On 15 Sep 2016, at 20:03, Stephen Paul King wrote:

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly. This seems to be an attack on the UD, which requires computational universality, but I assure you that it is very Digital Mechanism friendly. I am after Correct computers, not Universal computers. An example of such is the TauChain.


Robinson Arithmetic (which is basically only the succession, addition and multiplication laws) is *essentially undecidable*. It means that it is Turing complete (and thus undecidable and arithmetically incomplete) and, and that is what Tarski meant by *essentially undecidable, all its consistent extensions are (even those non computable).

Bruno






On Thu, Sep 15, 2016 at 1:54 PM, Brent Meeker <meeke...@verizon.net> wrote: According to Bruno it's in Platonia. It's timeless and doesn't "go", it just IS, like 2+2 IS 4.

Brent

On 9/15/2016 10:13 AM, Stephen Paul King wrote:
OK, but where is the "motivation" that pushes the execution of the UD coming from? Where is the "go!" in the numbers?

On Thu, Sep 15, 2016 at 1:11 PM, Brent Meeker <meeke...@verizon.net> wrote: In this case we have a lot of threads and along each thread there is an implicit order (the execution of the UD), but there is no inherent relative order of the threads.
Brent

On 9/15/2016 9:15 AM, Stephen Paul King wrote:
There is "time is a measure of change" concept, which lines up with what you're saying: "... 'time' is only a real number..." The numbers are labels, not the change itself.

On Thu, Sep 15, 2016 at 11:57 AM, Brent Meeker <meeke...@verizon.net> wrote:


On 9/15/2016 12:44 AM, Bruno Marchal wrote:

On 14 Sep 2016, at 02:13, Brent Meeker wrote:



On 9/13/2016 7:22 AM, Stathis Papaioannou wrote:


On Sunday, 11 September 2016, Brent Meeker <meeke...@verizon.net> wrote: In the UD model of the world, time as we perceive it, is emergent. The "execution" of the program is timeless and exists in Platonia. So the steps of the UD have no duration, they are logically prior to time and duration. On the other hand, I think so called "observer moments" must have duration in the emergent sense and must overlap. But their relation to the UD threads is more aspirational than proven.

I think it should be possible to pause and restart at any point a process underpinning consciousness and leave the stream of consciousness unchanged; otherwise there would be a radical decoupling of the mental from the physical. At the limit, this means the process underpinning consciousness can be cut up into infinitesimals.

Infinitesimals, I think not, at least not in Bruno's model. Each thread of the UD's computation can be cut and restarted, but underlying an "observer moment" or a "thought" are infinitely many threads and there is no reference by which you can define cutting them all at "the same time". So they make the "time" of consciousness essentially real valued.

Good point.

But that is where the "infinitesimal" comes in, I would say, be them in terms of Cauchy sequences or in term of Non Standard analysis, that's not important at this stage. It depends on the mathematics of the arithmetical measure on 1p experiences (we get them trough the math of self-reference, but are still a long way from an arithmetical Gleason theorem).

Bruno

PS wrote this mail yesterday, seems to not have gone through. Sorry if sent in double exemplars.

But the 'time' is only a real number if you can order the events in the different threads relative to one another. In the materialist theory of mind that is provided by physical time, the evolution parameter of the wave function. I think that means that in your theory you have to derive time in order to locate 'thoughts' or 'observer moments'; they are no givens that you can assume.

Brent
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