On 21 Aug 2017, at 18:59, Telmo Menezes wrote:
Bruno, sorry for the delay as usual -- I really appreciate your
replies but life gets in the way...
I understand. No problem.
On Sun, Aug 13, 2017 at 7:25 PM, Bruno Marchal <[email protected]>
wrote:
On 13 Aug 2017, at 01:46, Telmo Menezes wrote:
On Sat 12. Aug 2017 at 03:12, Bruce Kellett <[email protected]
>
wrote:
On 12/08/2017 3:22 am, Bruno Marchal wrote:
On 11 Aug 2017, at 13:40, Bruce Kellett wrote:
Are you telling us that P(W) ≠ P(M) ≠ 1/2. What do *you*
expect when
pushing the button in Helsinki?
I expect to die, to be 'cut', according to the protocol. The
guys in
W and M are two new persons, and neither was around in H to make
any
prediction whatsoever.
Fair enough.
You think the digital mechanism thesis is wrong.
Correct.
There is a fundamental problem with your person-duplication thought
experiments. This is that the way in which you interpret the
scenario
inherently involves an irreducible 1p-3p confusion. The first person
(1p) concerns only things that the person can experience directly
for
himself. It cannot, therefore, involve things that he is told by
other
people, because such things are necessarily third person (3p)
knowledge
Things that are told by othet people reach us as 1p experiences. We
accept
them (or not) based on our own internal models of reality. Some
people trust
evangelical preachers, others trust what is published in Nature. It
is only
by personal cognitive processes that we can make such choices.
There is no
such thing as pure 3p knowledge, that is nonsensical.
There is no 3p knowledge as such. But there is still a 3p
Theaetetical
possible knowledge, in a theoretical frame.
For example, just imagine that 2 + 2 = 4 is really really really
really true
(imagine!), then I would say that if a machine is such that
(B_(that machine) "2 + 2 = 4") is true about that machine, then,
assuming
Mechanism, (or not, I am not sure) we can say that the machine has
a correct
3p knowledge, even 0p knowledge if the machine itself bet on
Mechanism.
Isn't this the same as assuming an independent reality, that remains
consistent even when nobody is looking?
Yes. (But this can mean the same thing at different level). You need
to believe in a minimal number of things and relation between things
to have the notion of universal machine or number to make sense of the
mechanist hypothesis.
I'm not disagreeing -- nor an I saying that such a reality does not
exist. Just that it's an untestable assumption (albeit a very common
and useful one).
Yes, and with mechanism we can limit the assumption to the sigma_1
truth.
The universal machine(s) already say "tat tvam asi" to the universal
machine(s) :)
Note that the sigma_1 truth is NOT Löbian, but we can consider it as
the "knower of the sigma_1 true proposition", or just let open if it
is a thing (which it certainly is) or a person.
Assuming mechanism, ISTM that one would then assume that we are
"inside" the machine for which 2 + 2 = 4, which is what we do
The point is that 2 + 2 = 4 (and its friends) emulate all machines for
which 2+2=4.
but then
Gödel has something to say.. Right?
Gödel missed Church's thesis, and was reluctant to both mechanism and
materialism. But he is the first to realized that a very large class
of computable functions, can be represented in arithmetic, and that
through its arithmetization of meta-arithmetic he got an isomorphism
between arithmetical relation and metamathematics.
Let me quote the footnote 9 of his 1931 paper:
"In other words, the above-described procedure provides an isomorphic
image of the syestem PM in the domain of arithmetic, and all
metamathematical arguments can equally be conducted in this isomorphic
image".
But, he will miss explicitly the law of Post, alias Church's or
Turing's thesis. I think that in his 1934 paper he explains that
identifying computability with recursiveness, or formal system with RE
set, would be premature and would need a more careful analysis. A bit
like Post who see the thesis as a "natural law" of human psychology.
After reading Turing's paper, Gödel is convinced by Church thesis, and
consider rightly that the closure of the set of programmable functions
for the diagonalization procedure is a kind of miracle. It is, indeed.
Only Post, who anticipated everything in the early 1920, including the
Lucas-Penrose proof that we are not machine, and its correction, and
even get a glimpse of immaterialism (but still added in a later
footnote that this was a grave mistake, also changing his mind after
reading Turing, and so missing that the immaterialism he saw was a
consequence of mechanism).
Turing was a metaphysical naturalist. Gödel was skeptical on
naturalism, materialism and mechanism.
So, we don't have third person (3p) knowledge, OK, it would be non
sensical.
In fact knowledge is pure 1p.
But, in the frame of some axiom in metaphysics, like Mechanism, I
think that
a part of mathematics becomes a 3p knowledge (arithmetic!). You can
someone
observe the arithmetical truth from outside, and "see" all the
"diaries" of
all machines, and their astonishment when "opening" the doors, or
just
through birth, when they find themselves in this or that galaxy or
city ...
Assuming we're not crazy, ok.
Assuming 0 ≠ 1 is enough.
You can assume ~[]_Telmo (0 = 1), either at the metalevel, privately
or instinctively. You can make it explcit and stay consistent, also,
by becoming the "new Telmo", with higher provability matter, or you
can make it explicit and stay the same; and becoming inconsistent.
I think that for a believer in mechanism, who would based his
belief from
studying computer science (and not just obeying his doctor!),
arithmetic and
the core of computer science is 3p knowledge, and even 0p
knowledge: Nagel's
point of view of nowhere.
Ok, but I'm not sure what you mean by the distinction between 3p and
0p, or what you mean by 0p exactly. Is it something you can map to
"your" hypostases?
Yes. It is first one. The One. p in
p
Bp
Bp & p
Bp & Dp
Bp & Dp & p
It is 3p, you can even imagine it as the set of the Gödel number of
the (sigma) true arithmetical sentences.
But it is sigma_truth, not sigma_1 proof.
now, for p sigma_1, G* proves p <-> Bp.
But G does NOT prove that!!!!!!!!!!
God knows that you are God, but you are not suppose to believe that,
so to speak. Still less to say it aloud. That would desrve a
psychiatric/spiritual "treatment"!
I try to explain to David that identifying God (a person) with the
"ontological 3p truth" is close to a "blasphemy". The truth belonging
to G* minus G.
The (Gödel-Löbian) machine can prove the p -> Bp part of the
blasphemy (and indeed that is equivalent with Löbianity, it is a sort
of awareness of universality), but the honest/correct machine will not
prove/assert/believe Bp -> p) (Bf -> f is equivalent with Dt,
consistency!).
So, to avoid 3p = 1p (for god), but keeping a sort of personal view of
truth, the "0th person point of view" I discussed with David, makes
some sense, even more so that the truth of the arithmetical
proposition is out of space and time.
That 3p knowledge, is of course still only an 1p belief, from the
1p view. I
agree with you from the 1p view! I just make precise that in a
theoretical
frame, God can see that sometimes, some-relative-states I should
say, some
of our belief are true. I do think that this is the case for 2 is a
divisor
of 24.
Ok, I think we agree. I have no qualm here.
My point remains: the argument that Bruce makes against your theory
can be made against any theory, or the scientific endeavor itself.
Certainly. I am not sure I have put this in doubt.
For me, John Clark is more mysterious. I don't bother with the
circular discussion anymore (we've been through the loop too many
times).
I am a platonist neo-neo-pythagorean. I let him 10^(a billion)
attempts, but not one more.
I think he's just playing games with language, but I'm not
sure why.
I am not sure why too.
Maybe a protection mechanism. Some conclusions are indeed
scary,
I don't think he is afraid, except perhaps from losing an argument. He
gives his brain to unknown doctors, so I doubt he fears the first
person indeterminacy, or perhaps you are right, and he has the courage
of the one who deny the danger? I am not sure. Too many theories/
possibilities.
All the best to you and everyone else here,
Best wishes Telmo!
Bruno
They went to sea in a Sieve, they did,
In a Sieve they went to sea:
In spite of all their friends could say,
On a winter's morn, on a stormy day,
In a Sieve they went to sea!
And when the Sieve turned round and round,
And everyone cried, "You'll all be drowned!"
They cried aloud, "Our Sieve ain't big,
But we don't care a button, we don't care a fig!
In a Sieve we'll go to sea!"
(Edward Lear)
Telmo.
-- knowledge which he does not have by direct personal experience.
So
our subject does not know the protocol of the thought experiment
from
direct experience (he has only been told about it, 3p). When he
presses
the button in the machine, he can have no 1p expectations about what
will happen (because he has not yet experienced it). He presses the
button in the spirit of pure experimental enquiry -- "what will
happen
if I do this?" His prior probability for any particular outcome is
zero.
So when he presses the button in Helsinki, and opens the door to
find
himself in Moscow, he will say, "WTF!". In particular, he will not
have
gained any 1p knowledge of duplication. In fact, he is for ever
barred
from any such knowledge.
If he repeats the experiment many times, he will simply see his
experiences as irreducibly random between M and W, with some
probability
that he can estimate by keeping records over a period of time. If
you
take the strict 1p view of the thought experiment, the parallel
with the
early development of QM is more evident. In QM, no-one has the 3p
knowledge that all possible outcomes are realized (in different
worlds).
So, before pressing the button in H, his prior probabilities are
p(M) =
p(W) = 0, with probably, p(H) = 1. On the other hand, if you allow
3p
knowledge of the protocol to influence his estimation of
probabilities
before the experiment, you can't rule out 3p knowledge that he can
gain
at any time after pressing the button. In which case, the 1p-3p
confusion is complete, p(M) = p(W) = 1, and he can expect to see
both
cities. In that case, the pure 1p view becomes irrelevant.
This argument can be applied to any scientific theory whatsoever.
That is
what hardcore postmodernists do. Ok, but then you are just
rejecting science
as a whole.
Also, you are in profound disagreement with John Clark. The only
thing your
positions have in common is your disagreement with Bruno.
Good point.
Bruno
Telmo.
Bruce
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