On 03 Sep 2013, at 18:23, John Clark wrote:
On Tue, Sep 3, 2013 at 12:01 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
> indeed "free" does not add much to the will, except to emphasize a
local freedom degrees spectrum.
It doesn't even do that. "Will" is the set of things I want to do,
It is a bit circular, but that's not a problem. OK.
but some of those things may not be physically possible, and some of
my wishes may not even be logically consistent with each other, but
I want them all the same.
? Well, in that case you have a problem to solve.
> If you are imprisoned, you can keep the will, but have the free-
will quite constrained
I'm not imprisoned,
How do you know that?
however I very much want the cardinality of the Real Numbers to be
the same as that of the integers, but my wish remains unfulfilled.
Cardinality is a relative notion. All (first order) theories have an
enumerable model.
Your wish can be exhausted ... outside our universe.
Assuming comp it is "absolutely undecidable if our "universe" (if it
exists) is enumerable or not enumerable, but from inside it is
definitely not enumerable, and all we can hope is that the "outside
seen from inside" is constructively not enumerable, and this is the
case for the ideally correct Turing (Post, Church, ...) Universal
Machine.
Comp associates consciousness to computation, and computation is an
arithmetical concept (the proof of this is in all good textbook on
computer science (the best one on that topic are Boolos and Jeffrey,
Epstein & Carnielli, etc.). It follows also in an amazing way in
Matiyasevitch work. The additive+multiplicative structure of the
natural numbers does implement a universal dovetailer. (Probably just
the way primes distributed I would bet).
And this makes only possible to formulate the mind-body problem in
term of the statistic on the computations, obtained through a limit
based on the invariance of the first person for the computations below
their substitution level. If comp is false, this would still provide
tools to measure our degree of non-computability.
My point is that comp makes this amenable to computer science, which
is arithmetic, or take any base (universal system or language) you want.
I don't assume there is a physical universe, and ontologically there
is none, comp + arithmetic explain how to extract the beliefs in
stable lawful universe from a sort of statistics on which converge
ideally correct machines.
A Turing machine cannot know which computations run her, but can bet
that below her substitution level she is run by a sort of average on
an infinity of computations.
The mysteries are why unitary transformations?, why linearity?, etc.
There are results and open problems.
Of course, it is a different conception of "reality" than the usual
(Aristotelian) one (since always, except for some antic greeks during
a millenium, and Indian and mystic).
Bruno
John K Clark
We might use free-will as just will + freedom. It presupposes some
stable deterministic realities, at some level.
Bruno
http://iridia.ulb.ac.be/~marchal/
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