Bruno,
Thanks, I will look up those names. If you have the time to reference
specific papers, I would be grateful.
--Abram
On Sat, Dec 6, 2008 at 9:07 AM, Bruno Marchal <marchal.domain.name.hidden> wrote:
>
>
> Le 05-déc.-08, à 20:51, Abram Demski a écrit :
>
>>
>> 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 :).
>
> I have published this in french a long time ago, but then I have
> discovered that it has been publishe before by Montague and Kaplan (see
> also Thomason). It is related to the fact that Knowledge, like truth
> (cf Tarski), is not definable through an arithmetical predicate. In
> "conscience and mécanisme" I illustrate a similar fact by using
> (informally) the Lowenheim Skolem theorems.
> Then I think the provability logic put a immense light on this, in a
> transparently clear (arithmetical) frame, and that is a big part of my
> thesis (the AUDA part).
>
>
>
>> That is, if you
>> can show that huge amounts of set theory beyond ZFC emerge from
>> provability logic in some way...
>
> I guess I have been unclear, because I am not saying that. I am saying
> the more obvious (once we are familiar with incompleteness,
> indefinissability, uncomputability etc) fact that a machine can infer
> true but unprovable (by her) things about herself. It is just that a
> provability machine, having furthermore inductive inference abilities
> will generate more truth about itself than those which are provable by
> the machine.
>
>
>>
>> Anyway, I'd definitely be interested in hearing those ideas.
>
> Those ideas constitute the AUDA part. It is an abstract translation of
> UDA in the language of "the" universal machine. It is needed to extract
> constructively physics from computer science. I only get the
> propositional physics (which is a billionth of "real" physics, yet I
> got both the communicable physical logic and the uncommunicable
> physical logic, that is both the quanta and the qualia. In that sense
> it is already more than "usual physics", which (methodologically or
> not) put the qualia and its subject under the rug.
>
> Bruno
>
>
>>
>> --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/
>>>
>>>
>>>
>>>
>>>>
>>>
>>
>> >
>>
> http://iridia.ulb.ac.be/~marchal/
>
>
> >
>
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Received on Sun Dec 07 2008 - 00:23:24 PST