Reductio ad absurdum - an inefficient technique?

Reductio ad absurdum is the Latin term for a common device of rhetorical debate - the proof by contradiction. In high school mathematics, proof by contradiction was one of top few tools or methods employed to prove theorems. As a younger man, less comfortable with ambiguity and less familiar with probabilistic reasoning, I was absolutely in love with the device. You assumed that what had to be proved was not in fact true, deduced from it a result that was clearly absurd. Since the absurdity could not be true, the initial assumption must have been flawed and the proof inexorably followed. The result was clear, simple, strong, elegant and inescapable. Marvellous platonic beauty.

Proof by contradiction at its core relies on a simple but powerful element of formal logic that students of philosophy or computer science should instantly recognise - the equivalence of the contrapositive. Formally, this is stated as 

A -> B = ¬B -> ¬A, or 

If (the truth of) A implies (the truth of) B, then not B (the falsehood of B) implies not A(the falsehood of A), where A and B are both statements which could be true or false.

Perhaps all that sounds excessively jargon-y or convoluted, but the chain of reasoning is simple and essentially the same as that employed in high school math

1) Assume that statement A is true.

2) From that, deduce that statement B must be true.

3) Show (or it is perhaps common knowledge) that statement B is false.

4) Hence, statement A is false.

But  reductio ad absurdum isn't just about high school math. We often hear the distinction between necessary and sufficient arguments being made in less formal, verbal debate. Well, A -> B is the same as saying that the truth of A is sufficient (but not necessary) to show the truth of B, and the corollary that the truth of B is necessary (but not sufficient) to show the truth of A. And knowingly or unknowingly, we make a number of arguments and critiques that rely on embedded reductio ad absurdums.

A couple of recent examples have made me wonder if this is indeed a good way to make a point. My hypothesis is, reductio ad absurdums are likely to be misinterpreted even by intelligent people who are not sympathetic to your stand. Of course, that's plausibly true for all arguments, but the trouble with reductio ad absurdums is that you can be (mis)interpreted to be saying the exact opposite of what you set out to say. Let me illustrate using the two examples, from 'opposite' sides of a rather contentious issue in India, that are currently on my mind.

Example 1- Rajdeep Sardesai vs Swapan Dasgupta

First, we have Rajdeep Sardesai (RS), editor in chief of CNN-IBN, being accused of calling Dawood Ibrahim, India's most wanted criminal and terrorist, a patriot. The basis of this claim is an op-ed he wrote about a month after the Mumbai blasts of 1993. The op-ed is reproduced here. RS's article is a critique of the statements and politics of the now-deceased Shiv Sena chief Bal Thackeray and an impassioned plea that all Muslims must not be tarred by the same brush. The relevant controversial passage is this:

Indeed, the loyalty test is so patently superficial that it is bound to be exposed sooner or later.  For example,  Mr. Thackeray has always seen support for the Indian Cricket Team when it is playing Pakistan to be a mark of a true patriot.  He might be intrigued to learn that during the one-day internationals in Sharjah, one man who speaks fluent Marathi has been spotted waving the tricolour and vociferously cheering the Indian Team.  His name is Dawood Ibrahim."

The accusation started with people picking up on what another prominent journalist Swapan Dasgupta (SD) wrote on his blog after the Mumbai blasts of 2006. 

Working in the Times of India during those turbulent days, I recall the editorial savagery which greeted the suggestion that the ISI and Dawood Ibrahim had anything to do with the blasts. Rajdeep Sardesai even wrote an edit page article regretting that Dawood’s patriotism was being questioned by nasty saffronites

See what I'm driving at? RS's argument is of the type:

Statement A : (The Bal Thackeray Test) Those who support the Indian cricket team against Pakistan are true patriots.

Statement B: Dawood is a patriot.

Given the information that Dawood flies the tri-colour and cheers for India vs Pakistan in cricket, A -> B. But since we know that ¬B (it is common knowledge that Dawood can't possibly be a patriot). Ergo, ¬A. The Bal Thackeray test is false. QED. Proof by contradiction.

This is a correct and strong argument, almost trivially so. Yet, SD accused RS of implying that Dawood was a patriot. Of course poor RS says, directly, "the loyalty test is so patently superficial", so one would have thought that things would be clear. Apparently not. If someone doesn't share your politics or worldview, your reductio ad absurdum will be made to look like the exact opposite of what you're trying to say.


Example 2 - Meenakshi Lekhi vs Aakar Patel

Recently, NDTV had a panel debate on the implications of the Gujarat chief minister Narendra Modi's possible rise as the BJP's Prime Ministerial candidate for the 2014 general elections. Six panelists discussed and argued about a lot of things, especially around politics of development vs politics of identity. The video of the debate is here

http://www.ndtv.com/video/player/left-right-centre/modi-as-pm-candidate-is-it-dividing-the-nda/263419

Prof Najib Jung, the vice-chancellor of Jamia Milia Islamia made the claim that the BJP is likely to lose a significant share of the Muslim vote were Narendra Modi to ascend. BJP's representative on the show, Ms. Meenakshi Lekhi (ML) inferred this as saying that with Mr. Modi at least, the politics of identity is likely to overpower the politics of development in Muslim voting patterns. She counters this by saying (beginning at about the 27 minute mark in the video)

ML : I have a question for Mr. Najib, what does the Muslim want? Does the Muslim want to be.. going to Pakistan? Does the Muslim not have the same nationalistic fervour as anybody else? Does he not want his children to be going to the same schools as others? 

(interruptions)..This is a highly insulting....(interruptions)

ML: That's exactly my point, it's not insulting, you..you're insulting the intelligence of the common Muslim...

(interruptions and cacophony)

Aakar Patel (AP), another prominent journalist and a keen analyst of Narendra Modi, took strong exception  to ML's argument on the show and was driven enough to pen his coloumn in the Pakistani daily Express Tribune slightly ahead of his normal schedule, where he claimed that the Indian Muslim "lives on sufferance". He had this to say about the show in question

On Nidhi Razdan’s show on NDTV on the night of January 29, I was on a panel, discussing Narendra Modi as a prime ministerial candidate. In the Bharatiya Janata Party (BJP) corner was a woman called Meenakshi Lekhi. Midway through the discussion, she asked a soft-spoken man, Najib Jung, vice chancellor of Jamia Millia Islamia, if he thought Indian Muslims wanted Pakistan.

Why did she bring this up? I don’t know, and there was no occasion to. But it was dropped in casually because it’s the natural thing to say to a Muslim here — hey, are you guys Pakistan-lovers? Tell us the truth, now. 

Again, see where I'm driving at? The structure of Ms Lekhi's argument was :

Statement A : (Najib Jung's implicit contention) The Indian Muslim will relate more with religious identity than nebulous notions of development.

Statement B: The Indian Muslim relates with Pakistan , wants separate (religion-specific) schools.

Since Pakistan was a nation formed on the basis of religious identity and religion-specific schooling is again a question of prioritising religious identity over other things, A -> B. However, it is assumed to be common knowledge that B is not true. ¬B. Ergo, ¬A. Proj Jung's contention falls. QED. Proof by contradiction.

Now, the validity of parsing of Prof Jung's views may be questionable, but the argument as made by ML stands. It is logically correct. Yet, AP interprets it to mean that ML is calling into question the motives of Indian Muslims, while her argument stands precisely if one assumes that the motives of Indian Muslim are not based on religious identity and are above question.


Conclusion

Now obviously, there's a huge amount of meta-knowledge here about Rajdeep Sardesai, Swapan Dasgupta,  Meenakshi Lekhi & Aakar Patel that followers of the Indian political scene will be familiar with, that explains their statements and interpretations. But deconstruction is not what I'm interested in here.

My limited point is - even within the overall futility of trying to convince those that disagree, the reductio ad absurdum is particularly inefficient. People will either not pick it up, or interpret it to mean the exact opposite of what you intended. I will certainly try to avoid the proof by contradiction in informal debate.