On 05 Dec 2008, at 03:56, Russell Standish wrote:

>
> On Wed, Dec 03, 2008 at 04:53:11PM +0100, Bruno Marchal wrote:
>>
>> I really don't know. I expect that the mathematical structure, as  
>> seen
>> from inside, is so big that Platonia cannot have it neither as  
>> element
>> nor as subpart. (Ah, well, I am aware that this is counter-intuitive,
>> but here mathematical logic can help to see the consistency, and the
>> quasi necessity with formal version of comp).
>>
>
> This point rather depends on what Platonia contains. If it contains
> all sets of cardinality 2^{\aleph_0}, then the inside view of the
> deployment will be conatained in it.

I am not sure. In my opinion, to have a platonia capable of describing  
the first person views emerging from the UD entire work, even the  
whole of Cantor Paradise will be too little. Even big cardinals (far  
bigger than 2^(aleph_0)) will be like too constrained shoes. Actually  
I believe that the first person views raised through the deployment  
just escape the whole of human conceivable mathematics. It is big. But  
it is also structured. It could even be structured as a person. I  
don't know.


>
>
> I do understand that your concept of Platonia (Arithmetic Realism I
> believe you call it) is a Kronecker-like "God made the integers, all
> the rest was made by man", and so what you say would be true of that.


Yes the 3-Platonia can be very little, once we assume comp. But the  
first view inside could be so big that eventually all notion of 1- 
Platonia will happen to be inconsistent. It is for sure unameable (in  
the best case). I discussed this a long time ago with George Levy: the  
first person plenitude is big, very big, incredibly big. Nothing can  
expressed or give an idea of that bigness.

At some point I will explain that the "divine intellect" of a lobian  
machine as simple as Peano-Arithmetic is really far bigger than the  
"God" of Peano-Arithmetic. I know it is bizarre (and a bit too  
technical for being addressed right now I guess).

Have a good day,

Bruno


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




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