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Topic: TRANSFINITE would be very weak if there was an alternate theory
Replies: 284   Last Post: Jan 4, 2012 12:18 AM

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 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: TRANSFINITE would be very weak if there was an alternate theory
Posted: Jan 4, 2012 12:18 AM

> > > MoeBlee wrote:
> > > > "And indeed set theory is not consistent with the claim that
> > > > there are only finite sets. Set theory is not consistent with the
> > > > claim "there does not exist an x such that there is no bijection
> > > > between x and some natural number". And that's all you [WM] need to
> > > > say
> > > > about it.

OK I see how you try to substantiate sentence 1 with sentence 2.

But even sentence 2 is not true.

In HARD CONCRETE SET THEORY

E(y)A(x) x e y <-> P(x,y)] & PRV[E(y)A(x) x e y <-> P(x,y)]

You cannot prove ANYTHING to EXIST!

NOTHING EXISTS!

A MODEL in Pessimist Set Theory is a SET OF IMPLICATIONS.

*IF* something did exist
*THEN* this would also happen

There are NO OBJECTS at all in PURE SET THEORY.

Each model is a set of implications.

A -> C
and
A&B -> C

A collection of WHAT-IFs

Herc

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