Re: Why Regularity?


Rupert wrote:
zuhair wrote:
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

There is a mathematical analysis of the liar paradox. Tarski proved
that no language can define its own truth predicate. That's how the
liar paradox is avoided in mathematics.

Tarski is wrong! see set theory I have proposed, it has no problem with
a universe.
The set of all things in thereselfs, defines its own truth predicate.
see the set theory I have proposed, were I need you to formulate the
infinity axiom in it, that is if you are willing to help me.

As I say, I don't see what the liar paradox has to do with the axiom of
regularity.

.

Relevant Pages

  • Re: Why Regularity?
    ... finding consistency of statements of the that who always lies. ... ZFC with Regularity is consistent ... There is a mathematical analysis of the liar paradox. ... I said "no language can define its own truth predicate". ...
    (sci.math)
  • Re: Why Regularity?
    ... do with the liar paradox. ... that the class of well-founded sets is a model for ZF with regularity ... finding consistency of statements of the that who always lies. ... from a set theory is consistency, then it doesn't really matter if ZF ...
    (sci.math)
  • Re: JSH: Logic and paradox
    ... such examples like the liar paradox and even JSH ideas are consistant in the sence they show inconsistancy in the current state of logic and cantor set theory. ... are either inconsistant or incomplete. ... axiom system at hand ...
    (sci.math)
  • Re: Why Regularity?
    ... that the class of well-founded sets is a model for ZF with regularity ... finding consistency of statements of the that who always lies. ... Putting the axioms of regularity confines us to the lies ... There is a mathematical analysis of the liar paradox. ...
    (sci.math)
  • Re: JSH: Logic and paradox
    ... the idea is similar to liar paradox like euh bogus. ... i dont usually support JSH ideas, but i dont like the current bogus state of logic and cantor set theory. ... such examples like the liar paradox and even JSH ideas are consistant in the sence they show inconsistancy in the current state of logic and cantor set theory. ...
    (sci.math)