Aatu Koskensilta wrote: > Jiri Lebl wrote: > > Good thing you admit it. Yes you are very much mistaken. For example > > take A be the statement: "Is P(N) = aleph_1 true in ZFC". > > That's a question, and non-sense at that; sentences aren't true or false > in theories.
That's EXACTLY the point. It's true in one model of ZFC and false in another model of ZFC. Therefore A is nonsense, even though it does seem well formed. Most definately neither "A" nor "not A" is true. I could have used the statement "Banana question red appricot three" which also is neither true nor false. So there must be something more to state then just "A, not A" always exhaust all possibilities. Obviously it there are assumptions of what A is.
> Zick is no doubt mistaken about many things, but your > rebuttal of his ideas is itself rather confused. The continuum > hypothesis does not provide an example of an A such that "A, not A" do > not exhaust all possibilities.