ASSA vs. RSSA and the no cul-de-sac conjecture was (AB continuity)

[Johnathan Corgan]

While I wasn't around for the original ASSA vs. RSSA arguments on the
list here, and I'm sure I'm risking a rehash of things back then, the
recent traffic over "adult vs. child" and "AB continuity" seems to
revolve around this anyway.

It seems intuitively obvious to me that from a 1st-person perspective, I
have to treat successor observer moments with a /conditional/
probability.  My next observer moment I face would be selected from
among only those where a), I am conscious, and b) those with memories of
this one, or more generally, with a causal thread of continuity with
this one (unitary evolution of SW).  So my subjective expectation would
then be the absolute probability of those occurring conditioned on, or
given, that the one I'm in now has already occurred.

It is an open question (to me at least) whether there are any observer
moments without successors, i.e., where the amplitude of the SW goes to
zero.  If it does not, then this implies that the always branching tree
of observer moments has no leaf nodes--rather, it becomes an ever finer
filigree of lines, but any particular point will always have a
downstream set of forks.  This is the essence of the no cul-de-sac
conjecture, and the crux of the quantum theory of immortality.

If the above is true, then the absolute measure of an observer moment
becomes irrelevant; it's clear that as one traces through a particular
branch it would always be dramatically decreasing anyway.  But the
relative measure of my next observer moment to this one becomes the
thing that drives my expectations of what I am "likely" to experience.
Indeed, some version of me experiences all of them, but each split copy
of me can only say to himself, "what I am experiencing now was likely
(or unlikely) given where I was a moment ago."

Johnathan Corgan


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[Stathis Papaioannou-2]

2009/2/12 Johnathan Corgan <jcorgan@...>:

> It is an open question (to me at least) whether there are any observer
> moments without successors, i.e., where the amplitude of the SW goes to
> zero.  If it does not, then this implies that the always branching tree
> of observer moments has no leaf nodes--rather, it becomes an ever finer
> filigree of lines, but any particular point will always have a
> downstream set of forks.  This is the essence of the no cul-de-sac
> conjecture, and the crux of the quantum theory of immortality.

Does MWI suggest that everything that can occur does occur? The
following article suggests not:

http://scienceblogs.com/pontiff/2008/11/everything_and_nothing.php

I guess it is still possible that the no cul-de-sac conjecture is
correct even though some ways of avoiding death are impossible.


--
Stathis Papaioannou

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[Bruno Marchal]

Excellent post Johnatan.

Of course those who know a bit of AUDA (which I have already explained  
on the list) know that from the third person self-reference views we  
have cul-de-sac everywhere ("we die all the times", cf the  
"Papaioannou multiverses"), and this is what forces us, when we want a  
theory of observation (which by UDA is a probability or credibilty  
calculus) to define the probabilities by imposing the absence of cul-
de-sac. This is *the* motivation for the new box Bp & Dt.  Dt, by  
Kripke semantics, is equivalent to imposing the absence of cul-de-sac.  
Yet, by incompleteness Dt is not provable by the machine, and after we  
make the addition of the "non-cul-de-sac" principle (Dt), we loose the  
Kripke semantics. But this is a good news, given that we will have to  
manage (plausibly) continua of "next observer momen or historiest".

Apology for those who have not follow the (many) old modal posts, but  
we will soon or later come back to this. Read Boolos book (and  
mathematical logic books).

Bruno


On 12 Feb 2009, at 00:09, Johnathan Corgan wrote:

>
> While I wasn't around for the original ASSA vs. RSSA arguments on the
> list here, and I'm sure I'm risking a rehash of things back then, the
> recent traffic over "adult vs. child" and "AB continuity" seems to
> revolve around this anyway.
>
> It seems intuitively obvious to me that from a 1st-person  
> perspective, I
> have to treat successor observer moments with a /conditional/
> probability.  My next observer moment I face would be selected from
> among only those where a), I am conscious, and b) those with  
> memories of
> this one, or more generally, with a causal thread of continuity with
> this one (unitary evolution of SW).  So my subjective expectation  
> would
> then be the absolute probability of those occurring conditioned on, or
> given, that the one I'm in now has already occurred.
>
> It is an open question (to me at least) whether there are any observer
> moments without successors, i.e., where the amplitude of the SW goes  
> to
> zero.  If it does not, then this implies that the always branching  
> tree
> of observer moments has no leaf nodes--rather, it becomes an ever  
> finer
> filigree of lines, but any particular point will always have a
> downstream set of forks.  This is the essence of the no cul-de-sac
> conjecture, and the crux of the quantum theory of immortality.
>
> If the above is true, then the absolute measure of an observer moment
> becomes irrelevant; it's clear that as one traces through a particular
> branch it would always be dramatically decreasing anyway.  But the
> relative measure of my next observer moment to this one becomes the
> thing that drives my expectations of what I am "likely" to experience.
> Indeed, some version of me experiences all of them, but each split  
> copy
> of me can only say to himself, "what I am experiencing now was likely
> (or unlikely) given where I was a moment ago."
>
> Johnathan Corgan
>
>
> >

http://iridia.ulb.ac.be/~marchal/




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[Bruno Marchal]

On 12 Feb 2009, at 14:30, Stathis Papaioannou wrote:

>
> 2009/2/12 Johnathan Corgan <jcorgan@...>:
>
>> It is an open question (to me at least) whether there are any  
>> observer
>> moments without successors, i.e., where the amplitude of the SW  
>> goes to
>> zero.  If it does not, then this implies that the always branching  
>> tree
>> of observer moments has no leaf nodes--rather, it becomes an ever  
>> finer
>> filigree of lines, but any particular point will always have a
>> downstream set of forks.  This is the essence of the no cul-de-sac
>> conjecture, and the crux of the quantum theory of immortality.
>
> Does MWI suggest that everything that can occur does occur? The
> following article suggests not:
>
> http://scienceblogs.com/pontiff/2008/11/everything_and_nothing.php

OK. Even in MWI, proving that 0 = 1 remains plausibly impossible.
Of course believing that someone did proved that 0 = 1 remains quite  
possible.



>
>
> I guess it is still possible that the no cul-de-sac conjecture is
> correct even though some ways of avoiding death are impossible.


Just try avoid death by squaring a circle :)

Bruno

http://iridia.ulb.ac.be/~marchal/




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[russell standish-2]

On Thu, Feb 12, 2009 at 04:48:22PM +0100, Bruno Marchal wrote:

>
> Excellent post Johnatan.
>
> Of course those who know a bit of AUDA (which I have already explained  
> on the list) know that from the third person self-reference views we  
> have cul-de-sac everywhere ("we die all the times", cf the  
> "Papaioannou multiverses"), and this is what forces us, when we want a  
> theory of observation (which by UDA is a probability or credibilty  
> calculus) to define the probabilities by imposing the absence of cul-
> de-sac. This is *the* motivation for the new box Bp & Dt.  Dt, by  
> Kripke semantics, is equivalent to imposing the absence of cul-de-sac.  
> Yet, by incompleteness Dt is not provable by the machine, and after we  
> make the addition of the "non-cul-de-sac" principle (Dt), we loose the  
> Kripke semantics. But this is a good news, given that we will have to  
> manage (plausibly) continua of "next observer momen or historiest".

I'm a little confused. Did you mean Dp here? Dp = -B-p

>
> Apology for those who have not follow the (many) old modal posts, but  
> we will soon or later come back to this. Read Boolos book (and  
> mathematical logic books).
>
> Bruno
>

--

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[Bruno Marchal]

On 12 Feb 2009, at 22:12, russell standish wrote:

>
> On Thu, Feb 12, 2009 at 04:48:22PM +0100, Bruno Marchal wrote:
>>
>> Excellent post Johnatan.
>>
>> Of course those who know a bit of AUDA (which I have already  
>> explained
>> on the list) know that from the third person self-reference views we
>> have cul-de-sac everywhere ("we die all the times", cf the
>> "Papaioannou multiverses"), and this is what forces us, when we  
>> want a
>> theory of observation (which by UDA is a probability or credibilty
>> calculus) to define the probabilities by imposing the absence of cul-
>> de-sac. This is *the* motivation for the new box Bp & Dt.  Dt, by
>> Kripke semantics, is equivalent to imposing the absence of cul-de-
>> sac.
>> Yet, by incompleteness Dt is not provable by the machine, and after  
>> we
>> make the addition of the "non-cul-de-sac" principle (Dt), we loose  
>> the
>> Kripke semantics. But this is a good news, given that we will have to
>> manage (plausibly) continua of "next observer momen or historiest".
>
> I'm a little confused. Did you mean Dp here? Dp = -B-p

Fair question, given my sometimes poor random typo!

In the so called "normal" modal logic, that is those system of modal  
logic containing the formula K

B(p->q) -> (Bp -> Bq)

and which are closed for both the modus ponens rule (from p and p->q  
you can deduce q)  and the rule of necessitation (from p you can  
deduce Bp) , well, if you remind the definition of the Kripke  
semantics, you can see that

Bp & Dp

is equivalent with

Bp & Dt

Bp is true in the world alpha, means that p is true in all the worlds  
Beta accessible from Alpha.

Dp is indeed equivalent to -B-p, it means that B-p is false, so it is  
false that in all the worlds Beta, accessible from Alpha, -p is true  
in them. So it means that there is world, accessible from Alpha,  
where  -p is false, that means that there exists  a world where p is  
true.

Now if you have in a world, your world if you want,  Bp & Dp, you have  
at least access to a world in which p is true, and thus you have  
access to a world where t is true, given that t is true in all worlds.  
So you have Bp & Dt.
The inverse: now you have in a world Bp & Dt.  Thus you have Bp and  
Dt, of course, and by Dt you have access to a world where t is true.  
But you have also Bp, so you know that in all the accessible world,  
from your world you have p, so you have Dp.

A good and important exercise is to understand that with the Kripke  
semantics,  ~Dt, that is B~t, that is Bf, that is "I prove 0=1", is  
automatically true in all cul-de-sac world. It is important because  
cul-de-sac worlds exists everywhere in the Kripke semantics of the  
self-reference logic G.

If you interpret, if only for the fun, the worlds as state of life,  
then Bf is  really "I am dead".

Bruno

>
>
>>
>> Apology for those who have not follow the (many) old modal posts, but
>> we will soon or later come back to this. Read Boolos book (and
>> mathematical logic books).
>>
>> Bruno
>>
>
> --
>
> ----------------------------------------------------------------------------
> Prof Russell Standish                  Phone [phone] (mobile)
> Mathematics                        
> UNSW SYDNEY 2052                 hpcoder@...
> Australia                                http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>
> >

http://iridia.ulb.ac.be/~marchal/




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[Jack Mallah]

Hi Johnathan.  I see that there are some new people like yourself here.  I like to see new people and younger people take an interest in the philosophical issues, though at the same time it saddens me to see so many continue to fall victim to the the QS fallacy.

I have made an important discovery: the "save as draft" feature of email. Rather than shoot off quick piecemeal replies to the various threads on the topic, I will be posting a consolidated reply and several thought experiments, which I hope will explain everything.  (No, not yet the Platonic Everything.)

Jack




     


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[russell standish-2]

On Fri, Feb 13, 2009 at 07:31:29PM +0100, Bruno Marchal wrote:
> >
> > I'm a little confused. Did you mean Dp here? Dp = -B-p
>
>
> Fair question, given my sometimes poor random typo!
>

...
> deduce Bp) , well, if you remind the definition of the Kripke  
> semantics, you can see that
>
> Bp & Dp
>
> is equivalent with
>
> Bp & Dt
>
...

> Now if you have in a world, your world if you want,  Bp & Dp, you have  
> at least access to a world in which p is true, and thus you have  
> access to a world where t is true, given that t is true in all worlds.  
> So you have Bp & Dt.

Thanks. Alles ist Klar. I think I wasn't taking seriously enough the
idea of Kripke frames before...

...

>
> A good and important exercise is to understand that with the Kripke  
> semantics,  ~Dt, that is B~t, that is Bf, that is "I prove 0=1", is  
> automatically true in all cul-de-sac world. It is important because  
> cul-de-sac worlds exists everywhere in the Kripke semantics of the  
> self-reference logic G.
>
> If you interpret, if only for the fun, the worlds as state of life,  
> then Bf is  really "I am dead".
>
> Bruno

Yes, but I have difficulty in _simultaneously_ interpreting logic
formulae in terms of Kripke frames and B as provability. In the
former, Bp means in all successor worlds, p is true, whereas in the
latter it means I can  prove that p is true.

How does one reconcile such disparate notions?

Cheers
--

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[Bruno Marchal]

Hi Russel,

On 15 Feb 2009, at 03:41, russell standish wrote:

>
> On Fri, Feb 13, 2009 at 07:31:29PM +0100, Bruno Marchal wrote:
>>>
>>> I'm a little confused. Did you mean Dp here? Dp = -B-p
>>
>>
>> Fair question, given my sometimes poor random typo!
>>
>
> ...
>> deduce Bp) , well, if you remind the definition of the Kripke
>> semantics, you can see that
>>
>> Bp & Dp
>>
>> is equivalent with
>>
>> Bp & Dt
>>
> ...
>
>> Now if you have in a world, your world if you want,  Bp & Dp, you  
>> have
>> at least access to a world in which p is true, and thus you have
>> access to a world where t is true, given that t is true in all  
>> worlds.
>> So you have Bp & Dt.
>
> Thanks. Alles ist Klar. I think I wasn't taking seriously enough the
> idea of Kripke frames before...
>
> ...
>
>>
>> A good and important exercise is to understand that with the Kripke
>> semantics,  ~Dt, that is B~t, that is Bf, that is "I prove 0=1", is
>> automatically true in all cul-de-sac world. It is important because
>> cul-de-sac worlds exists everywhere in the Kripke semantics of the
>> self-reference logic G.
>>
>> If you interpret, if only for the fun, the worlds as state of life,
>> then Bf is  really "I am dead".
>>
>> Bruno
>
> Yes, but I have difficulty in _simultaneously_ interpreting logic
> formulae in terms of Kripke frames and B as provability. In the
> former, Bp means in all successor worlds, p is true, whereas in the
> latter it means I can  prove that p is true.
>
> How does one reconcile such disparate notions?

By Godel's theorems, Löb's theorems and Solovay theorems.

When B is seen as provability, it really means "I can prove that p is  
true"  *when* asserted by a self referentially correct universal  
machine, believing (or asserting, or proving) the induction axioms,  
like Peano Arithmetic, or Zermelo-Fraenkel Set Theory.

In that case the "B" is the corresponding (to PA, ZF, any Lobian  
Machine) Gödel provability predicate, and it obeys invariant  
mathematical provability laws.
It can be proved that the modal logic G is sound and complete for the  
arithmetical provability laws that the machine can prove, and it can  
be proved that the modal logic  G* is sound and complete for the true  
provability laws, with the propositional variable "p" interprete by  
closed arithmetical formula. I will (re)come back on this later  
probably.

The soundness is a quasi direct consequence of Gödel's and Löb's  
incompleteness theorems, together with the fact that the modal rule of  
inference preserve the arithmetical modal provability and correctness  
(for G and G* respectively).

The completeness is far more complex to prove, and it has been done by  
Solovay theorem. (Reference in my Post to Günther, or in my both  
thesis where this is explained with various details. The proof of  
Solovay is explained in Smorynski book, and in Boolos 1979 and 1993  
books in details. It is the base of AUDA, or the "interview of the  
Lobian Machine" (see any of my papers or theses).


You get the hypostases by introducing the Theaetical intensional  
nuances (Bp & p, Bp & Dp, Bp & Dp & p, etc.). G is really the third  
personne self-reference, "Bp & p" gives the first person self-
reference: the real one that the machine cannot even name. Bp & Dp  
gives intelligible matter, Bp & Dp & p gives the sensible matter, Etc.  
G* knows them equivalent, proving the same arithmetical theorem, but  
they obeys veruy different logics due to the fact that the machine  
cannot know them equivalent.
And you get the computationalist hypostases by restricting the  
interpretation of the propositional variables, p, to the Sigma-1  
sentences (which proofs provide the arithmetical Universal Dovetailing).

All this is the substance of AUDA, which leads to the theology  
(including the verifiable physics or the logic of the observable) of  
the Universal machine.
The corona G* minus G and its intensional variants, give the proper  
theological reality of the universal machine. What they can correctly  
hope or fear, and correctly bet, without being to prove.

See the second part of the Sane2004 paper for a short but precise  
account of AUDA (the first part is UDA(1...8).
See the Plotinus paper for a longer explanation of AUDA, and to see  
its use for providing an arithmetical interpretation of both Plotinus  
"theory of mind" and "theory of matter", or see the two thesis for  
detailed explanation and motivations. Or my old post on "the machine-
itself" and its "Guardian Angel" (if you remind?). Or wait to see if  
i will succeed to explain this on the list,  or out of the list. I  
have already tried with not so much success, but those matter are not  
so easy of course. But an understanding of UDA + an understanding of  
those mathematical theorems leads "automatically" to AUDA. And to the  
discovery that, about machine only,  there is already no unifying  
complete everything theory. On the contrary you will see that all  
universal machine which introspects herself discover or create an  
universal Everything *realm* in its own "head" ...

Best,

Bruno



http://iridia.ulb.ac.be/~marchal/




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[russell standish-2]

On Sun, Feb 15, 2009 at 06:41:08PM +0100, Bruno Marchal wrote:

> >>
> >> A good and important exercise is to understand that with the Kripke
> >> semantics,  ~Dt, that is B~t, that is Bf, that is "I prove 0=1", is
> >> automatically true in all cul-de-sac world. It is important because
> >> cul-de-sac worlds exists everywhere in the Kripke semantics of the
> >> self-reference logic G.
> >>
> >> If you interpret, if only for the fun, the worlds as state of life,
> >> then Bf is  really "I am dead".
> >>
> >> Bruno
> >
> > Yes, but I have difficulty in _simultaneously_ interpreting logic
> > formulae in terms of Kripke frames and B as provability. In the
> > former, Bp means in all successor worlds, p is true, whereas in the
> > latter it means I can  prove that p is true.
> >
> > How does one reconcile such disparate notions?
>
>
> By Godel's theorems, Löb's theorems and Solovay theorems.
>

...

The following snip did not answer my question on how one can
simultaneously have Kripke semantics and provability semantics. Never
mind.

I'm helping Kim Jones with the translation - maybe it'll make more
sense when we get to that bit.

Cheers
--

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[Bruno Marchal]

On 15 Feb 2009, at 23:00, russell standish wrote:

>
> On Sun, Feb 15, 2009 at 06:41:08PM +0100, Bruno Marchal wrote:
>>>>
>>>> A good and important exercise is to understand that with the Kripke
>>>> semantics,  ~Dt, that is B~t, that is Bf, that is "I prove 0=1", is
>>>> automatically true in all cul-de-sac world. It is important because
>>>> cul-de-sac worlds exists everywhere in the Kripke semantics of the
>>>> self-reference logic G.
>>>>
>>>> If you interpret, if only for the fun, the worlds as state of life,
>>>> then Bf is  really "I am dead".
>>>>
>>>> Bruno
>>>
>>> Yes, but I have difficulty in _simultaneously_ interpreting logic
>>> formulae in terms of Kripke frames and B as provability. In the
>>> former, Bp means in all successor worlds, p is true, whereas in the
>>> latter it means I can  prove that p is true.
>>>
>>> How does one reconcile such disparate notions?
>>
>>
>> By Godel's theorems, Löb's theorems and Solovay theorems.
>>
>
> ...
>
> The following snip did not answer my question on how one can
> simultaneously have Kripke semantics and provability semantics. Never
> mind.

It is technical. It just happen that the logic of the self-
referential, or Gödelian Beweisbar provability predicate is completely  
and soundly axiomatized by the modal logic G and G*. And the modal  
logic G belongs to the type of logic which possesses a  
characterization in term of a Kripke semantics. (note that G* losses  
the Kripke semantics).


>
>
> I'm helping Kim Jones with the translation - maybe it'll make more
> sense when we get to that bit.


Thanks for helping. I will think about how to explain AUDA in simple  
terms. UDA shows that physics is in your head. AUDA shows that physics  
is in the head of any universal digital machine. This transforms the  
mind-body problem into a pure mathematical problem, or sequence of  
mathematical problems. Then we can compare the physics in the head of  
the machine and physics "out there", and so we can test the comp hyp.

Let me give a short try, for helping to answer your question of the  
reconciliation of Kripke multiverse and provability. It is standard  
material.

Godel's second incompleteness theorem 1931 says that if the formal  
system Principia Mathematica PM is consistent then PM cannot prove  
that PM is consistent. Gödel did already completely understand that PM  
was able to prove its own incompleteness theorem (although the  
detailed proof will be given by Bernays and Hilbert later (and then  
brillantly simplified by Löb)).
PM can prove that if PM is consistent then PM cannot prove that PM is  
consistent. More simply: PM proves that "IF I am consistent, then I  
cannot prove that I am consistent":

PM proves    NOT(BEWEISBAR(FALSE)) ->  
NOT(BEWEISBAR(NOT(BEWEISBAR(FALSE)))

where BEWEISBAR is Gödel's 1931 provability predicate, and FALSE is  
some Gödel number representing the statement "0 = 1" in PM language.  
The whole is a first order arithmetical sentence.

Now that first order arithmetical sentence look like a modal  
statement. Writing NOT with "~", BEWEISBAR with a box "B", and FALSE  
with f, the formal, that is really the one output by the machine or by  
the formal system becomes

~Bf -> ~B~Bf

or with the diamond (B~p is equivalent with ~Dp, and D~p is equivalent  
with ~Bp). t is ~f.

Dt -> DBf, which provides the reading that "If I am consistent then it  
is consistent that I am inconsistent".


Already here, given that this is a modal statement, it is natural to  
ask oneself if there is a Kripke "multiverse" satisfying that modal  
statement.
A Kripke multiverse satisfies a statement when the statement is true  
in all worlds of the multiverse. A multiverse here is just a set of  
worlds with an accessibility relation.

How to find an accessibility relation making the statement "Dt -> DBf"  
true in all worlds of a multiverse?

If Dt is true in a world ALPHA, say, you need to have DBf true in that  
world ALPHA  too (you want "Dt -> DBf" true everywhere!). But to have  
DBf true in ALPHA, you have to be able to access (by the accessibility  
relation) a world where Bf is true. (By the definition of Kripke  
semantics). But Bf can be true only in cul-de-sac worlds (if not f  
would be true in some world). So ti have Dt->~BDt, or Dt->DBf, you  
have to live in what I called a Papaioannou multiverse, or a realist  
multiverse (in Conscience et Mecanisme), that is a multiverse where  
all worlds have an access to a culd-de-sac world.

The same remains for the generalisation Dp -> ~BDp (equivalently Dp ->  
DB~p).

Now, if you remember that ~p is equivalent to p -> f (or redo the two  
lines truth table), you can write consistency, Dt, that ~Bf as Bf->f,  
by simple transformations:

~Bf -> ~B~Bf is equivalent with
B~Bf -> Bf by contraposition. And this is equivalent (by Bf equivalent  
with Bf -> f).

B(Bf->f)->Bf

The generalization (f/p) of this formula gives the Löb formula B(Bp-
 >p)->Bp, which is the formal (machine) version of the theorem of Löb,  
which indeed says that if PM proves BEWEISBAR('p') -> p then PM proves  
p. (Curiously enough, Boolos 1993 gives five reasons to be  
astonished!). See the arithmetical placebo in the same2004, or the  
"proof" of the existence of Santa Klaus, in the archive or Bools'  
books, or better Smullyan which varies about that theme in Forever  
Undecided.

Solovay shows that in the normal modal logics, Löb's formula, B(Bp->p)-
 >Bp, axiomatizes completely the logic (G) of provabilty.

Now B(Bp->p)->Bp has more complex Kripke semantics, but one of them is  
given by the finite transitive irreflexive multiverse. You can verify  
this by hand on simple examples. Not only you have always access to  
dead end (cul-de-sac world), but all your path end somewhere. In term  
of life (which fortunately will NOT concern the first person), not  
only you can die at each "om", but you will eventually die. But as I  
say, and Torkel Franzen did see something similar here, the G world  
are not "OMs"; the G logic is really third person self-reference (its  
modal world are not OMs: it is more a logic of scientific  
communication than a logic a first person knowledge. The amazing  
things which I exploit, is that we can study the logic of the first  
person knowledge attached to the machine, despite it can be shown that  
the first person is not definable by the machine, or by PM, PA, ZF,  
whatever rich classical theory or Löbian machine. You cannot define  
the notion of first person, or of consciousness, or even the notion of  
Truth in the language of any (consistent) machines. Yet machines can  
reason about those notion indirectly. The trick is already in the  
Theaetetus of Plato, or even used by Plotinus (as Bréhier, the first  
french translator of Plotinus, suggested).
All this will concern all the mechanical or less mechanical consistent  
extensions of those machine or theories.

Hope this gives some clues. I guess we can come back on this. AUDA is  
technical for sure. G and G* is just two hypostases, but the others  
come from them.

Bruno



http://iridia.ulb.ac.be/~marchal/




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[Günther Greindl]

Hi guys,

I finally got around to writing the AUDA references page:

http://groups.google.com/group/everything-list/web/auda

Comments welcome.

Cheers,
Günther

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[Bruno Marchal]

Hi Günther,

Nice work Günther. Now my comment is longer than I wish. I really would insist on one change. See (**) below.

On 16 Feb 2009, at 22:54, Günther Greindl wrote:

Hi guys,

I finally got around to writing the AUDA references page:

http://groups.google.com/group/everything-list/web/auda

Comments welcome.

I would separate better the introduction to (general) mathematical logic ...

Enderton (you mention it)

Mendelson (one of the best introduction to mathematical logic)

Perhaps the Podniek web page

The book by Boolos and Jeffrey (and Burgess for the last edition), and the book by Epstein and Carnielli

Kleene's 1952 book on Metamathematics.

...from the  general book on computability (but those books are really needed already for the UDA, actually for the seventh step of UDA): so I would put them there: I am thinking about

Cutland

Rogers

And then come the most fundamental books on the logic of self-reference and/or provability logic per se (those are books on G and G*). This is part of AUDA:

First the main initial original papers : Davis 1965 (contain Gödel 1931, Church, Post, Kleene, Rosser). Then the textbook on self-reference (provability) logic:

Boolos 1979 

Boolos 1993

Smorynski 1985

Smullyan's Forever undecided (a recreative introduction to the modal logic G).

And then you can add some books on (general) modal logic (but they are not needed because the book on provability logic reintroduces the modal logic). You did already mentioned :

Chellas (excellent)

But the new edition of Hugues and Creswel is an easier one, and is very good too imo.

The relation between modal logic and provability is a bit like tensor calculus and general relativity. Modal logic is but a tool, provabilty logic (sometimes called self-reference logics) is the object of study. It is part of AUDA. "AUDA" really begins with Gödel's famous 1931 paper, and the very special modal logic G and G*, found by Solovay, is a machinery encapsulating all the incompleteness phenomenon.

(**) If you want make just one little change in the page:  in your sentence "For modal logic these are further guides:"  I would make clear you are referring to the modal logic G and G*, that is the logic of self-reference. Or just put "provability" or "self-reference" instead of modal.

I would not put the Solovay paper in "guide on modal logic". It is really the seminal paper on the self-reference logics.

The modal logic G and G* are really the logic of provability or self-reference on which AUDA is based.

I am aware we touch "advanced matter", which presupposes a good understanding of mathematical logic, or metamathematics, something which is usually well known only by professional mathematical logicians. Even a genius like Penrose got Gödel's wrong. By the way, Hofstadter got Gödel's right in his book "Gödel, Escher, Back". He is correct on computationalism too, but he missed the "matter problem", and even the universal machine, the first person indetermincay and its "reversal" consequences.

I have realized that some of my students have still a problem with completeness and incompleteness. In part due to the bad choice in the vocabulary (yet standard).

For example the theory PA (Peano Arithmetic) is complete in the sense of Gödel 1930, and incomplete in the sense of Gödel 1931.

Completeness: (PA proves A) is equivalent with (A is true in all models of PA). This makes "Dt" equivalent with "there is a reality": the basic theological bet.

Incompleteness: there are true arithmetical statement (= true in the standard model of PA) which are not provable by PA.

Don't hesitate to ask any question. Of course UDA is *the* argument. AUDA is far more difficult and is needed to pursue the concrete derivation of the physical laws (among all hypostases). UDA shows that physics is a branch of computationalist self-reference logic. AUDA begins the concrete derivation of physics from the existing self-reference logic (thanks to Gödel, Löb, Solovay).

Note that for a time i have believed that the hypostases were all collapsing. If this would have been the case, the comp-physics would have been reduced to classical logic, and what we call physics would have been a sort of comp-geography. The SWE would have been a local truth.

Ask any question, we are in deep water. People like Tegmark and Schmidhuber are on the right track concerning the ontology. The intersection of Tegmark work and Schmidhuber's work gives the "correct" minimal ontology: the mathematical elementary truth (on numbers or mathematical digital machine). My (older) work derives this from comp and  the imperative of the mind body problem, which both Schmidhuber and Tegmark seems not willing to take into account: they presuppose some mind:machine identity which the UDA shows impossible to maintain.

I cpntinue to think that for a non mathematician, a thorough understanding of the UDA is needed before AUDA. UDA is really the question,  including the consequences that the solution has to be given by the self-introspective universal machine; and AUDA is that beginning of the universal machine's answer. For a logician AUDA is far simpler than UDA, but only for them. My work, like the work by Penrose illustrates that mathematical logicians are not well understood by non logicians. Mathematical logicians lives in a ivory tower.

Best,

Bruno

http://iridia.ulb.ac.be/~marchal/

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[Günther Greindl]

Hi Bruno,

will incorporate your changes as soon as time permits :-)

Best Wishes,
Günther

Bruno Marchal wrote:

> Hi Günther,
>
> Nice work Günther. Now my comment is longer than I wish. I really would
> insist on one change. See (**) below.
>
> On 16 Feb 2009, at 22:54, Günther Greindl wrote:
>
>>
>> Hi guys,
>>
>> I finally got around to writing the AUDA references page:
>>
>> http://groups.google.com/group/everything-list/web/auda
>>
>> Comments welcome.
>
>
> I would separate better the introduction to (general) mathematical logic ...
>
> Enderton (you mention it)
> Mendelson (one of the best introduction to mathematical logic)
> Perhaps the Podniek web page
> The book by Boolos and Jeffrey (and Burgess for the last edition), and
> the book by Epstein and Carnielli
> Kleene's 1952 book on Metamathematics.
>
> ...from the  general book on computability (but those books are really
> needed already for the UDA, actually for the seventh step of UDA): so I
> would put them there: I am thinking about
>
> Cutland
> Rogers
>
> And then come the most fundamental books on the logic of self-reference
> and/or provability logic per se (those are books on G and G*). This is
> part of AUDA:
>
> First the main initial original papers : Davis 1965 (contain Gödel 1931,
> Church, Post, Kleene, Rosser). Then the textbook on self-reference
> (provability) logic:
>
> Boolos 1979
> Boolos 1993
> Smorynski 1985
> Smullyan's Forever undecided (a recreative introduction to the modal
> logic G).
>
> And then you can add some books on (general) modal logic (but they are
> not needed because the book on provability logic reintroduces the modal
> logic). You did already mentioned :
>
> Chellas (excellent)
> But the new edition of Hugues and Creswel is an easier one, and is very
> good too imo.
>
> The relation between modal logic and provability is a bit like tensor
> calculus and general relativity. Modal logic is but a tool, provabilty
> logic (sometimes called self-reference logics) is the object of study.
> It is part of AUDA. "AUDA" really begins with Gödel's famous 1931 paper,
> and the very special modal logic G and G*, found by Solovay, is a
> machinery encapsulating all the incompleteness phenomenon.
>
>
> (**) If you want make just one little change in the page:  in your
> sentence "For modal logic these are further guides:"  I would make clear
> you are referring to the modal logic G and G*, that is the logic of
> self-reference. Or just put "provability" or "self-reference" instead of
> modal.
>
> I would not put the Solovay paper in "guide on modal logic". It is
> really the seminal paper on the self-reference logics.
>
> The modal logic G and G* are really the logic of provability or
> self-reference on which AUDA is based.
>
> I am aware we touch "advanced matter", which presupposes a good
> understanding of mathematical logic, or metamathematics, something which
> is usually well known only by professional mathematical logicians. Even
> a genius like Penrose got Gödel's wrong. By the way, Hofstadter got
> Gödel's right in his book "Gödel, Escher, Back". He is correct on
> computationalism too, but he missed the "matter problem", and even the
> universal machine, the first person indetermincay and its "reversal"
> consequences.
>
> I have realized that some of my students have still a problem with
> completeness and incompleteness. In part due to the bad choice in the
> vocabulary (yet standard).
> For example the theory PA (Peano Arithmetic) is complete in the sense of
> Gödel 1930, and incomplete in the sense of Gödel 1931.
>
> Completeness: (PA proves A) is equivalent with (A is true in all models
> of PA). This makes "Dt" equivalent with "there is a reality": the basic
> theological bet.
> Incompleteness: there are true arithmetical statement (= true in the
> standard model of PA) which are not provable by PA.
>
> Don't hesitate to ask any question. Of course UDA is *the* argument.
> AUDA is far more difficult and is needed to pursue the concrete
> derivation of the physical laws (among all hypostases). UDA shows that
> physics is a branch of computationalist self-reference logic. AUDA
> begins the concrete derivation of physics from the existing
> self-reference logic (thanks to Gödel, Löb, Solovay).
>
> Note that for a time i have believed that the hypostases were all
> collapsing. If this would have been the case, the comp-physics would
> have been reduced to classical logic, and what we call physics would
> have been a sort of comp-geography. The SWE would have been a local truth.
>
> Ask any question, we are in deep water. People like Tegmark and
> Schmidhuber are on the right track concerning the ontology. The
> intersection of Tegmark work and Schmidhuber's work gives the "correct"
> minimal ontology: the mathematical elementary truth (on numbers or
> mathematical digital machine). My (older) work derives this from comp
> and  the imperative of the mind body problem, which both Schmidhuber and
> Tegmark seems not willing to take into account: they presuppose some
> mind:machine identity which the UDA shows impossible to maintain.
>
> I cpntinue to think that for a non mathematician, a thorough
> understanding of the UDA is needed before AUDA. UDA is really the
> question,  including the consequences that the solution has to be given
> by the self-introspective universal machine; and AUDA is that beginning
> of the universal machine's answer. For a logician AUDA is far simpler
> than UDA, but only for them. My work, like the work by Penrose
> illustrates that mathematical logicians are not well understood by non
> logicians. Mathematical logicians lives in a ivory tower.
>
> Best,
>
> Bruno
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
> >

--
Günther Greindl
Department of Philosophy of Science
University of Vienna
guenther.greindl@...

Blog: http://www.complexitystudies.org/
Thesis: http://www.complexitystudies.org/proposal/


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[Bruno Marchal]

Hi Günther,

Le 22-févr.-09, à 23:16, Günther Greindl a écrit :

> will incorporate your changes as soon as time permits :-)

Take all your time. I am myself rather busy. But thanks for telling me.
Actually I take this AUDA page as an opportunity for thinking about the
best books on Gödel's incompleteness theorems. I could send a list of
books with short comments, perhaps in April. All good books on
incompleteness and "provability logic" can be helpful on the AUDA,
given that the AUDA is entirely build on incompleteness.
Right now I think about the book "inexhaustibility" by Torkel Franzen,
which is very good, at least for the mathematically inclined reader.  
We have already talk about Franzen's little book on the abuse of
Gödel's theorems. Quite useful too, especially for non-logicians.

Bruno


http://iridia.ulb.ac.be/~marchal/


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[Günther Greindl]

Hello,

have incorporated most of Bruno's change wishes:

http://groups.google.com/group/everything-list/web/auda

Best Wishes,
Günther


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[Bruno Marchal]

Thanks, Günther.

Bruno



On 01 Mar 2009, at 23:34, Günther Greindl wrote:

>
> Hello,
>
> have incorporated most of Bruno's change wishes:
>
> http://groups.google.com/group/everything-list/web/auda
>
> Best Wishes,
> Günther
>
>
> >

http://iridia.ulb.ac.be/~marchal/




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