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Topic: Ping David C Ullrich
Replies: 94   Last Post: Jun 26, 2013 5:55 PM

 Messages: [ Previous | Next ]
 Peter Percival Posts: 2,623 Registered: 10/25/10
Re: Ping David C Ullrich
Posted: Jun 22, 2013 12:28 PM

dullrich@sprynet.com wrote:
> On Sat, 22 Jun 2013 01:16:16 +0100, Peter Percival
> <peterxpercival@hotmail.com> wrote:
>

>> Did you ever express the opinion that the continuum hypothesis was
>> neither true nor false?

>
> Seems possible.
>

>> I seem to recall that you did but I might be
>> mistaken. If you did, why so?

>
> NOTE that the following is just how it seems to me.
>
> Of course you know the story about how (assuming
> ZFC is consistent) CH is true in some models of ZFC
> and false in others.
>
> Saying that CH _is_ true or _is_ false is saying that
> it _is_ true or false in the universe of "real" sets,
> as opposed to the elements of some model.
> And it's not at all clear to me that there _is_
> such a thing as the universe of real sets in the first place!
>
> I've never seen an actual _definition_ of what a "real"
> set actually is. I'll admit that I do have an intuitive
> notion of what a real set really is. But
> S = {x : x not in x} shows that my intutive
> notion of what a real set is is _inconsistent_.

Thank you. So you wouldn't consider

a "real" set is an element of the cumulative hierarchy

to be a definition?

Is the definition (*) of natural number given in terms of sets one that
you are comfortable with?. And if so does that mean that "natural
number" is, so to speak, floating around because there are many models
of set theory? You probably anticipate my worry: if CH is neither true
nor false, might is not be that other, less recherché, mathematical
statements are also devoid of truth value?

I'm not unsympathetic to the idea that CH is neither true nor false, but
I'm worried that such indeterminacy might creep in to (seemingly) more
concrete statements too.

Mathematics--about which I know nothing--seems to be so interconnected,
that a flaw (is that too strong a word?) somewhere might mean a flaw
everywhere.

(*) "the definition": von Neumann's, say.

--
I think I am an Elephant,
Behind another Elephant
Behind /another/ Elephant who isn't really there....
A.A. Milne

Date Subject Author
6/21/13 Peter Percival
6/21/13 William Elliot
6/21/13 Peter Percival
6/22/13 Peter Percival
6/22/13 fom
6/25/13 Shmuel (Seymour J.) Metz
6/25/13 Peter Percival
6/25/13 Shmuel (Seymour J.) Metz
6/26/13 fom
6/26/13 fom
6/26/13 FredJeffries@gmail.com
6/26/13 fom
6/25/13 fom
6/22/13 David C. Ullrich
6/22/13 Peter Percival
6/23/13 David C. Ullrich
6/23/13 Peter Percival
6/23/13 namducnguyen
6/23/13 Peter Percival
6/23/13 namducnguyen
6/23/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 David C. Ullrich
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 fom
6/24/13 namducnguyen
6/24/13 fom
6/24/13 namducnguyen
6/25/13 Peter Percival
6/25/13 Peter Percival
6/25/13 namducnguyen
6/25/13 Peter Percival
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 namducnguyen
6/25/13 Peter Percival
6/25/13 Shmuel (Seymour J.) Metz
6/23/13 Paul
6/23/13 Peter Percival
6/23/13 Paul
6/24/13 Peter Percival
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Tucsondrew@me.com
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/24/13 Virgil
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/24/13 David C. Ullrich
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 namducnguyen
6/24/13 Peter Percival
6/24/13 fom
6/22/13 Paul
6/22/13 fom
6/22/13 Paul
6/23/13 Peter Percival
6/23/13 Peter Percival
6/23/13 FredJeffries@gmail.com
6/23/13 Peter Percival
6/24/13 David C. Ullrich