Re: Why Regularity?


Rupert wrote:
The reason why we have the axiom of regularity isn't really anything to
do with the liar paradox. It's just an indication of the fact that we
only want to study well-founded sets. In ZF-regularity we can prove
that the class of well-founded sets is a model for ZF with regularity
anyway.

I am speaking in a more philosophical manner, I see ZF as a theory of
finding consistency of statements of the that who always lies. All sets
in ZFC are lies. Yet , I said such M that all of its statements are
lies do have consistency, it is the consistency of the total lier,
though I call the later ( the opposite truth teller ) anyhow. This is
philosophical. Putting the axioms of regularity confines us to the lies
that are fairly consistent, it makes us avoid the lier paradox, which
reveal the philosophical truth to ZF. ZFC with Regularity is consistent
logically, but philosophically speaking, it is a system of consistent
lies, see the ulternative that I have proposed, I think this is the
HONEST set theory . But It seems not so practical. The Lieying ZF ( the
standard one ) is easier to deal with. And since all what we require
from a set theory is consistency, then it doesn't really matter if ZF
is philosophically a consistent lie. Since it easier to deal with, then
let it.

Zuhair

.

Relevant Pages

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  • Re: Why Regularity?
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