Re: Formulating sentences in a possibly consistent ZF

Chris Menzel wrote:
On Tue, 25 Nov 2008 00:10:13 -0700, Nam Nguyen <namducnguyen@xxxxxxx> said:
Chris Menzel wrote:
On Mon, 24 Nov 2008 00:09:55 -0700, Nam Nguyen <namducnguyen@xxxxxxx>
said:
Aatu Koskensilta wrote:
Chris Menzel <cmenzel@xxxxxxxxxxxxxxxxxxxx> writes:

Of course, again, the fly in the ointment here is that the ability
to state the view seems to presuppose a perfectly clear grip on the
distinction between standard and nonstandard models, the very
ability the view calls into question. So it seems to me to be
self-refuting.
I believe it was Bill Tait who once observed

If you know what non-standard means, you know what standard means.
Suppose red isn't the standard color, could we know what the standard
color be?

Suppose the currency of a 3rd World country isn't the standard money,
would we able to know what the standard currency the World is supposed
to use?

Suppose Euclidean geometry isn't the standard geometry, can we tell
which of Riemann and Lobachevsky geometries be the standard one?

What are you both really talking about?
Funny, I was gonna ask you the same thing. We're talking about the
standard model of arithmetic. Sorry you're having so much trouble with
that. I can suggest some good references.
That's right. "The standard" model is what CM et al. defined and any
non-standard one is well ... not standard!

Right. That's what you'll find in most any relevant text. Is it the
use of "standard" that is putting you off? As if all the nonstandard
models are deficient somehow? Would it help to call the standard model
the "minimal" model instead, so as not to cause offense to the others?
I really have no idea what you are ranting about. It seems as pointless
as raving about calling 1, 3, 5, ... "odd". "Standard model" is just a
label for a particular model of Peano Arithmetic. "Nonstandard model"
is just a label for any model of PA that is not isomorphic to the
standard model. That's all. There's nothing more to it. These are
just labels that have been introduced to make a useful mathematical
distinction.

It's not I don't see that; it's just in the abstraction of mathematics
there are similarities (e.g. homomorphism) that we should entertain
viz-a-viz the definition of "standard". So if you call one kind
of thing "standard", then how would that that help to call a similar
thing standard, or not. I do have a concrete finite mathematical model
of reproduction, should I call that "the standard" model of reproduction?
We do have a singleton-model of basic group theory, should we call that
"the standard" model of group theory, because of its "simplicity"?
Should we do so, why would we call a thing "the standard" model of real,
while its addition is non-standard?

Hope you understand where I've come from on this.



--
"To discover the proper approach to mathematical logic,
we must therefore examine the methods of the mathematician."
(Shoenfield, "Mathematical Logic")
.

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