Le 26-nov.-07, à 20:22, George Levy a écrit :
> Yes I am particularizing things... But "the end justifies the means".
> I am being positivist, trying to express these rules as a function of
> an observer. In any case, once the specific example is worked out, we
> can fall back on the general case.
> Your feedback about "exist" not really being adequate to express
> truth is well noted. Let me change the proposed rules to express truth
> as a function of an axiomatic system A existing as data .... either in
> the memory of M .... or as a axiomatic substrate for a simulated world
> W..... Let's try the following:
> In a world W simulated according to the axiomatic data system A,
> there is a machine M, data p and data q such that
> 1) If M has access to p (possibly in its memory), then p exists in W.
> (exist=being simulated in W according to A )
> 2) If M has access to p, then M has access to the access point to p.
> 3) If M has access to the information relating or linking p to q then
> if M has access to p, it also has access to q.
> Now we can make the statements reflexive ( I don't know if this is
> the right word) by setting data p = Machine description M.
> In a simulated world W following the axiomatic data system A there is
> a machine M=p and data q such that
> 1) If M has access to M then M exists in W. (reflexivity?)
> 2) If M has access to M, then M has access to the access point to M.
> (Infinite reflexivity? - description of consciousness?)
> 3) If M has information describing q as a consequence of M in
> accordance with A, then if M has access to M, it also has access to q.
> (This is a form of Anthropic principle)
> I am not sure if this is leading anywhere, but it's fun playing with
Sure. And playing is the best way to learn, as "nature" knows since the
> Maybe a computer program could be written to express these staqtements.
I certainly encourage you to do so. Note that for the general modal
theory, S4, or even the comp fist person S4Grz, programs already
By some aspect your attempt reminds me also of dynamic logic. This is
modal logic applied to computations (and thus a bit away from
"computability" which concerns my more "theological" global concern ;).
You could googelize on "dynamic modal logic". I am not at all an expert
on those logics, to be sure.
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