What Not To Say

Since I write philosophy, I often come across paradoxes. You know, like Zeno's paradox: before the arrow can get where it's going, it has to get halfway there, and before it can get the rest of the way, it has to make it half of the rest of the way, and so on. So: the arrow never gets where it's going. But of course, it does.

Philosophers tend to talk about paradoxes in a sort of stripped down way, and I don't blame them, really -- that's what philosophers do. But I'm always on the lookout for actual real life manifestations of paradoxes. Messy, real-life, stuff.

One kind of sort of paradoxical thing is self-reference. In its simplest form, "This sentence is false." If it's true, it's false, and vice versa.

Self-reference seems to me to come up a lot in real life problems. Consider the things you cannot say, and mean, because of self-reference.

Like, "Don't take this the wrong way." When someone says that in preface of some criticism, you're always more likely, rather than less, to take it "the wrong way." What the speaker wants to say is something like, "I don't want you to feel criticized." But in signaling that a criticism is coming, doesn't it sort of do the opposite?

I also get into a puzzle when I think about opinions I have about stuff that's being discussed too much. How can you express your opinion that all the discussion about poor Britney and her meltdown is sad and wrong, without adding yourself to all the discussion about poor Britney and her meltdown? There, now, I've just added to the Google hits for "Britney meltdown."

Speaking of Britney, by the way, I was just remembering this evening that crazy marriage she had with her old boyfriend before K-Fed. Remember? The teen sweetheart or something? And her family was like "No way, unh unh, girl, you are not marrying this guy." I remember saying at the time, "They should have let her stay married to him; it'd probably work out better than anything else." Well. Shouldn't they have?

We've had a request for some C and C political discussion (in comments to this post). Speaking for myself, I am going to vote democratic, and I will vote for whoever gets nominated eventually. I am no fan of Hillary, for many of the same reasons lots of other people aren't. Like her support for the war, etc. etc.

But the recent kerfuffle about her tears has me completely dumbfounded. I saw the tape at the gym, and I thought, "Oh, there must have been some other occasion when she was crying." But no, that was it. A catch in the voice. A catch in the voice while describing the fact that she had a lot of ideas on how to run the country.

Oooh, was it calculated? Was it honest?

All I can say is, wow, man, if that counts as crying, I am going to be carted off tomorrow for bi-polar disorder or something. Jeez-louise. Talk about something not worth discussing!

But, you know, you can't really blog about how dumb it is to discuss something. 'Cause, yeah, there you are discussing. Self-reference in action!

It was good old Bertie Russell and Kurt Goedel who really took the self-reference problem and made serious fucking hay with it. Russell used it to dismantle and disprove Frege's entire life's work of showing how to reduce mathematics to logic. Goedel used it to show that no list of axioms could determine as true or false every mathematical sentence.

Pretty lofty. But I always wonder. Did they encounter the everyday self-reference problems? Would they care about Britney and her troubles? Did they ever try to tell a loved-one, "Don't take this the wrong way, but. . ."

Probably they did. Russell went to jail for his pacifism, and Goedel died of starvation when his wife died, because he thought he was being poisoned.

It's a tough life out there, no matter how smart you are.

I Want You To Want Me

One of the main things about humans is that a lot of the stuff they want has to do with the desires of other people.

I want to be able to eat, but I want everybody else to be able to eat, too. I want my friends to be happy. I want birthday cake, but it's no fun having it alone: I want you to have some too.

Now, when people judge what is right, or fair, or just, or good, with respect to distributing the good things in the world, they often think in terms of satisfying simple desires or preferences.


The distributive justice of cats? (UPDATE: oh yeah, it's probably more like this.) Photo by Flickr user mvplante, here. (Used under Creative Commons license.)

Utilitarians, in their generous, inclusive way, think in terms of totals: the thing to do is the thing that maximizes such satisfaction. Just add it up for everyone. Usually this means a lot of *sharing*.

Contractarians, in their love of individual freedoms and self-direction, think in terms of rational exchanges. We're both better off if we cooperate, so sometimes it will be in my best interest to give up something in exchange for something else. Usually this means a lot of *I get to keep what is mine.*

Rawlsian contractualists, in their moderate way, think in terms of blind justice. Imagine you don't know who in society you will be, and consider how much inquality of preference-satisfaction you would put up with. Usually this means *You share some, you keep some.*

All different systems. But they're all based on different interpretations of the idea that it makes sense, generally, to arrange the world so that people get the things they want; sometimes this means moving things around; the question is how we think about that.

They also usually share one other striking thing. Namely, that when counting preferences, we only count a person's "personal preferences" -- that is, preferences for what one does or gets, and not one's "external preferences" -- that is, preferences about what other people do or get.

I only recently understood the reasoning behind this. The problem is "double-counting" of preferences. As David Gauthier explains, if I prefer that we each have an equal amount of cake, because we both like it, and if you just want as much cake for yourself as possible, then factoring in all preferences seems to lead -- on any of the views above -- to the conclusion that the right, fair distribution for us is for you to get three-quarters of the cake. But that seems wrong.

The solution is to consider only personal preferences: I like cake; you like cake; we each get half. It doesn't matter whether I want you to have some cake too.

This is highly intuitive in the case where we each end up with half the cake.

I start getting confused, though, when I think about cases in which the outcomes support inequality -- especially continued inequality.

I live in a city with homeless people. They don't want to be homeless. I also don't want them to be homeless. I have a strong external preference for them to be able to satisfy their preferences for a place of their own. Their unhappiness makes me unhappy.

It seems strange to me that this preference of mine plays no role when it comes time to figure out the proper distribution of goods, or the just way of organizing society.

It seems extra strange when you think that our general preference for the happiness of others is one of our better qualities, as humans. One of our more admirable, morally sensitive ways of being. What, this counts for nothing?

I want to say, "You know, it would be better all around if you wanted me to have cake, too." You know. Just saying.

Obvs, my preference for you to want me to want to have cake, too, doesn't get counted. That would be, like, double- or triple- or two-and-a-half-counting or something something . . . I was never any good at arithmetic. Wanting, though, I am an *expert* at: personal preferences, external preferences, you name it.

Theorem: When It Comes To Sex, The Typical Guy = The Typical Girl

Reading The New York Times yesterday, I was mystified by a story on math and sex. It's commonly reported that men have more sex partners than women. Some mathematicians have claimed this is impossible, on the grounds that men and women must have equal numbers of sex partners, since they have sex with each other (bracketing, I guess, the various complexities about homosexuality and "threesomes").

I was mystified because of all the people they asked, no one pointed out that there's a simple confusion here between "median" and "average." The mathematician's proof shows that the average number of partners are the same. But this leaves open the possibility that most men have more sex partners than most women.

As we all know, averages can be the same while distributions are very different. So, for example, if a few women have sex with lots of men, while many women have sex with only one man, then there is an obvious sense in which men have "more" partners: lots of men are having sex with more than one woman, while few women are having sex with more than one man. But the average number of sex partners will be the same.

For those who like this sort of thing, I drew up an example. Remember, the median is the number at which half the sample is above and half is below.

Suppose {1, 2, 3, 4, 5} and {A, B, C, D, E} have sex in the following combinations:

{1A, 1B, 1C, 1D, 1E, 2A, 3B, 4C, 5D}.

The median number of partners for numbers is Med {5, 1, 1, 1, 1} = 1
The median number of partners for letters is Med {2, 2, 2, 2, 1} = 2

There is a sense in which the numbers here have fewer sex partners than the letters: most numbers have only one partners, while most letters have 2. But the average number of partners for each is the same: 1.8.

I don't know if this is what it's like for women and men, but it seems possible. It's weird that none of the experts cited in the article mentioned this. The Times article even shifts between reporting results for "medians" when discussing the received view on sex difference, then moves to averages when discussing the impossibility of such difference.

What The Times should have been reporting on in this story is why the received view is based on medians and not averages. If a few women are having lots of sex, are those women less significant when it comes to making judgments about "how many"? Why so? After all, usually when we say "the typical person," we're talking about the average person. And as the mathematicians show, there's a sense in which the typical woman is having the same number of sex partners as the typical guy.

At least, this is so leaving aside complexities such as men going to prostitutes, who, the CDC researcher mentioned, are "not part of the survey," or going outside the country. These outlier factors may explain differences in averages, if there are any. But there is no need to invoke them to explain differences in medians.

UPDATE: The Times published a follow-up, here. It seems there are differences in reported averages as well as reported medians; indeed, the raw data of what is reported is, in a sense, internally inconsistent.