http://www.thebigquestions.com/2011/10/04/big-news/

Steven Landsburg notes that mathematician Edward Nelson has retracted his claim that the axioms of Peano Arithmetic are inconsistent.

The bit Landsburg cites indicates that the retraction was cordial and drama-free, the way a retraction should be--even a retraction of a claim as momentous as this one.

Now, is this kind of event more common in math than in other fields? Is it more common now than before? (Landsburg seems to attribute it in part to the existence of the Internet.) Your thoughts?

Religion apparently makes people happier. Is that evidence for the truth of religion, or against it?

(Of course, it matters which religion we're talking about, but let's just stick with theism generally.)

My initial inclination was to interpret this as evidence against theism, in the sense that it weakens the evidence for theism. Here's why:

1. As all Bayesians know, a piece of information F is evidence for an hypothesis H to the degree that F depends on H. If F can happen just as easily without H as with it, then F is not evidence for H. The more likely we are to find F in a world without H, the weaker F is as evidence for H.
2. Here, F is "Theism makes people happier." H is "Theism is true."
3. The fact of widespread theism is evidence for H. The strength of this evidence depends on how likely such belief would be if H were false.
4. As people are more likely to do something if it makes them happy, people are more likely to be theists given F.
5. Thus F opens up a way for people to be theists even if H is false.
6. It therefore weakens the evidence of widespread theism for the truth of H.
7. Therefore, F should decrease one's confidence in H, i.e., it is evidence against H.

We could also put this in mathematical terms, where F represents an increase in the prior probability of our encountering the evidence. Since that prior is a denominator in Bayes' equation, a bigger one means a smaller posterior probability--in other words, weaker evidence.

OK, so that was my first thought.

But then I had second thoughts: Perhaps the evidence points the other way? If we reframe the finding as "Atheism causes unhappiness," or posit that contrarians (such as atheists) are dispositionally unhappy, does that change the sign of the evidence?

Obviously, I am confused. What's going on here?

Related to: Self-empathy as a source of "willpower" and some comments.

It has been mentioned before that akrasia might be modeled as the result of inner conflict. I think this analogy is great, and would like to propose a refinement.¹

Here's the mental conflict theory of akrasia, as I understand it:

Though Maud appears to external observers (such as us) be a single self, she is in fact a kind of team. Maud's mind is composed of sub-agents, each of whom would like to pursue its own interests. Maybe when Maud goes to bed, she sets the alarm for 6 AM. When it buzzes the next morning, she hits the snooze...again and again and again. To explain this odd behavior, we invoke the idea that BedtimeMaud is not the same person as MorningMaud. In particular, BedtimeMaud is a person who likes to get up early, while MorningMaud is that bully BedtimeMaud's poor victim.The point is that the various decisionmakers that inhabit her brain are not always after the same ball. The subagents that compose the mind might not be mutually antagonistic; they're just not very empathetic to each other.

I like to think of this situation as a collective action problem akin to those we find in political science and economics. What we have is a misalignment of costs and benefits. If Maud rises at 6, then MorningMaud bears the whole cost of this decision, while a different Maud, or set of Mauds, enjoys the benefits. The costs are concentrated in MorningMaud's lap, while the benefits are dispersed among many Mauds throughout the day. Thus Maud sleeps in.

Put differently, MorningMaud's behavior produces a negative externality: she enjoys the whole benefit of sleeping in, but the rest of the day's Mauds bear the costs.

So, how can we get MorningMaud to lie in the bed she makes, as it were, and get a more efficient outcome?

We can:

• Legislate. Maud tirelessly tells herself to be less lazy and exerts willpower to get the job done. This is analogous to direct, blanket government action (such as banning coal) in response to a negative externality (such as once-verdant, now barren hillsides). But it's expensive, and it doesn't always work.
• Negotiate. Maud rewards herself when she gets up on time by taking a hot shower right away or eating a nice breakfast (the latter has a cost borne by MoneyMaud); or she allows herself to sleep in once a week. If MorningMaud follows through, then this one's a winner. Maybe this is analogous to Coasian bargaining?
• Deputize. Maud enlists her friend Traci to hold her feet to the fire. Or she signs up on Stikk, Egonomics, or some similar site.

The analogy's not perfect. (I can't see a way to fit in Pigovian taxes .)

But is it a fruitful analogy? Is it more than just renaming the key terms of the subagent theory--could one use welfare economics to improve one's own dynamic consistency?

¹I got this idea partly from a slip, possibly Freudian (I think I said "externality" instead of "akrasia"), and partly from this page on the Egonomics website.