On 16 Sep 2016, at 17:40, Stephen Paul King wrote:
On Fri, Sep 16, 2016 at 11:16 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 16 Sep 2016, at 01:29, 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
?
Possibly in a quite novel non standard sense, but I'm afarid this
could lead to confusion, especially with beginners.
The UD is typically a program without input. You enter its code in
the language of some universal machine, without giving it any input,
and it runs forever, meaning it has no output.
Extensionally, it is equivalent with the empty function from the
empty set to the empty set (the unique element of 0^0 in set
theoretical term, with 0 identified with the empty set).
Intensionally, assuming computationalism it is all activities of all
machines in all locally consistent context.
Some would like to add, all thoughts, but the thoughts remain stable
and make possibly sense only on the infinities on which the First
Person Indeterminacy operates.
In the 3-1 picture, we can attach a consciousness to a program/
machine/3-p-representation..., it is often polite, but in the 1-p
picture, that is, from the first person perspective "you" are
related to an infinity (2^aleph_0) of computational histories. The
UD "runs" you on all real oracles, notably.
Bruno
http://iridia.ulb.ac.be/~marchal/
Can the UD diagonalize with almost all possible versions of itself?
I have forgotten some details...
The giant miracle here is that the class of all programs is immune to
diagonalization, unlike any class of always stopping programs. So, to
get all stopping programs, we must generate all programs, and to get
all stopping executions, there is no choice other than dovetailing on
all executions, the stopping and non stopping one.
The closure of the set of partial recursive function for
diagonalization is the main conceptual argument in favor of Church
thesis, and it is what make the universal machines/numbers, truly
universal, so to speak.
So yes, the UD can be said to diagonalize itself, but it changes
nothing: the UD remains invariant for the application of the diagonal.
Best regards Stephen,
Bruno
--
Kindest Regards,
Stephen Paul King
Senior Researcher
Mobile: (864) 567-3099
stephe...@provensecure.com
http://www.provensecure.us/
“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
confidential and exempt from disclosure under applicable law or may
be constituted as attorney work product. If you are not the intended
recipient, you are hereby notified that any use, dissemination,
distribution, or copying of this communication is strictly
prohibited. If you have received this message in error, notify
sender immediately and delete this message immediately.”
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
