tl;dr: This is a magic trick, not a formal system. Reminds me of the definition of a magic trick from "The Prestige": “Every great magic trick consists of thr

tl;dr: This is a magic trick, not a formal system. Reminds me of the definition of a magic trick from "The Prestige": “Every great magic trick consists of three parts or acts. The first part is called "The Pledge". The magician shows you something ordinary: a deck of cards, a bird or a man. He shows you this object. Perhaps he asks you to inspect it to see if it is indeed real, unaltered, normal. But of course... it probably isn't. The second act is called "The Turn". The magician takes the ordinary something and makes it do something extraordinary. Now you're looking for the secret... but you won't find it, because of course you're not really looking. You don't really want to know. You want to be fooled. But you wouldn't clap yet. Because making something disappear isn't enough; you have to bring it back. That's why every magic trick has a third act, the hardest part, the part we call "The Prestige".” Kind of abstract but it's like... - The Pledge: Hello convict, here is your sentence. - The Turn: Actually just kidding, look at this giant loophole in my sentencing. Wow! Expectations subverted! - The Prestige: Haha, no, I'm just messing with you. There's no loophole but you lacked the context to discern that in The Turn phase. edit: This is pretty interesting. As the wiki says, how one defines a "surprise" is the whole bugger of the thing. If you use the magic trick metaphor, "surprise" is reframed as "context." The reason it's so murky trying to pick apart what actually happened is hard is because that's the point of the system. It's designed to be un-figure-out-able. I would love to know how you'd formalize a system whose output is "lack of context" edit2: Also if you zoom out a level, giving someone a link to the Unexpected Hanging paradox page is a repetition of the same Pledge->Turn->Prestige pattern - The Pledge: Here's a wikipedia page. You've looked at information on wikipedia pages. You share my confidence this info on this page will adhere to logical rules. - The Turn: Oh but buh-bam, now you are busy trying to unscramble a paradox. - The Prestige: You can't figure out paradoxes, that's their point. I will, however, confess this is a terrible magic trick.