On 04 Jul 2016, at 19:20, John Clark wrote:
On Mon, Jul 4, 2016 at 3:59 AM, Bruno Marchal <[email protected]>
wrote:
>> If it's really a well formed question then the personal
pronoun "you" could be replaced with "John Clark" , but that can't
be done without destroying the value of the thought experiment has
to the theory.
> Nope. It works very well with "John Clark" instead of "you".
OK fine, then the statement "John Clark will see BOTH Washington
AND Moscow" works very well.
>> In a world with people duplicating machines the question is
far too vague to have an answer,
> Nope. The question is clear, and has a definite answer, once
we distinguish the 1-self and [blah blah]
OK fine, then distinguish it. Do you want a prediction about the
Helsinki 1-self or the Moscow 1-self or the Washington 1-self?
> just as in our world the question "how long is a piece of
string?" has no answer. And please, don't start going on and on
about diaries again, two people remember writing that diary; which
particular person and which particular piece of string are you
talking about?
> Both of them of course
OK fine, if that's what Bruno Marchal means by "you", the person
who remembers writing the diary, then "you" will see BOTH cities.
And of course if something else is meant by "you" then "you"
will not see both cities, in that case what "you" will actually see
depends on what the 3 letter word "you" means. In the our everyday
world the meaning is obvious, but it wouldn't be in a world with
people duplicating machines.
>> So after one precise person had been duplicated and become
two precise people tell me which one of those two precise people
you're interested in
> We are interested in both discourse. Both agree with "W v M",
and both are wrong with "W & M".
That is just flat out wrong. If it was agreed before the
duplication that "you" means somebody who remembers writing the
diary, and assuming the ability to reason logically is retained by
both after the duplication, then both would agree that "You" saw
both cities. It all depends on what the word "you" means, and
that's why all personal pronouns should be banned from such thought
experiments.
> Keep in mind that we ask for the prediction in Helsinki.
Yes but who precisely was the prediction requested in Helsinki
supposed to be about? I assume it was about what further adventures
the man (or in this case the men) who remember being in Helsinki
would have in the future, but that is never made clear.
> By computationalism we know that we have to verify the
prediction for all first person involved in the reconstitution.
Until it's nailed down exactly what the personal pronoun "you"
means absolutely nothing can be verified or refuted, and thus it's
not a experiment, it's not even a thought experiment. So forget
personal pronouns and use proper nouns!
>> If that answer is unsatisfactory then give me a more precise
question.
> What can John Clark predicts about its future first person
experience in Helsinki?
If "its" means John Clark then John Clark would predict John Clark
would see both cities; not that predictions correct ones or
incorrect ones, have the slightest thing to do with the sense of self.
>> And if Everett is right then demanding a yes or
no answer to the question "will Schrodinger's cat breathe the
cyanide poison gas?" would be silly because it's a ill formed
question that has no answer, the same as "how long is a piece of
string?" or "what city will you see?".
> Or "what city will John Clark see".
John Clark will see both cities and Schrodinger's cat
will breathe the cyanide poison gas and Schrodinger's
cat will not breathe the cyanide poison gas. I plant an
apple tree and predict it will produce red apples and I predict it
will produce green apples and I predict it will not produce a apple
that is both red and green; does Bruno Marchal also believe that
prediction is ridiculous?
>> For the 42 time I DON'T CARE If MATTER IS PRIMARY! If
your interest is consciousness it's irrelevant, primary or not
primary matter is needed.
> Only because you stop at the third step of the reasoning,
Reasoning? The third step was the point where the blizzard of
unattributed personal pronouns became too dense to endure.
> It should be obvious, given the definition of 1p
The definition of the homemade term 1p is me, and the definition
of me is 1p. And round and round we go.
> using pronouns or name does not change anything here.
Then why does Bruno Marchal continue to use wall to wall personal
pronouns in thought experiments despite being begged for years not to?
OK. I will make a new attempt, and I am in a so good mood that I will
do it without using any pronoun, then I will explain what I have seen
that some other often still miss: how to define and eliminate any use
of 3p pronoun and proper name when we translate all this in arithmetic.
Note that the way I will not use pronoun below is different than the
way I eliminate the pronoun much below. In the first part, I use some
intuition of the first person, and in the second part I eliminate only
the 3p pronoun notions of self (like in "I have two hands")
So, it happens that some guy, name John Clark is in Helsinki, and is
about to live a WM duplication experiment, with annihilation of the
"original body" in Helsinki. John Clark is a computationalist, and so
has no fear using classical teleportation device. Such John Clark
knows that the survival through such experiment is guarantied by the
computationalist hypothesis and the default hypotheses.
In Helsinki, we ask John Clark (JC) to make a prediction, not about
where JC's two bodies will be reconstituted (everyone knows that the
answer here is "in Washington and in Moscow" as that is part of the
protocol), but about how many cities all the JC's involved will see
personally, in the direct way, and then which one, when the John
Clarks will open the door of the reconstitution boxes.
JC, suffering from acute allergy to pronouns, reasons a little bit,
and figure out correctly that one JC will see W, and not M, and one JC
will see M, and not W. So JC find the correct answer: all JC will see
only one city.
But now the question was "which one?". Well JC figures out that all JC
will see only one city among the two cities involved.
So it can only be, for *both* of them: W among {W, M}, OR M among {W,
M}. Then computationalism guarantied to all JC that they are both
respectable Helsinki-JC survivors, having survived a classical
mechanical teleportation, and so, by the numerical identity of the two
copies, there is no reason that one of the two personal experiences is
favored, leading to the theory which can be sum up by: which city is
unknown, but known to be among W and M (thus the experience is W v M,
without anymore precision possible), and the probability for the
Helsinki guy to feel having survived in anyone of those city is P = 1/2.
End of the elimination of pronoun in that piece of reasoning.
===================================
Now, for you and possible others: how do the mathematical logicians
and theoretical computer scientists eliminate the 3p pronouns.
I give you the intuitive idea: Imagine a duplicator D of expressions.
On some argument a; it gives a description of the duplication aa. Dx
gives 'xx'.
(where the quote is a meta-quote, it can be managed in the formal
systems, and this is illustrated below). But then, the usual second
diagonalization: DD, gives 'DD'. So basically, we see that a self-
duplicator, like DD, is a duplicator applied to itself, or a
recursively equivalent description of itself.
Now, fix a Turing universal (programming) language. Write a program
which enumerates all programs computing functions from N to N with one
argument P_0, P_1, P_3, ... That's the P_i. For them you can write
the corresponding functions: that are the phi_i (the partial
computable functions). I have already explained that if we want get
all total computable functions, the price is that we have the company,
among the phi_i which are computable on all N (domain of phi_i = N),
of the phi_i which have a domain which is only a subset of N: the w_i,
which happens to be the recursively enumerable sets.
All reasonable such system verifies two laws:
1) The existence of a universal number. That is a number u such that
phi_u(x,y) = phi_x(y).
u, when given program x and data y get the result of the program x run
on data y. I say that u emulates x on y.
(In this post, the universal numbers will not been used, except for a
mention)
2) the SMN theorem. I give the S21 and the S10 versions. Write a
program which enumerates now the programs computing the functions of
two arguments P^2_i.
Then S21 is a (meta) program with two arguments: a number k and a
program taken from P^2_i.
S21 output the P^2_i with one argument parametrized on k.
More simply with an example, S21 would transform the following
program, when given the number k:
Begin
Declare X Y numbers
output X + Y
End
into
Begin
Declare Y number
output k + Y
End
The S21 law: for all i, x, y phi^2_i(x,y) = phi_S21(i, x) (y) (the
program S21(i,y) applied on y.
Actually I will need S10, which transforms programs from P_i into
programs without input (some stop, some does not stop) P^0_i.
S10 fixes the only variable in the program from P_i.
Begin
Declare X number
output what-you-want(X)
End
into (S10 has still two inputs; the program just above and k)
Begin
output what-you-want(k)
End
The S10 law: for all x and y we have phi_i(x) = phi^0_S10(i,x) ().
SMN generally fixes likewise N arguments in a program with M
arguments. You can find variate such program which parametrize the
partial computable functions. They define themselves total computable
functions.
I need only S10 to eliminate the pronoun, and define a constructive
notion of 3-self (the 3p self, the "body" or any 3p description of the
body: it is a finite thing).
Now S10 can be programmed in that language, it is a computable
function from P_i to P^0_i, with the corresponding metafunction
(operator) from the phi^i_i (= the phi^1_i) to the phi^0_i.
And let us do the two diagonalizations.
Consider the function S10(x, x), (first diagonalization). It defines a
function with one argument, and so it has a code among the P_i, let us
call it r,
phi_r(x) = S10(x,x)
But by using the S10 law
phi_r(x) = phi^0_S10(r,x)()
Then, second diagonalization: let us put x = r:
phi_r(r) = S10(r,r) = phi_S10(r,r)()
e = S10(r,r) gives the solution: a program e such that phi_e() gives
its own indice or description e.
Similarly you can generalize with any computable function applied to
that description,
For all T you can find a e such that phi_e(x, y, ...) = T(e, x,
y, ...). (Kleene second recursion theorem)
Use some phi_r(x,y) + T(S(x,x) y) in the place of phi_r(x) = S(x,x),
and follow the same proof.
See my long text for a program P which dovetails on its own emulation
(using the universal number, which have not been used here), in two
different contexts (like some description of Washington and Moscow.
See my papers for applications in self-reproduction, self-
regeneration, self-reference, multi-self-emulation, etc.
Now, to define the 1-self is quite another story: no machine can do
that, despite it is what they know the best. We can define it by the
knower, and (meta)-defined it by the one in contact with the possible
reality (the glass-of-Milk). In this case the glass-of-Milk can be
first approximated by the notion of Arithmetical Truth (and with
computationalism, even with the Sigma_1 arithmetical truth, using G*
minus G to avoid the (fatal) blaspheme (confusing truth with belief or
assertions)). By restricting, necessarily non constructively, the
belief on truth, with [1]p = []p & p, ([]p = the arithmetical Gödel's
beweisbar) we get a knower, that the machine cannot define, but know
very well.
(Indeed, it asks for a civilization or education, I think, to separate
[]p & p from []p)
We can get many things from those definitions, including a multi-modal
logic in which we can ask about the 1-views on the 3-views on the 1-
views, ... and with no pronouns at any place.
I have already given often references on this. I realize that I have
rarely cited one of my (old) favorite paper in the field:
Smorynski Craig , Fifty years of self-reference in arithmetic. Notre
Dame Journal of Formal Logic Volume 22, Number 4, October 1981.
See also his book on modal logic and self-reference, which exposes
Solovay theorem (G is called Prl and G* is called Prl-omega).
But of course if you have the Boolos books it is enough, and for those
not willing to do to much math, Smullyan has written many introductory
books on the subject, notably a recreative book on Löb theorem and the
modal logic G ("Forever Undecided").
Bruno
John K Clark
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