[FOM] Disguised Set Theory "DST"

Frode Bjørdal frode.bjordal at ifikk.uio.no
Tue Oct 4 11:55:16 EDT 2011

> Dear Bjordal
> There is nothing in this theory that can prevent for example
> 0 from having a successor (as you defined a set that
> has 0 and its E-elements as the sole E-elements of it)
> of the form x={0,x}, and this in turn can have a successor
> y that is an e-element of itself that has only 0 and x as
> its E-elements and this can go on infinitely. The problem is that
> this will render your alleged infinite set N to be exactly {0}.

It does not seem to me that what I wrote up has been rendered in a
faithful faithful manner here.  I defined z'={u:uEzVu=z}. How would
one arrive at a fixed point x={Ø,x} with x=Ø'? Then we would have
{u:uEØVu=Ø}={x:x=ØVx={u:uEØVu=Ø}. That cannot be reaonable. Ordinal
succession as I defined it was anchored in Ø and succeeds along the
von Neumann ordinals.

Frode Bjørdal
Professor i filosofi
IFIKK, Universitetet i Oslo

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