Re: Incompleteness vs. Mechanical Reasoning

On Apr 5, 4:07 pm, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:
On 2008-04-04, in sci.logic, Rupert wrote:

How do you know that we have free will?

Being the predictable scoundrel I am, I would first ask just what it
means for us to have or fail to have free will. Isn't philosophy fun!

Consider a proposition P about a future contingency that is based on
the decision taken by a human being X. A human being has free will if
and only if that proposiiton is fundamentally undecidable right now,
in the sense that we human beings (including X) cannot ever hope to
have a theory (right now) that correctly decides P. Futher P remains
similarly undecidable right until that point of time at which X takes
the decision (in which case at least X can correctly assert the truth
or falsity of P).

At this point you would say "Right now we do have a theory T1 which
proves P and another theory T2 which proves ~P and one of these has to
correctly predict the truth or falsity of P; but we human beings have
no way of predicting which of these is the correct theory". This is
exactly equivalent to asserting that "Right now P is either true or
false, but we human beings have no way of saying which of these is the
case". And this is exactly what NAFL rejects. The *knowledge* that one
of these is the right theory can only come *after* P has been decided
by X and not before. Right now, we *cannot* have that knowledge
because if we did, X could contradict that outcome out of free will.
So *right now* there is no truth for P and in fact from the NAFL point
of view, P&~P is the case (meaning basically that we do not have a
proof of either P or ~P in our best possible theory at this point of
time). Later on we could discover, e.g., that "T1 was always the
correct theory", but this assertion is a temporal truth that only
applies *after* our discovery and not before. So there is no
contradiction with the earlier conclusion that P&~P is the case, which
is meaningful in NAFL as discussed. Note that NAFL is a temporal logic
that deals correctly with the time-dependence, which is crucial here.

An analogiy with quantum physics is in the Schrodinger cat example.
Right now, at time t0, the cat is in the sealed box and we cannot
possibly have any knowledge of its classically possible state (alive
or dead). So quantum physics asserts that right now the cat is in a
state of "alive and dead". From the NAFL point of view, the cat's
state changes when (and only when) we open the box and find out its
state. Until that time the cat remains in a superposed state. This
superposed state means in NAFL that we do not have a proof in our best
quantum physics theory T that the cat is alive and we do not have a
proof in T that the cat is dead. The cat's state changes when and only
when we open the box and determine it. Suppose we open the box at time
t1 > t0 and find that the cat is alive. Now classically, one would
assert that the cat was always alive, and its state was "alive" even
at time t0 when we could not have known that it was alive. This is
contradicted by quantum physics, which asserts that the cat's state
was "alive and dead" at t0 and until that point of time t1 when
"decoherence" occurred by our opening the box and exposing the cat to
the environment.

From the NAFL point of view, no "decoherence" occurred when we opened
the box. The only thing that happened was that we found out that the
cat is alive. In fact one could assert that the cat was always alive,
but *at time t0* this is a metalogical "reality" which NAFL does not
recognize. Even in NAFL, the cat's state was in a superposition state
at time t0. and this is the only "reality" that exists at time t0. The
reality that "The cat was always alive, even at time t0" can only be
asserted by us human beings *after* time t1, and so such a reality can
be validly concluded retroactively, *after* time t1, which does *not*
contradict the earlier-concluded superposed state at time t0. Here it
is crucial to realize that the superposed state expresses a
"reality" (from the NAFL point of view) that we humans cannot possibly
have any knowledge of the cat's physical state. Since the later
discovery that "the cat was always alive" is a temporal truth that
applies *after* time time t1, and the earlier superposed state does
*not* mean that the cat was "really" alive-and-dead, there is no
contradiction in NAFL (which is a temporal logic).

So what does the Schrodinger cat experiment have to do with free will?
From the NAFL point of view, the cat's state changed from "neither
alive nor dead" to "alive" (and in fact to ":the cat is and was always
alive") only because we human beings decided to open the box out of
our free will at time t1. If we had not done that and if we never ever
open the box, the cat's state would forever be "neither alive nor
dead" (as expressed by the superposed state) and no reality can ever
be concluded for the cat's physical state that is independent of our
minds (or equivalently in NAFL, indpendent of our best physics
theories which we have in mind). Or to put it more accurately, any
such "reality" will have to be metalogical, i.e., outside the purview
of logic, as far as NAFL is concerned.

Regards, RS
.

Relevant Pages

  • Re: Incompleteness vs. Mechanical Reasoning
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    (sci.logic)
  • Re: Murphy HMM problem
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    (comp.soft-sys.matlab)
  • Re: Murphy HMM problem
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