On 4/7/2013 8:39 PM, William Elliot wrote: > On Sun, 7 Apr 2013, fom wrote: > >> 1) >> >> A new axiom or set of axioms not directly asserting the continuum >> hypothesis would be required. > > No, there's an old axiom, Occam's Razor. >
I would hope that you might consider applying Ockham's razor more judiciously in the future.
If you bother to read the full posting of what I wrote or thought to consider whether my axioms actually do reflect what I suggest they might, then Ockham's razor would be eliminating a great many forcing models.
I am not claiming that an unmodified set theory is not interesting in its own right. Forcing depends on partiality. The inherent partiality of the current sense of the paradigms means that "truth persistence under forcing" may be the only sense of "truth" possible. But, it is not the classical definition.