4 ms·

The paradox doesn't depend on self reference at all, e.g.: Alen: What Bob is about to say is true. Bob: What Allen just said is false.

• sickofparadox 2y ago
  The paradox is the entire block after your colon, and it is still referencing itself.
  • rhelz 2y ago
    chuckle love the handle, and its an interesting point. Let's think about this. When you say "the entire block after your colon", you are reifying a new object, and then observing that that object is self-referential. For sake of argument, let's say that's a valid move. But what are the rules to this game? I mean, can I just say "I'm lying" and then, by fiat, construct a new object consisting of me and you, and claim that this new object is self-referential and therefore you are participating in a paradox too? What about the object which consists of the totality of what the human race has written thus far? Since one of the things we've written is the liar sentence, does that condemn the human race, for all eternity, into hopeless paradox?
• dredmorbius 2y ago
  That would be the "small set of closed relations" case I'd mentioned above. The system of two statements is self-referential, in that it references nothing outside itself, that is, it only concerns what Allen (presuming "Alen" is a typo) and Bob say, but no other larger-world context. A somewhat trivial and contrived counterexample might be: Allen: What Bob is about to say is true and water is wet. Bob: What Allen just said is false and water is not wet. Here, we'd have to consider the truth values of both assertions, whether or not what the other party said is true, and whether or not water is wet. Both assertions would have to be true for the full statement to be true, either assertion being false would falsify the combined statement. And it is possible that both statements are false.