Hal Ruhl wrote:
>>In what sense "4+1=" is a proof chain ? A proof must be a sequence of
>>formula each of which are either axiom instance or theorems.
>
>IMO it is ...
Definitions are not matter of opinion, but of conventional consensus.
> ... a sequence of:
>1) A formula which in this case is of the form ("data string" + ), it is a
>rule of inference acting on a initializing theorem.
"data string " + can hardly be considered as a formula. You should
decribe
the formal system you are using (if any ?).
Then you tell us it is a rule of inference as if it was possible for a
formula to *be* a rule of inference. I don't understand.
>2) The initializing theorem is "data string". Let us ignore the fact that
>the strings above are so short as to be individual alphabet elements.
Not an a priori problem, but not very helpful without a presentation of
your
formal system.
>The next step in the sequence is the axiom "1".
"1" is not an axiom. It is a symbol denoting the number 1. It is neither
an axiom, nor a formula.
>The value of this formula is designated by "=".
I see what you mean. This will not help us.
>>If you interpret the theorem "4+1=5" as 5 is a number, how will you
>>interpret 3+2=5 ?
>
>It is another proof the theorem "string "5" is a number or WFF" [ Again
>ignoring that this string is so short as to be a single alphabet
>element.] There can be more than one proof of a theorem.
Of course you can build a FAS such that the number will be considered as
theorem. But then it is a very ad hoc special fas which has nothing
to do with number theory, and Juergen's remark remains valid.
In another post Hal Ruhl wrote:
>Ok so "computation" is more than "prove" but prove is computation is that
>the idea?
If you consider an axiomatisable theory, you can consider
proof as a (partial) computable function defined on a set of
sentences and with value in {0,1}. If the theory is decidable then
the function is total.
Even a theory as weak as Robinson Arithmetic can be use to
compute all partial recursive function (programmable function): in
that sense "proving" is more than computation.
Well, you can compare proof and computation in a lot of manner, and
depending of the criteria you choose, proof or computation will
be more or less than computation or proof.
A good book is "Introduction to Mathematical Logic" by Eliott
Mendelson (third edition), Wadsworth & Brooks, California, 1987.
>Here it is in one line:
>
> ....N - N -> S; S + N -> N; N - N -> S....
>
>N is the Nothing and S is the Superverse.
>All information = no information
>N is no information.
>N - N is the smallest possible computable perturbation brought on by a need
>of N to test its own stability.
>S is all information absent the N. It is as close to the N as can be.
>S also needs to respond to the stability question via test because it
>contains almost all information which is almost no information. Like the
>UD it can not prove anything it just generates stuff. The smallest
>perturbation is to add back the N which results in all information and S
>becomes N. Both events destroy history.
>
>It is your scanner-duplicator acting at the lowest level.
>
>My difference is that when S is manifest it is not a UD but is like a vast
>collection of individual computers running in parallel. A great "dove
>tailed" structure. Each is isomorphic to a universe.
>
>I also introduce two additional arguments re each computer as to why
>determinism does not apply. 1) Deterministic cascades hit a complexity
>wall, 2) The random oracle is in S anyway - it gets used or it is a
>selection - it would be information unused by an exception. These plus the
>lowest level scanner-duplicator mean there is some degree of random oracle
>present in each one including those that have SAS or attempt deterministic
>cascades. There is an even distribution of universes since each computer
>is present an infinite number of times again to avoid any absolute or
>relative information in S.
>
>Since N and S can not prove anything it is good that they can nevertheless
>compute the respective perturbations that run the scanner-duplicator
>alternation.
I"m willing to believe you try to say something, but
I don't understand a bit. I'm sorry.
>After looking at all of your recent posts re my questions I conclude that
>my Superverse idea and your UDA idea are cousins. See also my just
>previous post re "Some progress I think".
The UDA is used to prove something, mainly that physics is
ultimately a branch of machine psychology.
>My argument carries a rationale for a lowest level repeating
>scanner-duplicator type of behavior [i.e. stability], my Superverse is
>generated immediately and repeatedly at one end of that behavior, the
>Superverse acts as "data food" for all my parallel computers which are
>actually comparators orchestrating isomorphic link shifts between all the
>patterns in the Superverse [link shifts = evolving universes], and it takes
>no selected information to construct all these computers since they are
>self contained in each link but such information though small seems
>necessary to construct the UD.
?
Bruno
