Re: Largest Set in ZFC?

On Mar 8, 9:45 am, "Peter Webb" <webbfam...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:

I wrote:

"I don't know the motivation of the actual people who wrote it, but
the
reason I personally would give is this: We don't NEED to be any more
specific, since separation does the rest of the job for us to get to
the specific set w that we want."

*** I know much less about this topic than you do, but it seems there is a
more fundamental reason for the vagueness of the definition of X. If anybody
could produce a specific such X, then they would have a model of ZF (a
collection of sets that satisfy ZF).

I don't see that at all.

What was asked boils down to why not just put the "and no more
elements" clause in the axiom itself. If we put that clause in the
axiom itself, there would be no harm. But it's not necessary since we
get it from separation anyway.

This would prove the consistency of ZF.
AFAIK, there is no theoretical reason why such a set X could not be
described, but none ever has, and its seems pretty obvious that none ever
will. Hence the requirement to vague it up a bit.

No, such a set IS described. We call it 'w'. This has nothing to do
with consistency.

MoeBlee

.

Relevant Pages

  • Re: Further on the proper use of the notion of *time* in science
    ... It is permissible to challenge an axiom, ... is always propagated in empty space with a definite velocity c which is ... Not such a gentleman, and bigoted Roberts: ... A man of intelligence and reason would determine something was seriously ...
    (sci.physics.relativity)
  • Re: Is sentience an emergent brain behavior?
    ... axiom believed to be obviously true. ... I suspect your belief that iterating operant conditioning ... and wrote off the critics of evolution via natural selection as ... Keep in mind there is no logical reason to be logical ...
    (comp.ai.philosophy)
  • Re: What are the chances of....
    ... People who believe in gods are, in the main, far more reasonable than ... "popularity falsity"), and how certain characteristics in populations ... Now if a believer wants to take the existence of God as an *axiom*, he can be perfectly reasonable, even flawlessly logical, in making deductions and inferences from that axiom. ... So I argue that both believers in God and non-believers can each use reason to deduce things from their respective axiom systems. ...
    (talk.origins)
  • Re: Which anime characters would you NOT want to wake up in bed with?
    ... if sober" clause, not on the "oh shit I'm gonna die" clause, because I ... Same reason as above, and also because I'd ... Because my mind would COMPLETELY ... S'LITTLES: Feel the loli. ...
    (rec.arts.anime.misc)
  • Re: Is sentience an emergent brain behavior?
    ... trust the power of correctly structured logical argument. ... axiom believed to be obviously true. ... I suspect your belief that iterating operant conditioning ... Keep in mind there is no logical reason to be logical ...
    (comp.ai.philosophy)
Loading