Unexpected Rationalussy Paradox

The unexpected rationalussy paradox is a paradox concerning one's expectations of a future event when one is told that it will happen at an unexpected time. The exact nature of the paradox is not agreed upon by philosophers, and it is variously interpreted as primarily a logical or an epistemological paradox.

## The Paradox

Eliezer Yudkowski tells you that he is going to tweet (or xeet) the word "rationalussy" in 2023, but that the day will be a surprise. More specifically, you will not be able to know what day it is going to occur on until he actually tweets it.

You conclude from this that he will not tweet it for the first time on Dec. 31, since then the day would not be a surprise: You would know as soon as 12/31 midnight comes around that he would be tweeting it on Dec. 31, since he had not tweeted it on any other day, and it is the last day of the year to do it. You therefore buy lots of NO shares in the corresponding market (though not too many - after all, he could tweet "rationalussy" multiple times, with only one of them being on the last day).

However, you then realize that it can't happen on Dec. 30 either. After all, if it hasn't happened by the end of Dec. 29, then you would know on midnight, Dec. 30 that it was going to happen that day, since you've already eliminated Dec. 31 as a possibility. And the same reasoning can be applied to Dec. 29, Dec. 28, and so on, all the way down to the current date. You conclude that was Yudkowski has said is impossible. There is no way he can tweet the word "rationalussy" in 2023 while keeping the day a surprise. So much for being a rationalist! You go about the rest of your year feeling smug about having schooled Eliezer Yudkowski in basic logic.

Then, on Dec. 29, 2023, Eliezer Yudkowski tweets the word "rationalussy", in a total shock to you, and to the market on the subject. Despite your seemingly valid argument, every part of Yudkowski's original announcement was true. He did tweet the word "rationalussy" in 2023, and you had no idea what day it was going to be until he actually made the tweet, despite being told in advance that he would do it on a surprise day.

The paradox asks how it is possible that the statement of the surprise is true despite the seemingly valid argument that it cannot be. Analysis hinges on what exactly is meant by surprise.

## Analyses

### Logical solution

One school of thought treats the paradox as a purely logical paradox, devoid of any epistemological considerations. When Yudkowski states that we will not know the day of the tweet in advance, this school treats this as meaning that we will not be able to deduce the day of the tweet from his assertion, as well as the fact that "rationalussy" has not been tweeted on any prior day. In other words, Yudkowski's statement is interpreted as,

"I will tweet the word 'rationalussy' in 2023, but you will not be able to validly deduce the day on which I will first do it using this statement and the fact that I did not tweet it on any previous days as premises."

This statement appears problematic because it is self-referential, thus raising the possibility that the paradox may have a similar solution as the liar paradox, the knower paradox, and similar self-referential statements. However, Frederic Fitch has shown that this statement can be formalized with a Godel numbering scheme, i.e., that for any set of arithmetical sentences φ1, ..., φn (which can be though of as standing in for the statements that "rationalussy" will be tweeted on the nth day after the announcement is made), there is some sentence ψ that is equivalent to '[φ1 and it is not provable that ψ implies φ1] or [φ2 and it is not provable that (ψ and ¬φ1) imples φ2] or ... or [φn and it is not provable that (ψ and ¬φ1 and ... and ¬φn-1) implies φn]'. The sentence ψ is a formalized version of Yudkowski's statement and is provably false by more or less the same argument used in the paradox to prove Yudkowski's statement false.

This analysis may shed some light on the paradox, but it does not explain why Yudkowski's statement actually ends up being true. Clearly his statement can not be equivalent to the self-contradictory ψ if it actually holds true in the real world, so perhaps the flaw in the paradoxical reasoning is assuming that it can be treated as equivalent.

### Rationalussy solution

One proposed explanation is that the paradox arises because you are not thinking rationalussy enough. While the argument made to show that Yudkowski cannot tweet the word "rationalussy" on a surprise day may seem *rational,* it is not *rationalussy*. This distinction explains why the argument is not able to correctly predict when the word "rationalussy" will be tweeted.