Le 22-sept.-06, à 19:10, Russell Standish a écrit :
> On Fri, Sep 22, 2006 at 02:59:09PM +0200, Bruno Marchal wrote:
>>> Any person's experience is obtained by
>>> differentiating - selecting something from that "nothing".
>>> The relationship between this zero information object, and
>>> arithmetical platonia is a bit unclear, but I would say that anything
>>> constructible (Sigma_1) must be extractable from the zero information
>> OK then. But this means you are an arithmetical realist, and that an
>> external "reality" exist, for example your strings, or your set of
>> strings, and I am still more confused by your saying there is not even
>> an immaterial external reality, which would be solipsism with a
> The set of all strings is the same object, regardless of
> interpretation, regardless of alphabet, and is the only object to have
> zero information. It is a good candidate for the Everything, but
> curiously it has the properties of Nothing.
Please allows me at this stage to be the most precise as possible. From
a logical point of view, your theory of Nothing is equivalent to
Q1 + Q2 + Q3. It is a very weaker subtheory of RA. It is not sigma1
complete, you don't get the the UTM, nor all partial recursive
functions FI or all r.e. set Wi. Actually you cannot recover addition
But it is neither "nothing". It is the natural numbers without addition
and multiplication, the countable order, + non standard models.
Or you have an implicit second order axiom in mind perhaps, but then
you need to express it; and then you have a much richer ontology than
the one expressed through RA.
> One simply cannot observe this zero information object, one can only
> observe somethings, descriptions in my terminology. Anything in
> Sigma_1 is such a something.
Sigma_1 is far richer. There are many sigma_1 true arithmetical
sentences (provable by RA, PA, ZF, ...) not provable in your system.
> Anything you can possibly to convey to me about
> any mathematical object must also be extractable.
Again, strictly speaking this is not true. (Unless your implicit axioms
> However, there are
> possibly mathematical things not within the zero information objects,
> but they are inherently noncommunicable (shades of you G*\G perhaps?).
You are very well below. You cannot even prove the existence of a prime
number in your theory.
> I think all that I say is that external reality is Nothing.
No. Even your very weak theory as infinite models, and models of all
cardinality. But it has no finite models, still less the empty model
(which logicians avoid).
> It is not
> quite the same as saying there is no external reality, but not far
This is too ambiguous. And too much sounding solipsistic.
> But solipsism is really about other minds, in any case, so its hardly
Which again show the external reality is very rich, but your ontic
theory cannot prove the most elementary thing about it.
I guess you are using some implicit supplementary axiom.
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