On 11 Jan 2014, at 23:11, meekerdb wrote:
On 1/10/2014 11:43 PM, Bruno Marchal wrote:
But what is the measure of "relative persistence"?
It is the measure almost defined by the material hypostases (in
S4Grz1, Z1* and X1*). It defines the comp physical laws.
How do those different logics define a measure over possible physics?
By defining a proximity space on computation or sigma_sentences proof.
Technically this use a representation theorem of quantum logic (due to
Goldblatt), which defines such measure, in term of a modal logic
(known as B), with main axioms Bp -> p, and p -> BDp. The logics above
prove those two theorem (and disprove BDp -> p, avoiding the collapse
into classical logic), and heve the exact properties such that the
translation of p into BDp acts as a quantization, close enough to
simulate a quantum computer, except from still unsolved problem.
Von Neumann defined a quantum logic to be "right", if it determines
all probabilities (not just the case of certainties). He failed to
find it, but if comp is correct, and if the classical notion of
knowledge is accepted, then the representation theorem shows how to
lift a Gleason like measure unicity proof from them, and so the
arithmetical quantum logic should be of the type of Von Neumann, ...
or comp and classical theory of knowledge are false.
One day, I will list (at least) the representation theorems making the
hypostases and quantization possible (and necessary).
Bruno
Brent
If they don't exist, comp has to be false, or we are in a
simulation, or the S4 theory of knowledge should be amended.
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