Disputatio:Reductio ad absurdum

Exempla absurda

At the moment, the text contains the following "example":

In elenchi forma:

Pater- Cur incepisti sigarella fumare??

Filius- Quod, pater, omnes amici mei ea fumant.

Pater- Dicin tu vere te, si omnes amici tui ex rupibus desalire incepissent, incepturum etiam?

Absurditas filii dialecticae monstratur: incipere actum ob amicos incipientes est stultum, quod amici nonnumquam mala vel stultitiam agere incipiunt.

This is not an example of "reductio ad absurdum"!!! A true "reductio ad absurdum" is a logically correct argument, leading to a false (i.e., "absurd") conclusion, from which you may deduce no fault in the argument but that one of the premises of the arguments must not hold.

Perhaps the example could be retained as an example of misunderstandings of the reductiones ad absurdum. Georgius B 10:44, 21 Decembris 2007 (UTC) .

I think it's there, but it's an enthymeme, not a syllogism.

The basic idea is that F. believes 'All my friends are doing something' is a valid defense for doing that thing. His reasoning (to expand it) runs thus:

(x = friends; y = taking up smoking; z = filius)

1. If all x are y, then z is justified in y. (unspoken premise)
2. All x are y. (explicit premise)
3. Therefore, z is justified in y. (1, 2)

P. tries to prove #1 absurd by replacing y with 'jumping from the crags' and adding a new unspoken premise:

1. z is not justified in y. (new unspoken premise)
2. If all x are y, then z is justified in y. (unspoken premise)
3. All x are y. (explicit premise)
4. Therefore, z is justified in y. (2, 3)

But z is already assumed to be not justified in y, per (1). So z is and is not justified in y, which is absurd—therefore one of the premises must not hold.

Now, the error might be in labelling it an elenchus, in which I don't think premises are so freely omitted, and certainly the sentence Absurditas filii dialecticae monstratur: incipere actum ob amicos incipientes est stultum, quod amici nonnumquam mala vel stultitiam agere incipiunt is absurd for nearly the same reason:

(x = filius, y = evil and stupid things, z = friends)

1. If x is doing y because z are doing it, then x doing y is stupid. (explicit premise)
2. x is doing y because z are doing it. (explicit premise)
3. Therefore, x doing y is stupid.

(The explicit premise "z sometimes do y" is not incorporated into the argument, and seems merely to be used to set the stage.) But replace y with something wholesome, like, 'becoming happy and successful in a socially acceptable way':

1. x doing y is not stupid. (unspoken premise)
2. If x is doing y because z are doing it, then x doing y is stupid. (explicit premise)
3. x is doing y because z are doing it. (explicit premise)
4. Therefore, x doing y is stupid. (2, 3)

But x doing y is already assumed to not be stupid, per (1). So x doing y is and is not stupid, which is absurd—therefore one of the premises must not hold. —Mucius Tever 03:20, 24 Decembris 2007 (UTC)

I agree that the boundary between showing logical afaults in an argument and proving tacit assumptions not to apply in the context, by means of reductio ad absurdum, sometimes is vague. However, refuting the logic of an argument is a broader concept; and whether or not it may be reinterpreted as a r. a. a., it is in itself something different. There are different levels of logic involved, when you claim a certain attempted deduction sceme invalid, because some applications of it would yield absurd results; or when you apply accepted deduction scemes, yielding the absurdity, in order to deduce the falseness of a premise.

I also believe the present text leans itself to a real misunderstanding (which may well have been also the authors's). "Absurditas filii dialecticae monstratur" really indicates that the falsness of the argument would be the "absurdity" in question; not "falseness of an unspoken deduction rule of the sun by means of a correct argument by the father". (Besides, the logical absurdity is depending on which premises you accept. There are several possible sources of errors in the father's arguments. One is, that the son may be convinced that unanimous actions of his friends never are bad; whence, accepting that jumping a cliff were bad, which from a classical Roman point of view is far from clear, implies that not all of his friends ever will jump from that cliff.)

Mucius Tever, do you think the present example should be retained, essentially in its present form? Georgius B 15:58, 25 Decembris 2007 (UTC)

Hejsan, Jörgen! Du har alldeles rätt, tycker jag. Artikeln i sitt nuvarande skick är rent skräp, för att sjunga ut min ärliga åsikt. Därför skulle jag vilja fråga dig om du är intresserad av att påbörja en ny version. Jag är förstås redo att hjälpa till, ifall du har svårigheter med språket. Well, I think the article in its present state doesn't give us the gist of the RAA. So, I suggest JoergenB start a new version of it. --Neander 04:42, 28 Decembris 2007 (UTC)

Gentlemen, so sorry to be so late contributing to a discussion my negligence has caused. I confess starting this article for the mere purpose of red link destruction. I have neither the philosophical knowledge requisite for offering a proper discussion of the topic, nor the research into any Latin explanations of the concept. By all means, may someone with more of both take over for me. Regards to all, and happy New Year.--Ioscius ^(disp) 05:02, 28 Decembris 2007 (UTC)