Re: The shocking truth about the naturals

On Aug 28, 12:46 pm, aatu.koskensi...@xxxxxxxxx wrote:
You're deluded. In reality, only uncountable and finite sets exist.
Countable sets are just a piece of fantasy.

There is no symmetry inherent in the arguments,
and you know it.

This thread is highly relevant to the other one in which such
insufferable
naifs as Rupert ask why people can't just argue their case in a
"civil"
manner.

It would be clearer to insist that "models" or even "sets"
are just "a piece of fantasy".

Nobody is alleging that any axioms are "true" AS OPPOSED to
fantasy. The axioms can ALL be fantastical for all we care.
We are only asking what follows from them, NOT how they got
to be established in the first place.

Countable v. its powerset in ZFC is a matter of DEFINITION in any
case.
As long as you have models, and as long as your method of model
formation relies on something like the axiom of separation, you will
have to countenance the existence of things that your model claims
don't exist. The axiom of sepration produces TWO subsets, one
of the things in your domain and one of things IN SOME LARGER
SET OUTSIDE it. If your model has a ZFC-set as its domain then
you are acknowledging from the outside that your model's opinion
about these questions IS NOT definitive (because it may not be
including
things that must exist).

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus


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