On 13 Jun 2016, at 06:16, Brent Meeker wrote:
On 6/12/2016 10:38 AM, Bruno Marchal wrote:
Mechanism implies observable obeys quantum logic and not any other
logic, and that the subject obeys intuitionist logic, and not any
other logic.
What does that mean?
Rationally believable is, for the ideally sound machine, modeled by
its arithmetical provability predicate ([]p).
Let [1]p be defined by []p & p, and [2]p by []p & <>t, and [3]p by
[2]p & p.
Then we have the following facts:
G* proves []p <-> [i]p (i = 1, 2, 3)
G does not prove any of those equivalence.
That implies that the logic of [1], [2] and [3] are different.
UDA (and generally Digital Mechanism) implies that physics should be
given by the self-reference modalities, and the probability one should
be given by those modalities obeying the "probability" modal axiom []p
-> <>p, and this restricted on the computable "events", which are the
leaves of the universal dovetailing, and can be shown equivalent to
the (true) sigma_1 sentences.
The math shows that they indeed provides quantization modal logic,
even quantum logic close to some already discussed in the physicists
literature.
[1]p gives intuitionist logic (which is nice for the internal first
person view)
[2]p gives sharable quantum logics (plausibly close the searched first
person plural notion), and its gives on p sigma_1 a quantum logic at
the star (true) level (use G*).
[3]p gives a curious logic which is both intuitionist and quantum, and
is supposed to be, at the G* minus G level, the logic of qualia. Note
that quanta are particular qualia, but that is equivalent with Everett
QM, the worlds are sharable dreams.
[1]p gives the knower, the soul, the internal god, .... (named
different according to different tradition, history).
[2]p gives the observer
[3]p gives the feeler (if I can say).
Physics should be entirely determined by the measure one logic, and so
we can expect an equivalent of Gleason theorem in all models (in the
logician sense) of the logic of [3]p (at least).
It is really incompleteness which introduces all those nuance between
the way a machine can apprehend itself with respect to the
arithmetical reality or truth.
Bruno
Brent
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