Re: Small set theory.


Jesse F. Hughes wrote:
"zuhair" <zaljohar@xxxxxxxxx> writes:

Jesse F. Hughes wrote:
"zuhair" <zaljohar@xxxxxxxxx> writes:

No, it is contradictive.

y={x|xex}

if yey -> yey
if y!ey -> y!ey
therefore y is both regular and irregular at the same time. which is
contradicitive.

Man. You're simply incapable of fundamental reasoning.

The fact that y e y -> y e y is *not* a contradiction.

Today is either warm or not. If it is warm, then it is warm. If not,
then not. Big deal. This fact is not "contradicitive".

I want wonder why such a stupid man like you will not get my point! the
contradiction doesn't lie in yey -> yey, the contradiction lie in y
being in itself and not in itself at the same time stupid.

The sentences y e y -> y e y and y !e y -> y !e y are tautologies and
hence do not contradict each other.

Your statement is simply, stupidly false. And there is no
contradiction to be had from assuming that the set { x | x e x }
exists. At least none that I see.

(Note: I'm speaking of Zuhair's teeny set theory and not some other
theory.)

--
"You got more out of it
than I put into it last night.
Who were you thinking of when we were loving last night?"
-- Texas Tornadoes

Ok, I should develop axiom 6, the axiom that I have posted latelly
contradicts logic as you said, but I am sure you know what I mean after
development of this axiom. anyhow.

Still nobody answered my simple question, if y={x|xex} is yey or y!ey.

There is difference between Ontology and Epistemolgoy. y exists since
there is no contradiction involved with its existance, but
Epistemologically speaking we do not know if y is a member of itself or
not.

If I accept y to be a set in this theory, then I think it would be a
unique set. y would be the only set which we do not know weather it is
a member of itself or not. so I think tha y is unique, like how {} is
unique.

Anyhow , it is clear as I mentioned before that , the axioms of
separation, replacement,power and choice are inconsistent with this
theory( I mean these axioms as present in ZFC).

I realize that separation is important, and I think that it should be
changed in a manner as to be consistent with the other axioms. But
still I didn't work it out.

However this set theory will be as follow:

Primitive e

1) Axiom of Extentiality
2) Axiom of Empty set
3) Axiom of Pairing
4) Axiom of Union
5) Axiom of Infinity
6) Axiom of Universe

ExAy yex

7) Axiom of Multiplicity

ExEzAy yey /\ xex /\ zex /\ z!ey

8) Axiom of Cautious separation. Not completed yet.

1)2)3)4)5) are as in Z.

Do anybody think that this axiomatic set theory is inconsistent?

Zuhair

.

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