5 ms·
I don't understand your reasoning to justify that "half of all possible statements are true". It seems to me that of the undecidable statements, some (such as t
by a3_nm 15y ago
I don't understand your reasoning to justify that "half of all possible statements are true". It seems to me that of the undecidable statements, some (such as those of Gödel's construction) are true or false, but that some simply have no truth value. Did I get something wrong?
[Indeed, this is all assuming that ZFC is consistent. Thanks mjw.]
- p4bl0 15y agoThat's also how I understand it. Anyway, you people should upvote a3_nm, he is the one who did the job (for Falso and the Security Password Checker), I only encourage him and host the pages :-).
- omaranto 15y agoI wouldn't say undecidable statements have no truth value. In any given model of set theory each statement is either true or false. If something is provable it is true in every model, and if something is refutable it is false in every model. Undecidable statements can't be proved to be either true or false within a given proof system, but (1) in any given model are either true or false, as I said, and (2) can sometimes be shown to be true (or false) by arguments outside of the proof system considered.