Lately I’ve been reading a lot and working things over, so not much to say on the philosophy of mathematics front. . . maybe not for a little while.  I’ve got some ideas brewing on the following topics: (1) category theory vs set theory foundations, (2) whether the application of SU(n) in physics and the discoveries derived from that application are “more surprising” than widely discussed examples in the history & philosophy of science (e.g. the discovery of Neptune), and (3) whether a wannabe-nominalist who accepts naturalized epistemology can answer Burgess and Rosen’s anti-nominalist arguments.  Even granting that a blog is a space for working through ideas in progress, I’m not sure I’m ready to say a whole lot about these things just yet, at least not until I work through at least some of the stack of books and articles I’m accumulating.

So, dear mathematically inclined readers (all three or four of you!), you’ll have to settle for something non-mathematical but hopefully interesting.  I had a very nice, intellectually stimulating evening last night in two parts.  It was a nice break from mathematical/logical slogging that lead to some free thinking about more open-ended questions.  First, Jason Hanna from U Colorado gave a colloquium titled “Ulysses Contracts and the Moral Relevance of Actual Consent”.  Second, Beth and I had dinner with a new professor in the political science department and his wife that lead to an interesting discussion of the voter paradox.  I will explain for you what these contracts are and what this paradox is, then relate the two issues and share some thoughts on them.

Ulysses contracts: Ulysses tells his crew to tie him to the mast and plug their ears.  Sail past the sirens so he can hear them sing.  Do not, under any circumstances, untie him.  Even if he begs, he insists that they not let him down.  A Ulysses “contract” (the word is a bit misleading since they need not be technically binding) is when one requests at timeA not to have one’s requests at a later timeB honored.

The philosophical issue that arises is how to deal with cases where we’re instructed by someone not to obey their future instructions.  These are not just philosopher’s fantasies.  Examples may arise in applied medical ethics.  For example, an expectant mother may tell her doctor not to administer an epidural even if she begs for it.  Suppose she does indeed beg for the epidural.  What is the ethical thing for the doctor to do?  How can the doctor best respect the woman’s autonomy?

In different cases our intuitions may be different.  We may think that Ullyses crew definitely should not let him down, but that the doctor definitely should administer the epidural.  The philosopher’s task is to see if there’s a principled way to account for all of the judgments that seem intuitive.  Here’s one suggestion: Honor the most recent request unless it’s obviously deficient.  Ullyses’ request to be let down is paradigmatically deficient because he’s under the spell of the siren song.  But the mother’s request is not obviously deficient.  It is made under the duress of pain, to be sure, but there’s a sense in which that makes it a more informed choice than her earlier decision and hence closer to the optimum.  The matter is debatable, but that implies that it’s not obvious.  This was not the account that our speaker gave.  He was pressed by Greg Landini and Richard Fumerton to come up with a “pure case”.  It seemed like all of the cases where we have the intuition to honor the earlier choice were cases where the later choice was made under the influence of addiction, delusion, mental illness, etc.  Is there any case where we are inclined to honor the earlier choice even though the latter choice is closer to optimally rational?

Which brings me to:

The voter paradox: The expected utility of voting is really, really low. After all, one vote is not going to have any impact on the election. So it is irrational to vote.

Of course, this isn’t a paradox if you accept the conclusion, but I think that a lot of people will be disinclined toward accepting that conclusion and it is at least worthwhile to explore the account of rationality that leads to the conclusion and to think about alternatives.  Before we do that, however, I want to return to the Ulysses contracts and offer what I think may be a pure case.  The relevance of the voter paradox will become clear as we proceed, so keep it in mind.

Suppose I tell my wife the following.  We’re going to the gym tomorrow before class.  I know that I’ll want to sleep in, but no matter what I say don’t listen.  Drag me out of bed if you have to.  Even if I tell you that I take everything I’m saying now back, I want you to bang on pots and pans until I get up…  Ok, you get the picture.  It’s at least plausible that my wife should honor my initial decision even though I take it back in the morning.  In a discussion of weakness of the will, Donald Davidson argues (citation not handy) that it can be irrational to brush one’s teeth if one believes one will in the future brush one’s teeth regularly.  That case is similar to this one.

But wait!  When in the morning langor rises, reaching to shut off the alarm isn’t it the case that I’m making a deficient decision, one clouded by grogginess.  So is this really a pure case?  I say that it is.  In fact, in the morning I’m more informed about how good it will feel to sleep in.  Furthermore, I’m not under the influence of addiction or mental illness or anything like that.  In particular, I reason that skipping the gym just this once maximizes my expected utility.  After all, one day skipped is not going to have any impact on my overall health. My decision to sleep in is more rational than my decision the night before to tell my wife to drag me out of bed whatever it takes!  (By the same type of reasoning that led to the voter paradox, that is).

In my gym case, the intuition to honor the earlier decision is, I maintain, at least respectable.  But it’s not a case where the later decision is over-ruled because it’s deficient in some obvious way.  I claim, in fact, that the later decision is more rational than the earlier decision by the standard of expected utility.  Yet, the voter paradox seems to point to some problems with that standard and I think so does the gym case.  After all, if every rational voter reasons that it’s irrational for them to vote then only irrational people will vote, which can’t be good.  Similarly, if I reason every morning that I should sleep in rather than go to the gym then I’ll never go to them gym, and this will have predictably rotund consequences.  Just as the voter paradox relies on the supposition that other people will not reason as you do, the gym case relies on the supposition that my future selves will not reason as I do now.

So, here is what I think is suggested.  Rationality is not a simple matter of maximizing expected utility with each individual decision taken in isolation.  If it were, the person who tells him or herself every day that tomorrow is the day that they’ll start eating healthy and working out would be rational, even if tomorrow never comes.  We need to make, as it were, Ulysses contracts with ourselves in order to consistently make decisions that have good results in aggregate, even if in each of the moments that we make them they have low expected utility.  It really is (sort of) like this for me, with a internal voice of conscience speaking: “Self, you swore to yourself that you’d go to the gym and I’m holding you to it even if you don’t like it”.  I don’t think that the voter paradox is really that different.  To be sure, it’s members of a group (i.e., citizens of a democracy) making a sort of Ulysses contract with one another to act as an aggregate in a way that everyone agrees is good in aggregate but everyone recognizes does not maximize expected utility individually.  The voice of conscience thus speaks on behalf of the shared interests of the group rather than the interests of the trans-temporal self, but I don’t see that this is a difference that makes the solution good in the gym case but bad in the voter case.

So, what’s the upshot of all of this?  Well, maybe my pure case is not so pure afterall, if voter paradox style reasoning is in fact deficient reasoning.  My discussion has suggested that it is deficient for the following reason.  The locus of rationality ought not to be thought of as the present self.  Assessments of rationality may equally well be made from the standpoint of the transtemporal self (which argues: sure that makes sense now, but what if you always thought like that) or from the standpoint of shared interests and intentions (which argue: sure that makes sense for each of us individually, but what if we all thought like that).  From these standpoints, the gym case and the voter paradox reasoning are obviously deficient since such reasoning will leave me fat and governed by morons, maybe even rotted of tooth. It is the deficiency of these decisions (not to go to the gym, brush my teeth, vote, etc.) that warrants the voice of conscience to enforce (e.g.,through guilt) the Ulysses contract.

Your thoughts?  Are there reasons to answer the gym case or the voter paradox differently than I have?  Are there relevant disanalogies?  Have I left the self too splintered into too many “voices”?  See my post on Lackey’s counterexamples to knowledge as the norm of assertion for more splintering along these lines (though not exactly the same); I worried then as I do now that the kinds of analyses I’m suggesting will leave us all with philosophical mutliple-personalities.