Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance))

On Dec 23, 11:11 pm, lwal...@xxxxxxxxx wrote:

Yes, tommy1729 says he adopts an _empty set axiom_, but
as it turns out, it's not _the_ same empty set axiom as
the one in ZFC.

WHERE previous to my proof of inconsistency does this "turn out" in
tommy1729's posts? He was asked at least a few times for any
clarifications on his axioims. As to the "axiom of the empty set" he
said:

"perhaps i should drop the axiom the empty set or clarify : empty set
exists"

It is only reasonable for me to take him as meaning there is a set
that has no members.

He says (no matter what else he says, and despite his confusion in
thinking this perhaps requires "dropping the axiom of the empty set"),
"the empty set exists".

Without him stating some special variant, it is quite reasonable that
one would take him to mean the ordinary empty set axiom. He stated no
other empty set axiom and he did not stipulate that he doesn't mean
the ordinary empty set axiom, and even his confused qualification
restates that there exists an empty set, so it is only reasonable to
take him to mean that there is a set that has no members. If I tell
you that I adopt "axiom of the empty set" and/or that "the empty set
exists" I would never fault you for taking me at face value: there is
a set that has no members.

You are grasping at infinitesimal straws (and losing more and more
credibility) when you try to make out that it is MY fault for taking
him to mean the ordinary empty set axiom when he does not specify
otherwise and when indeed he even reiterates "the empty set exists".

Here's a better analogy. Scrap what I wrote before.

Then why did you bother to leave it in and have me read it?

In an earlier thread, I was wondering how NBG could
have an Axiom of Pairing, after MoeBlee pointed out that
the Axiom of Pairing implies that every object must be a
set rather than a proper class. MoeBlee's response was
that the _ZFC_ Pairing Axiom implies that every object
is a set, but the _NBG_ Pairing Axiom is distinct from
the ZFC Pairing Axiom and _doesn't_ imply that every
object is a set.

So just as ZFC and NBG have distinct Pairing Axioms, we
see that ZFC and TST have distinct Empty Set Axioms.

No we don't "see". Rather YOU argue spuriously. The analogy doeesn't
hold. The pairing axiom is different in NBG from ZFC because there is
a relativization to sets. tommy1729 mentioned no relativization,
exception or variation. IF he had, then that would be a different
story. But he didn't. And in the case of the pairing axiom in ZFC as
opposed to NBG, you will see that ordinarily the exact distinction is
part of the very formulation. In NBG, the formulation of the pairing
axiom IS stated differently from than in ZFC. This contrasts with
tommy1729 who, when he first posted "axiom of the empty set" did NOT
stipulate that he means something other than the ordinary empty set
axiom. If he had meant a formulation other than the ordinary exmpty
set axiom, then he should have provided that formulation. Your analogy
is terribly off.

And
since MoeBlee directed me to the Stanford site, I see
that the Stanford Empty Set Axiom (or "Bottom") is more
appropriate for TST than ZFC's Empty Set Axiom.

That is a DIFFERENT question. That one can find some other axiom that
would be consistent is not at issue. tommy1729 did not state any such
axiom of "bottom". (By the way, though this still has no bearing on
what tommy1729 wrote, is this called the 'Stanford Empty Set Axiom' or
are YOU just CALLING it that? And what exactly is the axiom?)

Just as I should've known that the NBG Pairing Axiom is
more appropriate than the ZFC Pairing Axiom when there
are proper classes floating around, MoeBlee should have
known that the Stanford Empty Set Axiom is more
appropriate than the ZFC Empty Set Axiom where there is
a flattened mereology floating around.

(1) I just addressed the matter of the analogy. (2) My proof of the
inconsistency of tommy1729's axioms was addressed in the context in
which his stated axioms were given. He did not specify that these were
not the ordinary set theory axioms as he had listed them by name, and
he didn't stipulate that this was a theory of a "flattened mereology"
so that his simply named set theoretic axioms should be understood in
some OTHER sense NOT even mentioned by him! You are just beyond
credibility arguing that people are not reasonable to take such things
as "axiom of the empty set" and "the empty set exits" in the context
of a set theory to mean the ordinary empty set axiom rather than some
other axiom about "bottoms" from some other theory that has not even
been mentioned. You conflate on the one hand, your willingness to -
AFTER THE FACT - RECONSTIUTE a theory with variant axioms and on the
other hand, the axiomatization as it was originally given and which
does NOT include such measures of reconstitution.

And just as MoeBlee criticized me for attempting to use
ZFC's Pairing Axiom to prove NBG inconsistent, I am
criticizing MoeBlee for attempting to use ZFC's Empty
Set Axiom to prove TST inconsistent.

Again, a terrible comparision, for the reasons I mentioned above.

Hopefully this is a much better analogy than my first.

Pathetic.

MoeBlee

.

Relevant Pages

  • Re: Axiom of Pairing, Scheme of Replacement from others
    ... separation follows from the axiom of replacement together with the axiom ... Your hypothesis has uniqueness but not existence. ... Proof of separation from replacement: ... empty set is required. ...
    (sci.math)
  • Re: Uncountable sets in CZF?
    ... >>were sets as opposed to a theory where numbers are primary objects. ... >idea that numbers were primary objects in ZF and ZFC??? ... so it can be called the Axiom of Existence; ... exists x (empty set in x and for all y in x exists z in x for all t ...
    (sci.math)
  • Re: Axiom of Pairing, Scheme of Replacement from others
    ... separation follows from the axiom of replacement together with the axiom ... empty set is required. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... The theorem "There is only one empty set" uses no axiom of ZFC aside ... Do you think it's *not* a theorem of ZFC? ... empty set exists requires more than just extensionality. ... also be introduced as an axiom. ...
    (sci.math)
  • Re: the return of the master : tommy1729
    ... I don't recall using the empty set in my argument (maybe I did; ... existential instantiation from 4 ... There is an x such that for all y, y not in x (_empty set axiom_). ... existence and uniqueness. ...
    (sci.math)