Re: Cantorian pseudomathematics

Tony Orlow wrote:
> MoeBlee said:
> > Tony Orlow wrote:
> > > Randy Poe said:
> > > > > There you say it ! But *I* don't think that "alternate decisions
> > > > > could be made from the same axioms". And *I* dont think
> > > > > that those theorems are "false", in the sense that they do
> > > > > not follow from the axioms. What *I* think is that the axioms
> > > > > themselves are false.
> > > >
> > > > What does it mean for an axiom to be false?
> > > >
> > >
> > > It means that they contradict other axioms. Now, you have some small set of
> > > axioms that don't contradict each other, but in the larger scope of mathemtics
> > > at large, the conclusions drawn from those axioms contradict conclusions drawn
> > > from other axioms of mathematics regarding sets such as Han is discussing. In
> > > the context of those other areas of math and their axioms, the axioms of set
> > > theory are flawed, as conflicts arise between them and the more solid
> > > computational axioms of the rest of mathemtics, and reality in general. The
> > > conclusions derived from the axioms are not correct.
> >
> > Please cite a theorem of set theory such that its negation is a theorem
> > of some other axiomatized theory that you hold to be important. And
> > what are these "other axioms of mathematics" that you have in mind?
> >
> > MoeBlee
> >
> > MoeBlee
> >
> >
> No one axiom needs to be the exact negation of another for contradictions to
> arise between them.

I didn't ask for an example of an AXIOM and its negation. I asked for
an example of a THEOREM and its negation.

> Certainly, the notion of an infinite number of increments
> never achieving an infinite value flies in the face of infinite series, where a
> sum can only converge to a finite value if the terms have a limit of 0 at oo.
> The constant increments of 1 have no such limit.

That is gobbedlygook. I don't know of theorems of set theory that have
terms 'infinite number of increments', 'acheiving a value', and
'constant increments'. I asked what THEOREM, that is, what provable
FORMULA of set theory is the negation of another THEOREM of another
theory that you hold to be important. Name the formula of set theory,
and name YOUR theory that has a theorem that negates the theorem of set
theory. Otherwise, your claim about "axioms" is just hot air.

> Wherever the axioms for
> addition are stated, I am sure they are stated so as to avoid this issue, but
> addition should always mean making greater, and subtraction should mean making
> less.

Name your axioms, name your theory. Otherwise, your claim about
"axioms" is just hot air.

> It may be by an infinitesimal fraction of the whole, but it should not be
> nonexistent. That aleph_0-1=aleph_0 makes no sense to me.

There is a bijection between Omega~{{0}} and Omega. In another post,
you recognized that such bijections exist. That is all that is at
stake. The rest is notation, which is NOT deductively creative (except
that a cardinality operation does use either the axiom of choice or the
axiom of regularity to formulate; but the 'equinumerosity' predicate
does not), as I've explained ad nauseum.

So, name your axioms, name your theory. Othewise your claim about
"axioms" is just hot air.

> COncepts of set
> density have been developed, but not gotten far enough to really remedy the
> situation. Han seems to consider transifnite set theory to eb at odds with
> probability theory, and has given some quotes and diatribes on the subject,
> though I cannot say with great depth what foul conclusions set theory has
> postulated for infinite samples of values. My guess is they suck and he's
> right, even if he is a finitist. :)

"Concepts of density". Name your axioms, name your theory. Othewise
your claim about "axioms" is just hot air. And, by the way, set theory
posits axioms; every conclusion is either itself an axiom or provable
from the axioms in classical first order logic. Whatever "foul
conclusions" you think are "postulated" are ones that you can only
reject by rejecting either classical first order logic or an axiom of
set theory. So far, over thousands and thousands and thousands of
posts, you still haven't said what logic you do approve of and/or what
axiom of set theory you reject.

MoeBlee

.

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