Hipparchia's Paradox

The most famous cynic philosopher was Diogenes of Sinope, who lived in an old wine jar and told Alexander the Great to get out of his light. But he wasn’t the only cynic; there was a whole bunch of them. The second or third most famous cynic was Hipparchia. (The third or second was Crates, Hipparchia’s husband.) Hipparchia doesn’t seem to have written much if anything, as tended to be the way with the cynics, but history has recorded at least one of her arguments, via an anecdote about an exchange she had with some jackass called Theodorus at a party one time. Here’s how Diogenes Laertius (not to be confused with Diogenes the jar-dweller) tells it:

Theodorus, the notorious atheist, was also present [at Lysimachus’s party], and she posed the following sophism to him. ‘Anything Theodorus is allowed, Hipparchia should be allowed to do also. Now if Theodorus hits himself he commits no crime. Neither does Hipparchia do wrong, then, in hitting Theodorus.’ At a loss to refute the argument, Theodorus tried separating her from the source of her brashness, the Cynic double cloak. Hipparchia, however, showed no signs of a woman’s alarm or timidity. Later he quoted at her lines from The Bacchae of Euripides: ‘Is this she who abandoned the web and women’s work?’ ‘Yes,’ Hipparchia promptly came back, ‘it is I’. But don’t suppose for a moment that I regret the time I spend improving my mind instead of squatting by a loom.’ [Lives of the Ancient Philosophers 6: 96-8; pp45-6 in Dobbin]

I’ve quoted the context as well as just the argument, the alternative being to quote it out of context. I think it’s pretty clear that Hipparchia is the winner of this story, although it’s possible the reality of the situation was pretty unpleasant for everyone concerned. But having acknowledged the context, I’d like to think a bit about the argument in isolation. Here’s the argument laid out neatly:

• Anything Theodorus is allowed, Hipparchia should be allowed to do also.
• If Theodorus hits himself he commits no crime.
• So neither does Hipparchia do wrong in hitting Theodorus.

The first premise is about universalizability: morality is supposed to apply equally to everyone. It’s a bit less clear what the theoretical basis of the second premise is. It seems like a part of most people’s common sense morality that if someone wants to hit themselves then that’s their own business, and while it might be inadvisable, it isn’t immoral. Common sense morality changes from place to place, but I guess this is part of it that my society has in common with Hipparchia’s. You could explain the truth of the second premise in various ways, some of which will mean qualifying or restricting it, and I think that how exactly we explain it will affect how the paradox gets resolved. The conclusion is meant to be absurd, showing that something is wrong with either the premises or the inference.

I think the most obvious way to try to resolve the paradox is to interpret the permission in the second premise as being explained by a general permission for people to hit themselves, rather than a general permission to hit Theodorus. The action that Theodorus is allowed to do is hitting oneself, not hitting Theodorus. Hipparchia is allowed to do the action hitting oneself too, so universalizability is saved.

There’s a problem with this, though: Theodorus is also allowed to do hitting Theodorus. He’d better be, because if an action is immoral under some description, then it’s immoral. This means there is something he’s allowed to do and Hipparchia isn’t, and so universalizability isn’t saved. Universalizability isn’t the idea that some of morality applies equally to everyone; it’s the idea that all of morality applies equally to everyone. Now, I don’t mean to be disingenuous. I’m not saying that Hipparchia’s paradox shows that universalizability is bunk; I’m just saying there’s more work to do. I don’t think there can be much doubt that it somehow matters that the description of the action as hitting oneself applies to Theodorus’s action and not Hipparchia’s. It just doesn’t resolve the paradox completely, and it’s perhaps more of a restatement of the paradox than anything else. Sometimes a restatement of a paradox is more or less all you need, but in this case I don’t think the restatement is enough.

Here’s another line of attack. Maybe on any given occasion it really is only OK for Theodorus to hit Theodorus if it’s OK for Hipparchia to hit Theodorus. The difference is that occasions when he hits himself will be those rare occasions when he wants to be hit, whereas occasions when she hits him are likely to be occasions when he doesn’t want to be hit. (And also he won’t hit himself harder than he wants to be hit.) This kind of reasoning is behind some anti-paternalist thinking in political philosophy. The classic anti-paternalist work is On Liberty, which was published under John Stuart Mill’s name but was probably coauthored with Harriet Taylor Mill, if you take its dedication literally. (It’s possible the Mills were the greatest philosophical power couple since Hipparchia and Crates. I can’t think of a greater one in the roughly 2150 years betweeen them, although perhaps you can, and perhaps there’s an obvious one I’m missing. [UPDATE: A friend pointed out I forgot Abelard and Heloise.]) They argued that the state shouldn’t be interfering with you if you’re not doing anyone else any harm. Here they are:

The object of this Essay is to assert one very simple principle, as entitled to govern absolutely the dealings of society with the individual in the way of compulsion and control, whether the means used be physical force in the form of legal penalties, or the moral coercion of public opinion. That principle is, that the sole end for which mankind are warranted, individually or collectively, in interfering with the liberty of action of any of their number, is self-protection. That the only purpose for which power can be rightfully exercised over any member of a civilised community, against his will, is to prevent harm to others. His own good, either physical or moral, is not a sufficient warrant. [On Liberty: p17]

People disagree over how far you can reconcile this with the consequentialism you find in Utilitarianism, but if you’re trying to reconcile them it usually goes roughly as follows. People will do things that have good consequences for themselves, so if their actions don’t have bad consequences for anyone else then they don’t have bad consequences for anyone. Given consequentialism, that means the actions aren’t bad. That means the state shouldn’t be interfering with them. It’s a bit of a Swiss cheese of an argument, and I think it remains so even if you’re properly doing justice to it, but I also think they were on to something important.

A classic example of paternalism is seatbelt laws. Idealizing a bit, the set-up is this: by not wearing a seatbelt you’re not putting anyone at risk but yourself. But by having laws demanding people wear seatbelts, you can save lives. Let’s consider a couple of things a libertarian might have to say about this:

• “If I value my life so much and my convenience so little that the small chance that wearing a seatbelt will save my life is worth the inconvenience of wearing one, then I will wear a seatbelt.”
• “The only person who stands to get hurt here is me, and I’m fine with it. Mind your own business.”

The first is a simple consequentialist argument: we don’t have to worry about people not wearing seatbelts in situations where the expected consequences are negative. (It also takes the relative value of someone’s life and convenience to be the relative value they themselves assign to them, but maybe that’s not so silly at least in the case of most adults.) The second libertarian response is harder to categorize. It can still be made out as consequentialist in a way, but it says that people are allowed to waive consideration of negative consequences to themselves. The first objection, where it applies, flows straightforwardly from a simple consequentialism that says the right thing to do is the thing with the best consequences. The second applies more generally, but it says that sometimes it’s OK to do the thing that doesn’t have the best consequences. If we’re allowing people to waive consideration of consequences to themselves in the moral evaluation of their own actions, this raises questions about what other kinds of waivers are allowed:

• Can I waive consideration of consequences to myself in the moral evaluation of someone else’s actions?
• Can I do this on an action-by-action basis, or at least a person-by-person basis, or do I have to waive it for all people or all actions if I waive it for one?
• Can I waive consideration of some but not all negative consequences to myself?
• Can I waive consideration of bad things happening to me even if someone else cares about me and so these would also be negative consequences to them?
• Are there ever situations where someone can waive consideration of a negative consequence to someone other than themselves?

None of these seem to me like they have obvious answers, with the possible exception of the last one, even if we grant that people can waive consideration of harm to themselves in the moral evaluation of their own actions. I expect some readers will think some of the answers are fairly obvious (and that the last one is obviously obvious), or will at least have views on some of the questions, perhaps based on the literatures which presumably exist on each of them. To be clear, I’m not saying that a consequentialism with a self-sacrifice caveat can’t be made coherent. You could say that an action is permissible iff it either maximizes expected utility or has an expected utility for other people at least as high as the expected utility for other people of some permissible action. That seems to get the right results. The problem I have is that if waivers are a thing, then there are other waivers we might want to include in our theory as well, and after a while our theory might end up not looking much like consequentialism at all.

One way to avoid these questions is to deny that people can waive consideration of themselves in the first place. But then Hipparchia’s paradox comes back, at least a little. The problem with this simple consequentialist response to the paradox is that people don’t always do what’s best for them. Unless we supplement the response somehow, it will mean that whenever Theodorus hits himself and it isn’t what’s best for him, he is doing something wrong after all. (At least when he had enough information to work out that it probably wouldn’t be best for him.) Is this what we want to say?

I can sort of see how some people might want to bite this bullet. If you’re an agent-neutral consequentialist, then you think that the only information relevant to whether an action is wrong or not is how good its consequences are. Who did the action isn’t relevant. So this kind of consequentialist should say that Theodorus hitting himself really is immoral whenever it’s inadvisable. If someone gets on their high horse with you about how you’re not doing what’s best for yourself, they actually do have the moral high ground. Perhaps this is right. But it’s weird.

I don’t really feel like I’ve got very far with this. But my main aim was to present the argument as something worth thinking about, because I do think it’s worth thinking about. I’ll close by presenting another argument, which is also a Swiss cheese of an argument, but which I’m also worried might be on to something.

• Hipparchia’s paradox shows that fully agent-neutral consequentialism is absurd.
• The only promising arguments for consequentialism are arguments for fully agent-neutral consequentialism.
• So there are no good arguments for consequentialism.

References

• Dobbin, R. 2012: Anecdotes of the Cynics, selected and translated by Robert Dobbin. Penguin Random House.
• Mill, J. S. 1859/2011: On Liberty, Project Gutenberg ebook #34901, http://www.gutenberg.org/files/34901/34901-h/34901-h.htm
• Mill, J. S. 1863/2004: Utilitarianism, Project Gutenberg ebook #11224, http://www.gutenberg.org/files/11224/11224-h/11224-h.htm