Hi Jesse:
To clarify - the All contains all information simultaneously [see the definition in the original post] - including ALL Truing machines with ALL possible output tapes - so it contains simultaneously both output tapes re your comment below. It is not a time dependent or belief dependent issue. If one could go fishing in the All as an evolving Something essentially does - you would eventually pull out both tapes in random order just like the order in which someone catches a big fish or a little fish. The fish and the fisherman are also in no fixed relation - no selection. The boundary defining a given Something moves through the All and will encompass these various tapes in no fixed order - no selection - it is random input to that Something. Once a Something incorporates a particular kernel of information its boundary necessarily moves according to that total content - it is a new Something and it is a journey towards completion for that configuration. The fisherman catches the big fish and goes home happy never catching the little fish, or, or , etc., etc. The boundary of each Something takes an unknown and unknowable [random] path.
Here all states of universes are encompassed [the instant of "physical reality"] again and again.
Some [most I suppose] states can be quite messy but so what? They are logically possible within the venue as are neat ones. However, long long strings of neat ones absent large deltas between the states that are given "physical reality" and having small deltas that are "reasonable" happen.
The idea that some of these strings of states could be simulated on a computer is also in the All but the computer must have one port that allows random input.
Hal
At 01:49 AM 12/7/2004, you wrote:
Hal Ruhl wrote:
Hi Jesse:
I think you miss my point. The All contains ALL including Turing machines that model complete FAS and other inconsistent systems. The All is inconsistent - that is all that is required.
You mean because "the All" contains Turing machines which model axiomatic systems that are provably inconsistent (like a system that contains the axiom "all A have property B" as well as the axiom "there exists an A that does not have property B"), that proves the All itself is inconsistent? If that's your argument, I don't think it makes sense--the Turing machine itself won't behave in a contradictory way as it prints out symbols, there will always be a single definite truth about which single it prints at a given time, it's only when we interpret the *meaning* of those symbols that we may see the machine has printed out two symbol-strings with opposite meaning. But we are free to simply believe that the machine has printed out a false statement, there is no need to believe that every axiomatic system describes an actual "world" within the All, even a logically impossible world where two contradictory statements are simultaneously true.
Godel's theorem is a corollary of Turing's.
As you say a key element of Godel's approach to incompleteness is to assume consistency of the system in question.
But do you agree it is possible for us to *prove* the consistency of a system like the Peano arithmetic or the axiomatic system describing the edges and points of a triangle, by finding a "model" for the axioms?
The only way I see to falsify my theory at this location is to show that all contents of the All are consistent.
Hal
I think you need to give a more clear definition of what is encompassed by "the All" before we can decide if it is consistent or inconsistent. For example, does "the All" represent the set of all logically possible worlds, or do you demand that it contains logically impossible worlds too? Does "the All" contain sets of truths that cannot be printed out by a single Turing machine, but which could be printed out by a program written for some type of "hypercomputer", like the set of all true statements about arithmetic (a set which is both complete and consistent)?
Jesse
