T C A Srinivasa-Raghavan: When in doubt, try logic

L'affaire Lalit is like a 1970s Bollywood multi-starrer. Only the songs are missing

For the last 10 days, millions of Indians have been trying to make sense of the Lalit Modi-Swaraj-Raje-Jaitley-Chidambaram-Pawar-Srinivasan-ED-BCCI-et al episode. Without much success because TV news has muddied the waters even further with its wild inferences.

As a result, in Amitabh Bachchan's immortal words "The confujun is utter". No one knows what the hell is really going on.

To cope with such situations, logicians have - self-servingly, naturally - laid down a golden rule: when bewildered, look to formal logic to find some sort of satisfactory answer.

The sorites paradox
The first of these is the paradox of the heap. The Greeks (actually a fellow called Eubulides) who lived next to the sea and didn't have much to do - just as they don't do now - came up with it some 2,500 years ago.

The question is this: if you remove one grain from it at a time, when does a heap of sand cease to be a heap? The modern version is when does a beard cease to be a beard if you remove one hair at a time? The same logic, by the way, can be used in the case of baldness. When do you become bald?

The government - first the United Progressive Alliance and now the National Democratic Alliance - is trying to remove one grain at a time, for example, Lalit Modi, Vasundhara Raje and Sushma Swaraj. Earlier it was Shashi Tharoor and his late wife.

If they persist, they will need to remove a lot of grains, belonging to possibly all political parties. But even then, in the end, they will be left with the problem that bothered old Eubulides: does the heap cease to be a heap only when every grain has been removed?

The Enforcement Directorate can tell us.

Boiling frog solution
Since the heap or beard or baldness look like an impossible problem, some other logicians came up with the parable of the boiling frog. Mathematicians think of it as continuous functions.

The question that the philosophers asked - albeit not Greek ones this time - was this: if you drop a frog in boiling water, it will jump out. But if you put it in cold water and then heat the water slowly, it will allow itself to get boiled.

This is important because the law assumes binary states - you know, 0/1, guilty/not guilty - whereas in real life what you get is continuums. And this is exactly the problem with this Lalit Modi business.

There are no pure states of guilt and innocence. Everyone associated with it is tainted in some way but the sand heap problem is getting in the way.

Masked man fallacy
To sort that problem out, some other logicians came up with the 'masked man fallacy'. The name of the fallacy comes from the example used to prove it.

This is a situation where two objects are identical in all respects but one. Minds untrained in simple logic - such as TV news anchors - often use this to show that the two objects are identical.

They are wrong said the German philosopher Gottfried Leibniz because you can say "I know X" and "I do not know who the masked man is" and be right. But from that you cannot say X is not the masked man.

The third statement does not follow from the first two.

The problem arises, the philosophers tell us, because while knowing is one thing, believing it is quite another. It is a fine distinction that is worth keeping in mind.

A variation on the theme is Moore's paradox where you look out of the window and see the sun is shining but choose not to believe that. Prime ministers, when it comes to some Cabinet colleagues, are especially prone to this paradox.

This sort of contradiction, by the way, is what eventually led to the new discipline called fuzzy logic. It is based, though not knowingly, on the ancient Indian concept of ardha narishvara.

That is, the same entity could be a male and a female at the same time. Come on RSS, pick it up now.

Danish donkey paradox
Then there is the Danish donkey paradox or Loki's wager. A donkey called Loki lost a bet, which had stipulated that the winner would cut off its head. The donkey then stipulated that it would not give up any part of its neck.

But no one could agree where the head ended and the neck began. So while they argued about it, the donkey managed to live for the rest of its natural life.

But it had to agree to something else: to get his lips stitched as a punishment for his subterfuge.

Samjhe, Lalit bhai?