Logic question about reductio ad absurdum

[Underseer]

If the existence of the universe demands that there must be a creator (God), then the existence of God demands that He (She/It) must also have a creator.
Variants of this argument have been used by nontheists plenty of times when debating theists. I didn't use the argument myself, but in discussing someone else using it, I agreed with it and was accused of reductio ad absurdum.

Turning to the Wikipedia entry for reductio ad absurdum, I found
There is a fairly common misconception that reductio ad absurdum simply denotes "a silly argument" and is itself a formal fallacy. However, this is not correct; a properly constructed reductio constitutes a correct argument.

So, uhm, what exactly constitutes a "properly constructed reductio" argument? Where is the dividing line between a reductio and reductio ad absurdum?

I defended myself by pointing out that I was not taking the premise to an extreme, but simply using it exactly as was and extending it to something else. Of course, I have no idea if this defense means anything, and more importantly, I don't know if the above argument is indeed reductio ad absurdum. Is it? Should we stop using it? If it isn't, then how do we explain that what we are doing is not reductio ad absurdum?

[Hydra009]

Variants of this argument have been used by nontheists plenty of times when debating theists. I didn't use the argument myself, but in discussing someone else using it, I agreed with it and was accused of reductio ad absurdum.Which wouldn't be much of an accusation, because afaik, reduction to absurdity isn't a fallacy. Nope, don't see it anywhere over here (http://en.wikipedia.org/wiki/List_of_fallacies#Formal_fallacies).

Perhaps you could ask them to elaborate on why they believe that argument is flawed?

So, uhm, what exactly constitutes a "properly constructed reductio" argument?From my understanding, a properly constructed reduction to absurdity has to follow the logical structure of its parent argument and has to come to a contradictory or patently absurd conclusion.

For example, a person argues that a war was wrong, and his opponent asserts that the person is claiming that all war is wrong, and since WWII was a just war, that person's argument is absurd and his objections are wrong. This is not a reduction to absurdity, this is a strawman argument.

It's somewhat difficult to get a good example of a reduction to absurdity. How about this:

P1 - Differing views should be taught in school classes.
P2 - Creationism is a differing view from Darwinism.
C - Creationism should be taught in biology classes.

Reduction to absurdity:

P1 - Differing views should be taught in school classes.
P2 - Geocentrism is a differing view from heliocentrism.
C - Geocentrism should be taught in astronomy classes.

I defended myself by pointing out that I was not taking the premise to an extreme, but simply using it exactly as was and extending it to something else. Of course, I have no idea if this defense means anything, and more importantly, I don't know if the above argument is indeed reductio ad absurdum. Is it?Imo, the argument at the beginning is a reduction to absurdity, and is a valid argument.

So let's go to your example - "If the existence of the universe demands that there must be a creator (God)" That's a little brief of an argument, and holds quite a few hidden assumptions, for example, what properties of the universe "demand" there to be a creator? It doesn't say. And why a God, as opposed to some other type of mythological being? So, for convenience's sake, I'll grab a more formal version of the argument from design:

P1 - The universe is too (complex, orderly, etc) to have occurred randomly or accidentally.
C - Therefore, the universe must have been created by a God.

Reduction to absurdity:

P1 - God is too complex to have occurred randomly or accidentally.
C - Therefore, God must have been created by another intelligent being.

Looks like a valid reduction to absurdity to me.

[Underseer]

It's not even a logical fallacy? Cool.

Thank you!

[kennethamy]

Variants of this argument have been used by nontheists plenty of times when debating theists. I didn't use the argument myself, but in discussing someone else using it, I agreed with it and was accused of reductio ad absurdum.

Turning to the Wikipedia entry for reductio ad absurdum, I found


So, uhm, what exactly constitutes a "properly constructed reductio" argument? Where is the dividing line between a reductio and reductio ad absurdum?

I defended myself by pointing out that I was not taking the premise to an extreme, but simply using it exactly as was and extending it to something else. Of course, I have no idea if this defense means anything, and more importantly, I don't know if the above argument is indeed reductio ad absurdum. Is it? Should we stop using it? If it isn't, then how do we explain that what we are doing is not reductio ad absurdum?

People use reductio ad absurdum arguments ("reductio" is just short for, "reduction ad absurdom) all the time. Here is an example:

A defense lawyer argues:

My client is accused of murdering the victim, who was in Chicago, at 10 pm. But I have irrefutable evidence that my client was in Mexico City at 10 pm.
Therefore, in order to have murdered the victim, my client would have had to have been in two places at the same time. But that is absurd. Therefore, my client could not have been the murderer.

I don't see how your argument could be construed as a reductio, but as you can see, reductio's are perfectly fine arguments. They are used in mathematics and in logic all the time when an assumption is deliberately made in order to deduce an absurdity (usually a contradiction) from it, to show it is false, since what implies what is false (and a contradiction is false) is, itself, false.

Not that I think your argument is a good one. It does not follow that because an explanation requires an explanation, that it is not a good explanation. Suppose I explain the fact that ice formed by the fact that the temperature was lowered to 0 degrees F. Suppose I don't know why water turns to ice at 0 degree F. Does that show that lowering the temperature to 0 degrees F, does not explain why the water turned to ice? I may not be able to explain what created God, supposing that anything did. But why would that be a reason for thinking that God did not create the universe?

[punkforchrist]

Here's a formalized example of the reductio ad absurdum.

Prove A: Dogs are animals.
Here we start with a statement that is generally conceived as being patently true.
Assume ~A: Dogs are not animals.
The above statement is what we are trying to reduce to absurdity.
~A --> B: If dogs are not animals, then dogs are not living organisms with sense perception.
We now test the claim that dogs are not animals by defining what an animal is and observing whether dogs fit with this description.
~B: Dogs are living organisms with sense perception.
Here we observe that that dogs actually do fit the description of an animal.
~~A: by modus tollens.
Hence we may conclude that the claim that dogs are not animals is incorrect.
Therefore, A: by the law of negation, dogs are animals.
Thus, by constructing a double-negative, we demonstrate that dogs are animals.
Q.E.D.
Latin: quod erat demonstrandum, "which has been proved." We've proven (A) from the impossibility of the contrary, since (~A) is reduced to absurdity.

Reductio ad absurdum is a syllogism rather than a fallacy.

[mac_philo]

RAA is not a fallacy but rather a valid form of argument.

In mathematics or logic you can either prove something directly or indirectly. RAA is an indirect proof in which you assume the opposite of what you want to prove, then derive a strict contradiction.

In some logical systems it isn't a valid form of proof, and some mathematicians (intuitionists) reject it. This has to do with different conceptions of what it is to be provable, and isn't very relevant to everyday argumentation.

When people talk about it as a fallacy they usually just don't know what they are saying, but sometimes they might mean that your argument itself has absurd consequences (though not contradictory) that you didn't acknowledge.

Some of the examples given above are not examples of RAA. It doesn't have anything to do with going to extremes or reaching a conclusion that is absurd in the everyday sense of the word, or taking a given argument and turning it into absurdity. All it involves is making a single assumption that allows you to derive a contradiction, as a means to prove the negation of the assumption. So in fact, this thread does not yet contain a single strict example of a completely explicit RAA with no steps skipped or condensed. Here's one, albeit dull:

P1: All men are mortal.
P2: Socrates is a man.
3: Not(Socrates is mortal.) (Assume for RAA)
4: Socrates is mortal. (From P1 & P2)
5: Not(Socrates is mortal) & Socrates is mortal. (From 3 and 4) **contradiction**
6: NotNot(Socrates is mortal) (From 3 and 5 by RAA)
7: Socrates is mortal. (From 6 and law of double negation)