Re: Why Regularity?


zuhair wrote:
Rupert wrote:
zuhair wrote:
Rupert wrote:-
I'm not talking about an inconsistency, I just doubt that the resources
of the language you're using are sufficient to say what you want to
say. There are well-known limits to the expressive power of first-order
languages, for example you cannot formulate the sentence "There are
finitely many x such that P(x)" in a first-order language. You need to
use a second-order language to say this. I may be able to prove that
first-order languages are not sufficient to do what you want to do. I
will work on it.
.............................

Hmmm.........

so you think the following doesn't describe what I wanted to say:

Axiom of Infinity: EN: UeN /\ ( Ax:xeN -> { m|mex or m=x' } e N )


That implies that the set {m|mex or m=x'} exists, and since every set
is a member of itself it will be either x or x'. So either xex' or
x'ex, but since we have xex and x'ex' that's a contradiction.
Perhaps you are right I don't know, but It seem working to me.

This is not understandable to me. I don't know what you are talking
about?


The argument is mistaken. I confused membership and equality.

.

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