This is my 200th post: Problematic self reference?

Consider the statement (call it p):

This statement is false.

Is p true or false? If it is true, it contradicts itself. So it must be false. But that is what p states, so it must be true. Liar’s Paradox.

On the face of it, it seems that the problem with this paradox is either self-reference or bi-valued logic itself. If the problem is bi-valued logic, it seems that a lot of math is suspect, in particular proof by contradiction. Proof by contradiction is a staple of math as I know it, and giving it up would be difficult.

For a long time, I thought that the problem here was inappropriate self-reference. But not all forms of self-reference lead to contradictions. Self-referencing statements are even used in proofs of theorems, the Godel’s incompleteness theorem for example. The title of this post “This is my 200th post” is a self-referencing statement (incidentally, it is true). It does not lead to any contradiction. If the problem is inappropriate self-reference, what forms of self-reference are problematic? Change the liar’s paradox to “This statement is true.” and there is no contradiction. The form of self-reference is clearly the same. What then?

q: This statement is true.

If q is false, it contradicts itself. So q must be true. This does not lead to any contradiction. Assuming bi-valued logic is valid, q is true. But what does q mean? What is true? As I see it now, the problem with the liar’s paradox is that just like q, it is empty, devoid of any content. There is nothing in it that can be either true or false. In other words, it is not a statement at all because it does not state anything about the world. Mere adherence to rules of grammar does not produce statements.

Delhi gang-rape: Some answers – 2

As I write this, the victim in the Delhi gang-rape case is no more. Despite the best efforts of the state to provide medical help.

The protests will continue and demands for capital punishment for rape will intensify. These demands are little more than an instinctive reaction. The first thing that came to my mind when I read about this case was: I would like to kill the perpetrators. Combine that thought with the inability to really do anything of the sort and the Indian habit of seeking a state solution for every problem, and the result is a demand for state action: Stricter laws, more policing, capital punishment.

Consider this report from Tehelka. It is titled: The rapes will go on. Along with some commentary, it describes the views held by senior police officers in and around Delhi. Most of the police officers believe that of the cases that are reported, most are not really rapes at all. That in itself, may not be surprising. Somewhere in the report there is a parenthetical reference to studies indicating that for every reported case of rape, more than 50 go unreported. Most genuine cases are perhaps never reported and the once that are fall through, given the attitude of the police officers. What is noteworthy (though not surprising) about the report is that the police primarily blame the dressing and behavior of the victims for the rise in rapes.

It is all too easy to demand things of the state. In this case, it might even seem right to demand that the state provide a safer environment. Crime is after all, a state subject. But the question that the protesters seem to be missing is: Can the state really do anything about it? Can it ensure that the police have the same outlook on our modern lifestyles that we do? Can it punish the perpetrators in cases that are never reported? Can it remove the stigma attached to rape?

But the state can indeed attempt to do the things the protesters want it to do. The state can create new laws (which will never be implemented, just as existing ones aren’t), it can allocate more funds to recruit more police (who will drink Chai at the corner shops and collect bribes from hapless non-rapists), it can declare capital punishment for rapes (further reducing the already dismal conviction rate). And clueless politicians who have no idea how to deal with the protests will indeed be too happy to to oblige.

Is this what we want?

Look below the surface and it is clear that the rising number of rapes (and other crimes against women) are social and cultural issues. The state is entirely powerless to do anything about these underlying issues.

Thank you, Sachin

“Poetry,” wrote Aristotle, “is a more philosophical and a higher thing than history: for poetry tends to express the universal, history the particular.”

A similar argument may be made for sport. Sport reduces life to its essentials and expresses its fundamentals in their purest form. Just as poetry expresses the universal through particular characters, sport expresses fundamentals through the actions of individual sportsmen. But unlike the characters in poetry, who are after all, mere figments of the poet’s imagination, the sportsmen are real. Sport then, is likely to fall short of poetry in its power to inspire, to embody the values of life. Perfection and purity is easier to achieve in poetry than in the life of a sportsman.

But once in a while, a sportsman comes along to prove that the difficult is not impossible, that a single-minded dedication can be maintained, that ability can be turned into excellence, that consistency can triumph over uncertainty. And such a sportsman transcends the sport, lends it meaning, makes it real.

Sachin Tendulkar is such a sportsman, and I am fortunate to have grown up at a time when my values could be shaped and sustained by the example of his greatness.

Thank you, Sachin.

Delhi gang-rape: Some answers – 1

Read my last post for context.


Numbers are hard to come by but it appears that the number of reported cases has doubled in the last two decades.


To determine why the number of rapes as against other crimes is increasing, it might be useful to distinguish between rapes that are perpetrated by ordinary criminals who cannot control their sexual desires and those that are perpetrated by seemingly normal men. The former category probably correlates with crime in general, it is a law and order issue. The latter category is the one that explains the rise and it is the one that is particularly worrying. This kind of rape has little or nothing to do with sexual desire. It is a reaction to women who dare to assert themselves. Recall that in the Delhi case, one of the accused admitted that he went berserk when the girl tried to resist the men and defend her friend who was being attacked. A woman asserting herself is unimaginable to those who still live by a traditional value system. What is this system? In this system:
A woman does not marry a man. She marries into the man’s family.
A woman does not marry by choice. She is given to another family (Think of Kanyadaan).
A woman is the property of her family.
The honor and status of the family is derived from the property it possesses.
A woman is honorable as long as she is untouched (unused) by anyone outside the family. (Think of Sita in Ramayan)
Sex is taboo unless it is between husband and wife.

To a man who who is steeped in these values, what is the worst he can do to a woman? Destroy her honor by using her sexually, rendering her unfit for use by anyone else. Hence rape.

Rapes of this kind are nothing new. They have been perpetrated by soldiers after winning a war and by rioters wanting to teach a lesson to members of a community they hate. What is frightening is that they are now being perpetrated by ordinary men against women who dare to challenge traditional values.

The typical profile of such a rapist is a man steeped in traditional values who resents the social changes that challenge his values in general and is angry enough by some act of resistance to forget common decency in a moment of madness.

The typical profile of a rape victim is simply any woman who dares to reject the traditional value system by choosing to marry against the rules of her village, wearing western clothes, going out with a boy friend, refusing to accept harassment, rejecting someone’s advances etc.

To be continued…

Delhi gang-rape: Some questions

Over the last few years I have experienced an alarming routine. Open the newspaper, read about rapes, stabbings, molestations and murders, shake my head and carry on with my life. The Delhi gang-rape is not the first and sadly will not be the last either. Perhaps it is just the sheer brutality of this case that sends a chill down my spine. Perhaps I have finally had enough. Regardless, it is time to attempt to make sense of what is happening around me. To ask some questions. To come up with some answers. Here are some questions that come to my mind.


Is the number of rape cases increasing? Reported cases? Actual cases? As a fraction of the population?

Is the number of convictions for rape increasing? As a fraction of the reported cases? Actual cases?


Is there something that most rapists have in common? Religion? Caste? Language? Region? Lack of education? Wealth? Power? Marital status? Social status? Age? Attitudes towards gender roles, sex, relationships, lifestyle? What (if any) is the typical profile of a rapist?

Is there something that most victims have in common? Religion? Caste? Language? Region? Education? Wealth? Power? Marital status? Social status? Age? Attitudes towards gender roles, sex, relationships, lifestyle? What (if any) is the typical profile of a rape victim?


Will increasing the penalty for rape reduce the number of crimes?

Will increasing the penalty for rape increase the number of convictions?

Will imposing the death penalty for rape increase the number of murders?

Will imposing restrictions / enacting new laws reduce the number of crimes?

Will imposing restrictions / enacting new laws make it easier to implement the laws?

Ethical questions:

Does a rapist deserve to live?

Should rape be punishable by death? (Note that this is not the same as the previous question)

What kind of restrictions are acceptable (assuming they are effective)? (Example: If women are banned from all public places, the number of rapes would go down. Would that be acceptable?)


My uncle died today after having seemingly recovered from a fall, with less than a week left for his son’s planned marriage. I didn’t know what to say when I went to visit my cousin. Instead, I spent a long time listening to others attempting to console him and my aunt. And thinking about what was being said.

My cousin was blaming himself for giving his father some medicines, wondering whether they had an adverse effect. I listened to people consoling him by talking of fate, how people die when their “time comes”, and how nothing that he did or did not do would have changed that “time”.

My aunt was mourning the tragic timing of the death. I listened to people consoling her by telling her that one’s entire life is determined when one is born, but we don’t know it and have to live through it.

I listened to people say that one should not grieve over the dead because it causes anguish to the dead man’s soul.

I listened to people say that my uncle would be reborn as my cousin’s child.

Inevitably, the occasion brought back memories of the time when I lost my father almost 10 years back. I was 19 then. Nowhere as mature in my thoughts as I am now. But I didn’t believe in fate, souls or rebirth then. I knew that the loss was permanent. I remember refusing to pay tribute to my father’s body saying “That is not my father”. For weeks, I was aware of the loss in every conscious moment. Thanks to Ayn Rand, I held on to one thought: I will not allow this to affect me. I succeeded.

Sad as it is, the death of one’s loved ones is a part of life and all of us have to deal with it at one time or another. Death always gives us a rude shock, it shows us that our plans can be overturned in an instant, that we are not fully in control of our lives. To deal with that, one needs to find some way to reduce the anxiety one feels when one is not in control. And fate is the way people have invented to do that. Instead of serenely accepting a world where there are many things over which they lack control, people prefer a world where everything is out of their control. Perhaps it helps them. I don’t know. It wouldn’t help me.

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