George Levy wrote:

>> BM:..Positive integers exists. Nothing else.

>This is a integercentric statement if I ever saw one. 

Oh ! George. You don't met Pythagore, or Xenocrate, ...
in the plenitude. Do you?

>And Kroenecker was an old fuddy daddy.

Old and even dead (here and now for sure). But fuddy ?
I don't know. What does fuddy mean?
 
Note that I don't appreciate what Kronecker (the man)
did to Cantor.
And I love Cantor, for it is the first who gives rather
strong glimpse on the bigness of the first person
plenitude. Cantor call it INCONSISTENZ (modulo german orthograph)


>If I was a negative number I would be deepely offended! 

I have some negative number friends.


>Why not say
>negative number exist and nothing else? 

Because when I say that, most people, from almost all 
universes, ask me "why *negative* number?"

I take natural numbers because without natural numbers (or things
recursively isomorphic to them) I cannot get them, and
with them I got all the rest.
You can see them as my "base" for the (first person) plenitude.

>In fact all you need is the null 
>set to
>begin the number description. 
>The set comprising the null set could represent
>one. That set which holds the "null set" and the "one set" could represent 
>"two,"
>and so on...

Yes but then I need sets, and if I take sets I take much more.
Also there are a lot of non equivalent theories for sets, and each
such theories are very rich and have a lot of non equivalent models.

>Even with the null set I have my doubt. Why not use the Not(null set) 
>..... which
>is the plenitude eh???  :-)

Classical logics can be used to get the whole universe (model of your
standart set theory) from the null set with an intersection. The "not"
can only be used in a subset. (I will not insist here).
That is formal game. To define intersection axiomatically you
need a theory and this one gives you all the universes (all the model
of your theory).
It is really Church thesis which refutes the traditional refutation
of Pythagore idea that "everything are numbers or "ratio" between
numbers". (cf. appendices of my thesis). 

>> It is true that physics and science has evolved through the abandon
>> of the first person (Galileo, Einstein).
>
>Wow! Hold it. Be careful. One could argue that the opposite has actually
>happened. In a conjugate fashion to the objective movement, the 
>abandonment of a
>geocentric system forced us to view each individual observer as the center 
>of the
>universe. 

You know I agree.

>>With Copernicus, Galileo, Newton, Einstein we have moved toward 
>>a full
>>relativistic point of view. 

You know I definitely agree.

>The MWI  gives us the chance to go all the way 
>and
>places each "I" at the center. 

How weird. That would have been a nice sum up of what I try to say;
with COMP instead of MWI.
But COMP implies MWI (Note that Schmidhuber and me agree on that,
but we disagree on what *are* the (many) worlds MW).
Schmidhuber associate worlds to some programs, I associate
worlds on machine's projection from shared computational histories
The projection is first person plural. 

>The trend is actually to accept the first 
>person
>point of view!

A welcome trend. But that is not a reason to forget the third person.
In fact, the sentence " to accept the first person point of view" seems
to me ambiguous. It could mean "let us listen to people's personal
believes" But there is a risk of inflation of information and it is 
natural
to ask to the people to make these belief the more communicable possible.
One way of doing that is science. To limit oneself to verifiable third
person statement. 
And then, here is the ambiguity, we can, with hypothesis like COMP, 
"accept the first person point of view" as a subject matter of science,
by elaborating third person discourse on the first person.
Of course, we must locally agree on definition of what the first person
is.


>>> >    So does it mean feces? [JM]
>>>
>>> You mean faeces ?  [BM]
>>>
>>
>>Are faeces real ?

Are white rabbit's faeces real?

Bruno












http://iridia.ulb.ac.be/~marchal



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