On 16 Sep 2016, at 03:27, Stephen Paul King wrote:
The idea is to think of computations as discrete, they do one thing:
process one algorithm and halt.
or not halt. You limit yourself to halting computation.
If each halting computation is simpler than arbitrary computations, it
happens that the notion of halting computations is more complex than
the notion of arbitrary computations.
For example, there is no universal halting machine, and there is no UD
computting all and only all halting computations.
The only way to generate all halting computations necessitate the
generations of all computations, the halting one and the non halting.
There is no algorithmic means to separate the halting machine from the
non halting one.
yet, the halting computations, when you get them all, is what
structure the "measure space", and that is exploited to get the
measure one case by the intensional ("material") variant of the self-
reference logic, restricted to the "halting computations", modeled by
the true sigma_1 sentences.
Obviously I am not talking about Turing machines...
?
We seem to miss a precise idea of what you are talking about, I'm
afraid.
Bruno
On Thu, Sep 15, 2016 at 9:03 PM, Brent Meeker <meeke...@verizon.net>
wrote:
On 9/15/2016 4:29 PM, Stephen Paul King wrote:
On Thu, Sep 15, 2016 at 6:47 PM, Brent Meeker
<meeke...@verizon.net> wrote:
On 9/15/2016 11:03 AM, 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
I don't understand what you mean by that. I assume "theories"
refers to axiomatic systems. If I take one such system, like
arithmetic, I can keep adding the unprovable Godel sentences as
axioms and so create an unbounded "tower" of systems. Is that what
you mean?
Yes, sorta.
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.
That's the view of an algorithm as computing a function; so given
an input there is a certain correct output. But the UD doesn't
have any input.
It has itself as an input. :-P
I suppose you can think of it as a null input. But it also has not
output. It doesn't halt. So I'm not sure what you mean by
computing one algorithm efficiently and correctly.
Brent
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