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Topic: some amateurish opinions on CH
Replies: 57   Last Post: Apr 16, 2013 8:12 PM

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dan.ms.chaos@gmail.com

Posts: 409
Registered: 3/1/08
Re: some amateurish opinions on CH
Posted: Apr 9, 2013 12:27 PM
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On Apr 9, 8:34 am, fom <fomJ...@nyms.net> wrote:
> On 4/9/2013 12:15 AM, William Elliot wrote:
>
>
>
>
>
>
>
>
>

> > On Mon, 8 Apr 2013, fom wrote:
> >> On 4/8/2013 11:24 PM, William Elliot wrote:
> >>> On Mon, 8 Apr 2013, fom wrote:
>
> >>>>> Remember the engineers' KISS and the beauty of simplicity. What
> >>>>> more simple than invoking Occam for V = L and no inaccessible?
> >>>>> Face it, that's all the set theory needed for all of math.

>
> >>>> Do you believe that?
>
> >>>> What about Grothendieck universes arising from category theory?
>
> >>> What good are they?
>
> >> Technically, I think they let algebraists work without concern for
> >> set-theoretic paradoxes.  That would come into play in the
> >> representation theory.  But, I am not knowledgeable enough to assert
> >> that with confidence.

>
> > It's likely as useful ast the category theory topology, pointless
> > topology, ie pointless.

>
> >>>>> BTW, Quine's NF denies AxC.
>
> >>>> I need to look at Quine's work more carefully at this
> >>>> point.  I doubt I would like it because I do not
> >>>> agree with his views on the nature of identity.

>
> >>> At Quine's time it was assumed AxC was compatible.  Decades later, it
> >>> turns out to be violated for some large constructed sets.  Would you like
> >>> the reference for the paper?

>
> >> Yes.  Thank you.
>
> > Ernst P. Specker, "The Axiom of Choice in Quine's New Foundations
> > for Mathematical Logic," pp 972-975, Vol. 39, 1653, Proc. N.A.S.

>
> > I'd be interested in your comments.
>
> >>> AxC is needed for infinite products of sets to be not empty.
> >>> Anyway, I'm a prochoice mathematician.

>
> >> :-)
>
> >> Yes.  I see what you difference you are making.
>
> >> Historically, the question of identity is related to Leibniz' principle
> >> of identity of indiscernibles. But, Leibniz logic had been intensional.
> >> He viewed logical species as more complex than logical genera and his
> >> reasoning had been based on the fact that more information is required
> >> to describe a species than is required to describe a genus.

>
> > Philosphy isn't math.
>
> Sadly, set theory is philosophy.  It should
> not be, but it is.  When Kunen or Jech are
> deferring to first-order logic with identity,
> they are deferring to this
>
> http://plato.stanford.edu/entries/identity-relative/#1
>
> Perhaps it would be more correct to simply say
> that deciding on "any favorite set theory" that
> sometimes appears in texts is a hard decision.
> It throws philosophy in your face even if you
> did not really mean to pursue it.
>
>
>
>
>
>
>
>
>
>
>

> >> I think about identity in those terms.  Topologically,
> >> that would involve something along the lines of
> >> Cantor's intersection theorem for closed sets.  So,
> >> identity of an individual might require an "infinite
> >> description".

>
> > Just the DNA and the google governement file on the person which
> > has superceeded the old fashion time, date and location of birth.

>
> >> In topology, the metric relations and non-metric notions
> >> of closeness come together in uniform spaces.  And,
> >> of course, one can think about the diagonal of a
> >> model in relation to the definition of uniformities.

>
> >> If I am permitted to be ambivalent about the role of model theory, I am
> >> in agreement with your prochoice affiliation.  Stop worrying about
> >> models, and the axiom of determinacy becomes almost preferable.

>
> > What's that?  The determination to needlessly multiply entities?
>
> The axiom of determinacy is inconsistent with the
> axiom of choice.  Under the axiom of determinacy,
> every set of reals is Lebesgue measurable.
>
> It probably trades one set of needless entities for
> another.


The universe of ZF + AD appears to be, in all respects, 'smaller'
than ZF+AC .
So, it does eliminate a set of entities,but it doesn't seem to
generate another .
Anyway, may be a little off topic, I found this paper
interesting ,even though I don't agree with everything it says :
http://arxiv.org/abs/0905.1675



Date Subject Author
4/7/13
Read some amateurish opinions on CH
fom
4/7/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/7/13
Read Re: some amateurish opinions on CH
Bergholt Stuttley Johnson
4/7/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/7/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/7/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/7/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/7/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/7/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/7/13
Read Re: some amateurish opinions on CH
Virgil
4/8/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/8/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/8/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/8/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/8/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/8/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/8/13
Read Re: some amateurish opinions by WM
Virgil
4/8/13
Read Re: some amateurish opinions on CH
Virgil
4/9/13
Read Re: some amateurish opinions on CH
apoorv
4/8/13
Read Re: some amateurish opinions on CH
Virgil
4/7/13
Read Re: some amateurish opinions on CH
Virgil
4/9/13
Read Re: some amateurish opinions on CH
Guest
4/9/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/9/13
Read Re: some amateurish opinions on CH
fom
4/10/13
Read Re: some amateurish opinions on CH
Guest
4/10/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/10/13
Read Re: some amateurish opinions on CH
fom
4/10/13
Read Re: some amateurish opinions on CH
JT
4/11/13
Read Re: some amateurish opinions on CH
apoorv
4/11/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/11/13
Read Re: some amateurish opinions on CH
apoorv
4/11/13
Read Re: some amateurish opinions on CH
fom
4/15/13
Read Re: some amateurish opinions on CH
apoorv
4/15/13
Read Re: some amateurish opinions on CH
fom
4/16/13
Read Re: some amateurish opinions on CH
Shmuel (Seymour J.) Metz
4/16/13
Read Re: some amateurish opinions on CH
fom
4/7/13
Read Re: some amateurish opinions on CH
Virgil
4/7/13
Read Re: some amateurish opinions on CH
William Elliot
4/7/13
Read Re: some amateurish opinions on CH
fom
4/7/13
Read Re: some amateurish opinions on CH
fom
4/8/13
Read Re: some amateurish opinions on CH
William Elliot
4/8/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
William Elliot
4/9/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
William Elliot
4/9/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/9/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/9/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/9/13
Read Re: some amateurish opinions on CH
fom
4/10/13
Read Re: some amateurish opinions on CH
fom
4/11/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/11/13
Read Re: some amateurish opinions on CH
fom
4/11/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/11/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
fom

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