On 28 Dec 2013, at 04:44, Stephen Paul King wrote:

Hi Jason,

"The first, second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's execution are mathematical facts ..." Umm, how? Godel and Matiyasevich would disagree!

No logicians at all would ever disagree on this. They are the one who proved this.



If there does not exist a program that can evaluate whether or not a UD substring is a faithful representation of a "true theorem", then how is it "a fact"?


It does not need to be a fact. *you* recognize you are conscious, even if no one can prove it by looking at your code and state, and that is enough to proceed in the reasoning.

bruno






On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch <jasonre...@gmail.com> wrote:



On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King <stephe...@provensecure.com > wrote:
Hi Jason,

Could you discuss the "trace of the UD" that LizR mentioned? How is it computed? Could you write an explicit example? I have never been able to grok it.


Bruno has written an actual UD in the LISP programming language. I will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the integer i
   Program P = createProgramFromInteger(i);

   # Add the program to a list of programs we have generated so far
   listOfPrograms.add(P);

# For each program we have generated that has not halted, execute one instruction of it
   for each (Program p in listOfPrograms)
   {
     if (p.hasHalted() == false)
     {
        executeOneInstruction(p);
     }
   }

# Finally, increment i so a new program is generated the next time through
   i = i + 1;
}


Any program, and whether or not it ever terminates can be translated to a statement concerning numbers in arithmetic. Thus mathematical truth captures the facts concerning whether or not any program executes forever, and what all of its intermediate states are. If these statements are true independently of you and me, then the executions of these programs are embedded in arithmetical truth and have a platonic existence. The first, second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's execution are mathematical facts which have definite values, and all the conscious beings that are instantiated and evolve and write books on consciousness, and talk about the UD on their Internet, etc. as part of the execution of the UD are there, in the math.

Jason



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