As usual when I ask a question like this, if the answer is available in a text on logic or elsewhere, please just tell me where to look.
..I'm also interested in the implicit use of time, or sequence, in many of the ideas discussed here.
For instance you might say that some of your Somethings are 'bitstrings' that could make up one of Bruno's or Jürgen's worlds/observers.
Remember that comp, as I present it, make "worlds" non computable. It is a consequence of
of the self-duplicability, when distinguishing 1 and 3 person points of view.
Part of our idea of a string is the convention that one element comes first, then the second, then the third, et cetera.
However, the information that accounts for that convention is not contained in the string itself. 'Taking' a Something as a bitstring involves some degree of external convention.
Indeed, it needs a universal machine, and even an infinity of them. But all that exists and describes by the set of (sigma1) true arithmetical propositions. See Podniek's page
http://www.ltn.lv/~podnieks/gt.html
So my question is, what do you mean when you say "a universe that has a sequence of successive states that follow a set of fixed rules?" What could make one state "give rise" to the "next" state? Citing "causality" just gives a name the problem; it doesn't explain it.
I completely agree with you. The primitive "causality" of the comp platonist is just the
"implication" of classical propositionnal logic. Most of the time (sorry for the pun) time of a computation can be described using no more than the axioms of Peano Arithmetic, including especially the induction axioms: that if P(0) is true and if for all x (P(x) ->P(x+1) ) then for all x we have P(x).
(Witten B(0) & Ax(B(x)->B(Sx)) -> AxB(x) in
http://www.ltn.lv/~podnieks/gt3.html#BM3
(S x) is x + 1
And I don't think introducing a Turing machine helps with this basic problem, since in any automaton you have rules that say e.g. state X at time T begets state Y at time T+1, again placing a convention of sequence (time, here) external to the system itself.
But that "time" can be substituted by natural numbers, enumerating for exemple the states of some universal machine (itself described in arithmetic).
This question doesn't engage with your schema head-on; it's more of a side detour I've thought of asking about many times on the list; I thought it might get explained at some point. Well, now I'm asking.
Now, if you ask where natural numbers comes from, that's a real mystery.
But then I can explain you why no Lobian Machine can solve that mystery, and why, if we want to talk about all the natural numbers, we are obliged to postulate them at the start.
Kind Regards
Bruno
http://iridia.ulb.ac.be/~marchal/
