the same as having that thing.
Frank isn't engaging in RAA. They're engaging in a straw man argument. Miles simply made a claim. They didn't state what premises they have that they think support that claim. When Frank says "by that logic", there is no "that logic", so Frank is engaging in behavior that is all too common, namely simply making stuff up, and pretending that the other person said it.
Generally speaking, arguments that start off "by your logic" are not in fact arguing based on the other person's logic, they are based only simply imagining what they other person's logic might be, and then responding to that without actually trying to understand what the other person's logic really is, and don't even say what they think the other person's argument is.
If you want to make an Reductio ad Absurdum argument, you first start explicitly stating what you think the other person's logic is, and you be prepared to defend your claim that the other person is saying that. If the other person hasn't said what their logic is, then you should ask them to explain what their logic is before trying to argue against it.
If you say "A implies B", then, assuming that B is false, and the other person did in fact claim that A is an argument for C, then you have indeed presented a valid argument for why their argument for C is flawed (although you haven't presented an argument for C itself being false).
