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


georgie wrote:
The context of my statement was a response to a discussion about
the how meaningful things are.

Well, the falsfiability criterion was more from science than math.
As has already been pointed out, existentials are hard to falsify
and universals hard to verify. As should be obvious, as a general
rule, if "x" is meaningful then "not x" is equally meaningful, since
the meaning of "not" is well-known. But one of them will be
falsifiable
and the other will not, in a logical context, so that guideline doesn't
work as well here.

In science, however, it still works; it sort of admonishes you that
you should ALWAYS be looking FOR general laws (universals) and
AVOIDING even hypothesizing the existence of particular individual
things that aren't "proven" from what you already have. It's sort of
like Occam's razor. In other words, the scientific position (as
opposed
to the religious one) is that nothing that we have thus far observed
qualifies
as a supreme being. You can take that as a tenet of a scientific
theory
on the grounds that if such a being exists, it is perfectly capable of
falsifying
it in a way that we can understand.

Meaning in the logical context arguably comes from proofs.
Theorems have meaning.
Everything else arguably doesn't, simply because it could have
the opposite truth-value in a different model.

.

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