Cosmologists HATE him: I'm now a halfer about sleeping beauty because of this one weird trick

This post presupposes knowledge of the sleeping beauty problem and will be tough going if you don’t have it. Click here for more info.

I’m a simple man. I work on ethics and political philosophy for the most part. I don’t have no truck with dark arts like mathematical philosophy, and witch-magic like calculus. Yet I saw something in a dream that frightened me.

I used to be a thirder. I’ve even argued for it on this blog, but one day I woke up with this idea like a bolt from the blue. I’m concerned that a simple reductio absurdum shows that if the thirder position on sleeping beauty is right, we must take on a number of absurdly strong cosmological and physical positions.

Suppose you think that, on the scientific evidence, there is a 50/50 chance that we are in a many-worlds interpretation universe. This is in some sense equivalent to God flipping a coin to decide whether the universe will be many worlds or single world. Now you wake up in the morning. You know that if you live in a many-worlds interpretation universe, an infinity of you will make this observation. You know that if you don’t, one of you will make this observation. There is of course nothing special about waking from sleep, any moment will do.

It seems to me that if you’re a thirder in the sleeping beauty case, you should update your beliefs to be infinitely near certain that the many worlds’ interpretation is true if you started out thinking that the probability is anything greater than zero.

But this leads to interesting problems even if you believe the reasoning in the many worlds case. I’m not up on transfinite probabilities, but, for example, suppose there were some highly unlikely theory T (let us say one billionth as likely as the many worlds theory) which suggests there are even more worlds than in the many worlds interpretation, a higher cardinality of infinity. Now observe:

(Number of times where you have observation X on theory T)*(prior probability theory of T theory) > (Number of times you have observation X on many worlds theory)*(prior probability theory of many worlds theory)

If you place any finite probability on the truth of T, this should come out true, I think? Though again, I’m not up on transfinite probabilities. So, on thirder type reasoning, you should believe T is infinitely more likely than many worlds, and since there are unfathomably more worlds on T theory than on many worlds theory- but frankly this seems like cheating. In fact, we can keep constructing theories that imply the existence of arbitrarily more worlds. A lot of people, myself included, will find even the initial inference that we need to believe the many worlds interpretation is vastly more probable than single worlds interpretations highly implausible.

But it gets worse.

If one is faced with the question “does the universe eternally reoccur” – if the prior is >0, and you are a thirder, you must conclude yes. Similarly, if you’re pondering two hypotheses- on one of which you are unique, and on the other there are countless simulated versions of you, you must prefer the latter on thirder reasoning for any arbitrary theory. Even worse, we can just keep making theories with bigger and bigger numbers of us all day.

We can’t get out of this by just rejecting the possibility of actual infinities. Consider the theory T*. On T*, there are a finite but enormous number of you. Let’s say greater than (100^100^100^100^100…^100) of you experiencing this present moment in finitized version of the many worlds interpretation. Unless T* is unimaginably prior-improbable, it will vastly outweigh the standard view that there’s only one of you.

The answer seems to me to reject thirderism, and take these results as a reductio ad absurdum of the position. If anyone has any alternate proposals, sound off in the comments.

Also, If:

1. This is a genuinely novel idea, (v. doubtful) and

2. Not obviously wrong to someone who knows what they’re talking about and

3. You have some expertise in the area

Let me know if you’re interested in writing a paper on it.