On 20 Jul 2016, at 23:44, John Clark wrote:
On Wed, Jul 20, 2016 at 9:34 AM, Stathis Papaioannou <stath...@gmail.com
> wrote
There would be a discontinuity if you go into the teleporter in one
city and get out in another, but there is also a discontinuity if
you fall asleep on the train.
Except at death conscious is always continuous,
With computationalism, it can be shown (in different ways) that
conscious is continuous even at death, although it is here that we
have to take the 1-3 distinction the most into account.
That is almost trivial. Your first person is associated with
infinitely many computations, making conscious continues, and this
with some intuitionistic semantic topology (as provided through the
mathematical 1p: S4Grz1 and X1*)
There is an inflation of type of immortality, and some depends on what
you identify yourself with.
Now, nobody can know for sure that computationalism is true, nor can
know for sure its own substitution level. But everyone can bet, as you
already did.
We don't need to believe in the theology of numbers, and we can
consider it as a "toy theology", but it is interesting that it can be
tested, and that what is weird and shocking in QM becomes trivial, and
I guess as much shocking, when we assume explicitly the digital
mechanist thesis. This happens at the intuitive level (step 7), and in
arithmetic (from theoretical computer science).
I am aware this is step 7 level advanced computationalism (grin), and
it requires a good understanding of the extensional and intensional
Church-Turing-Post thesis (non grin), and some knowledge on how
recursive functions and predicate can be represented in (very weak)
arithmetical theories, like RA.
I insist anyone interested (having studied a bit the Mendelson book,
or Boolos & Jeffrey) take a look on the three papers of Tarski,
including the important --Mostowski, Robinson, Tarski paper, where RA
is born and shown essentially undecidable (undecidable and so for
*all* its consistent extensions and theories in which they can be
interpreted).
People should understand well that the notion of computation is not
just a well defined mathematical concept, but that it is also an
arithmetical concept, indeed a Sigma_1 complete one, like, notably
Gödel's beweisbar predicate []p, or [0]p, which is axiomatized by G
(at the machine justifiable level) and G* (at the truth level).
although the outside world may not be.
With mind-digitalism (the mechanist hypothesis in the *cognitive*
science) there are infinitely many universal numbers which compete for
making you believe in an sensible and stable world. What does that
give? We can only do the math.
Bruno
In your example it's the train that behaves discontinuously,
instantaneously it jumps many miles ahead.
John K Clark
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