Bruno,
Are you asserting this based on published findings concerning
provability logic? If so, I would be very interested in references. If
not, then your results obviously seem publishable :). That is, if you
can show that huge amounts of set theory beyond ZFC emerge from
provability logic in some way...
Anyway, I'd definitely be interested in hearing those ideas.
--Abram
On Fri, Dec 5, 2008 at 4:20 AM, Bruno Marchal <marchal.domain.name.hidden> wrote:
>
>
> 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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Received on Fri Dec 05 2008 - 14:51:19 PST