Re: Why? [was Re: Cantor`s powerset theorem is false?]


William of Ockham wrote:
david petry wrote:
William of Ockham wrote:

My objection is that his claim is so wide-reaching that it rules out
many things as meaningless which many people would count as meaningful
(including the assertion that there exists a set containing every
subset of N, which is not on the face of it meaningless).

As I understand it, you are claiming that it is obvious to you that the
assertion that there exists a set containing every subset of N is a
meaningful assertion.

No. Do read what I say. I did not say it was obvious that the
assertion was meaningful. I said "It is not not on the face of it
meaningless", i.e. that it's not obvious that it is not meaningful.

So let me ask you a question. Applying the same logic or intuition
which forces you to believe that such an assertion is meaningful, would
you not also be forced to the conclusion that the assertion that there
exists a set containing every set is meaningful? I'd really appreciate
it if you would go into some detail about why or why not that would be
the case.


Again, while it is not obvious that it is meaningful, it is not obvious
that it is not meaningful. It is not the case, of course, but once
again I think you are getting confused being something not being the
case, and something not being meaningful.

It's not "on the face of it" meaningless to assert the existence of a
set containing every set. It seems to assert something meaningful, but
false.

It seems rather odd that the "set of all sets exists" is
false. I believe you say that because a theory that
allows such a thing might lead to a paradox. But Cantor's
diagonal proof that leads to "larger than infinitely
sized" sets is not looked at as paradoxical. It sure
is strange what some people think is meaningful.

.

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