Re: A calculus of personal identity

2006-07-13 Thread James N Rose

Thank you for your responses, Bruno.
I will reply in return.  

As an overview to my original theme, I believe you
missed several key notions.First, yes, I am bothered
by interpretations of Godel's Incompleteness Theorems,
but I avoid getting entangled in debating 'interpretations'
by getting to deeper theorems-criteria and analyzing 
those.


When I read the Theorems - which I do not have at hand
to quote - it was apparent that invariant - systemwide
information compatibility was and is a founding requirement --
when attempting to assess and invoke those -situations and
conditions- whereby 'some' information becomes segmented and
partitioned away, producing a 'self-evaluation incompleteness'.

Godel expressed the projection that non-present data or rules
may at some future time be made present and then-inclusive, 
allowing for satisfactory completion of true-false statement
assessments;  with the always receding horizon ... where new
true-false assessments arise that are undecidable under the new
added information/relations expansion.

But the scenario depends upon the criteria presumption that
no information is permanently incompatible with any other 
information. 

That is, he begins and foundations his entire assessment
on a true-false statement that is most definitely 
Intuitionist.  And a constructive keystone as well -- 
because invariant induction is at the heart of 
existence and of mathematics -- before any 'local'
differentiations produces conditional-incompleteness states.

A mathematics and systemic analysis that key on
alpha-omega compatibility are far superior and 
more productive than those built on 'incompleteness'.

But I see that no one is doing that, and they
are missing critically important new understandings
because they are not doing that.



As far as your reaction that some of my statements
were 'vague'.  You might try re-reading and re-interpreting
them.  They were in fact rather explicit.  There are
very real relational analogues that scale very nicely 
and exactly between tiers of existence and different
fields/subjects/topics also.

You need to think of metaphors as a real-form
of transduction, with all mapping validity retained.

Best of luck Bruno ; someday 'the lightbulb'.  :-)

James 

 



Bruno Marchal wrote:
 
 Le 09-juil.-06, à 17:20, James N Rose a écrit :
 
 
  from July 2, 2006 (lightly amended and then addended)
 
 
  Bruno,
 
  I have found myself in this lifetime to be a staunch
  OP-ponent and challenger to Godel's incompleteness theorems.
 
 Are they other math theorems you are opposed too?
 To be frank, I could imagine that you believe having find an error. If
 that is the case let me know or try to publish it. I doubt it of
 course. Until now I have been able to find the error of all those who
 have pretended to me having finding such an error.
 Sometimes people does not challenge Godel's proof, but some
 interpretation of it. That is a different matter, and obviously less
 simple.
 Did you realize that I have, just last week, give an astonishingly
 simple proof, based on Church thesis,  of a stronger form of Godel's
 incompleteness? Did you try to follow it?
 
 
  In the way that they are structured - with the premises
  Godel preset: of initial boundaries for what he was
  about to design by 'proof' - his theorems -are- both
  sufficiently closed and constituently -accurate- in
  their conclusion and notions.
 
 OK you are cautious. So you criticize an interpretation of Godel's
 theorem.
 
 
  _But_ what I find disturbing about them is that they are
  RELIANT on a more formative -presumption-, which presumption
  enables an analyst to draw quite a -contrary result- to what
  Godel announced. A self-discontinuity _within_ his theorems,
  as it were.
 
  Clearly, this:
 
  He tacitly identifies any information resident -outside- any that
  current/known, as -eventually accessible, connectible, relatable-;
  even if it means restructuring known-information in regard to
  alternative/new criteria and standards definitions, descriptions,
  statements.   A presumption/definition of universal information
  compatibility - of all information - whether known or unknown.
 
 You could say this about my proof, or about Emil Post's one, or about
 some simplified version of it. But it is 99% unfair to say Godel made
 those presumptions. You could argue like that a little bit by invoking
 its use of the omega-consistency notion, but then that case is closed
 after Rosser's amelioration of Godel's proof. The Godel-Rosser proof
 does not rely in any way on any semantical notion, not even AR.
 Godel's proof is even constructive and completely acceptable, even for
 an intuitionist.
 
 
  It is through this process of add then re-evaluate that new
  paradigms are achieved.  But, it is dependent on the compatibility
  of the -whole- scope of all the information present at that moment of
  evaluation; and the eventual capacity to coordinate statements with
  all content 

RE: A calculus of personal identity

2006-07-13 Thread Stathis Papaioannou


Lee Corbin writes:

 Thereisanimportantdifferencebetweennormativestatementsanddescriptiveorempiricalstatements.QuotingfromWikipedia:  "Descriptive(orconstative)statementsarefalsifiablestatementsthatattempttodescribereality.Normative statements,ontheotherhand,affirmhowthingsshouldoroughttobe,howtovaluethem,whichthingsaregoodorbad, whichactionsarerightorwrong."  Yes;it'salwaysgoodtokeepthatinmind.CatchmeifIslip;-)  Supposesomepowerfulbeingsetsupanexperimentwherebyorganismswhobelievetheyarethesameindividualdayafter dayareselectivelyculled,whilethosewhobelievethattheyarebornaneweachmorninganddiewhentheyfallasleep eachnight,butstillmakeprovisionfortheirsuccessorsjustaswemakeprovisionforourchildren,areleftaloneor rewarded Youwouldthenhavetogranttheday-peoplethattheirbeliefisjustasgoodasours, thedifferencebetweenusjustbeinganaccidentofevolution.What'smore,tobeconsistentyouwouldhavetograntthat aduplicateisnotaself,onthegroundsthatthegreatmajorityofpeopledonotbelievethisandourverylanguageis designedtodenythatsuchathingispossible(onlytheBritishmonarchuses"we"tomeanwhatcommonersrefertoas"I").  Ofcourse,actionsspeaklouderthanwords.Asyoupointout,peoplehave believedmanyseeminglystrangethings.I'msurethatsomemedieval scholastics,orperhapspeopleinaninsaneasylum,haveconsistently heldmanypositions.Whatdeterminessanity,aswellaswhatone's truebeliefsare,isthewaythatoneacts.
This is just the point I was making above: there are (at least) two different kinds of craziness. On the one hand there is the person who jumps off a tall building because he doesn't care if he lives or dies, and on the other hand there is the person who jumps because he thinks he is superman and will be able to fly. The resultis the same - both will probably be killed - but one is deluded while the other is not.
 Inyourexample,indeedpeoplecouldgoaroundsayingthattheywere notthesamepersonfromdaytoday.But(asyoualsopointout) evolutionmightcullcertainbeliefs.Nowwhatisimportantisthat someone*acts*asthoughtheyarethesamefromdaytoday.Andin fact,nomatterhowpeople'slipsmove,wewouldfindthatallbut theseriouslyderanged*act*asthoughwhathappenedto"them" tomorrowmattered.  SoIcanimaginepeople*saying*thattheyarenotthesamefrom daytoday,butIcannotimaginesuccessfulhumanorganismsacting asthoughttheywerenot.
In the world which we actually live in evolution has, in fact, culled those who don't believe they are the same person from moment to moment, which is why it is such a rare belief. But in the example I gave with the day-people, evolution has had the opposite effect. Intelligent and rational day-people, as described, completely agree on the objective facts of their existence with you, me, and every other rational species. They know that they are made up of substantially the same matter and have mostly the same memories and other mental attributes from day to day, but they report that theybelieve themselves to be different people from day to day. This would be a false belief regardless of how it evolved if continuity of personal identity were equivalent to physical and/or mental continuity. In our culture, this equivalence is generally taken for granted. But just about everyexampleother than the single branch, birth to death existence with which we are familiar shows that thisview is deeply problematic: teleportation, duplication, time travel, fission, parallel universes, alternate evolution, ad hoc psychological changes can all result in "paradoxes" of personal identityif we stubbornly stick to the intuitive, naive theory we have grown up with.
 Survivalandcontinuityofidentityconsistsolelyinthefactthatwe*believe*wesurvivefrommomenttomoment.  WhereasIbelievethathowweactiswhatisimportant,andthatour languageshouldsimplyreflecthowweact.Sincepeopledoinfact trytosavetheirskinsoverdays,insomesensethismakesthemat leastthesame"vestedinterest".  Inyourscenario,languagewouldevolve,althoughperhapsawkwardly, toaccountforpeople'sbehavior.Forinstance,contractscouldno longerbebetweenpersons(exceptoneswhosetermsexpiredwithin thecourseofasingleday),butinsteadwouldspecify"vested interests"orsomethingthatmeantthesamethingasweordinarily meanby"person".
Not at all. A system could develop so that people feel responsible for the actions of their predecessors and successors, like a stronger form of the responsibility that we feel for the actions of family members. Some people in our society care more about the welfare of their children than they care about their own welfare, and feel that they will somehow "live on" in their children after their own death, but they certainly don't believe that they are the same person as their children. However, this is beside the point. If truth were a matter of utility, then we could argue that people should believe in heaven and hell if it could be shown that such a belief would have positive social consequences.
 You'reright,ofcourse[inthat]Thebeliefthatwearethesame personfrommomenttomomenthasacertainutility,otherwiseit 

Re: Infinities, cardinality, diagonalisation

2006-07-13 Thread Quentin Anciaux
Hi, thank you for your answer.But then I have another question, N is usually said to contains positive integer number from 0 to +infinity... but then it seems it should contains infinite length integer number... but then you enter the problem I've shown, so N shouldn't contains infinite length positive integer number. But if they aren't natural number then as the set seems uncountable they are in fact real number, but real number have a decimal point no ? so how N is restricted to only finite length number (the set is also infinite) without infinite length number ?
Thanks,QuentinOn 7/13/06, Tom Caylor [EMAIL PROTECTED] wrote:
I think my easy answer is to say that infinite numbers are not in N.Ilike to think of it with a decimal point in front, to form a numberbetween 0 and 1.Yes you have the rational numbers which eventually
have a repeating pattern (or stop).But you also have in among themthe irrational numbers which are uncountable. (Hey this reminds me ofthe fi among the Fi.)To ask what is the next number after an infinite number, like
1...1... is similar asking what is the next real number after0.1...1...Tom

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Re: Infinities, cardinality, diagonalisation

2006-07-13 Thread Jesse Mazer

Quentin Anciaux wrote:


Hi, thank you for your answer.

But then I have another question, N is usually said to contains positive
integer number from 0 to +infinity... but then it seems it should contains
infinite length integer number... but then you enter the problem I've 
shown,
so N shouldn't contains infinite length positive integer number. But if 
they
aren't natural number then as the set seems uncountable they are in fact
real number, but real number have a decimal point no ? so how N is
restricted to only finite length number (the set is also infinite) without
infinite length number ?

Thanks,
Quentin

The ordinary definitions of the natural numbers or the real numbers do not 
include infinite numbers, but in at least some versions of nonstandard 
analysis (which as I understand it is basically a way of allowing 
'infinitesimal' quantities like the dx in dx/dy to be treated as genuine 
numbers) you can have such infinite numbers (I believe they're the 
reciprocal of infinitesimals). I know the system of the hyperreals 
contains them, see http://mathforum.org/dr.math/faq/analysis_hyperreals.html 
for some more info. I'm not sure if infinite hyperreal numbers have the sort 
of decimal expansion that you suggest though, skimming that page it seems 
that infinite hyperreals are identified with the limits of sequences that 
sum to infinity, like 1+2+3+4+..., but different sequences can sometimes 
correspond to the same hyperreal number, you need some complicated set 
theory analysis to decide which series are equivalent. Since the hyperreals 
contain all the reals, the set must be uncountable...I don't know if it 
would be possible to just consider the set of infinite hyperreal integers 
or not, and if so whether this set would have the same cardinality as the 
continuum.

Jesse



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Re: Infinities, cardinality, diagonalisation

2006-07-13 Thread Tom Caylor

N is defined as the positive integers, {0, 1, 2, 3, ...}, i.e. the
*countable* integers.   (I am used to starting with 1 in number
theory.)  N does not include infinity, neither the countable infinity
aleph_0 nor any other higher infinity.  Infinite length integers
fall into this category of infinities.  As you have shown, the infinite
length integers cannot be put in a one-to-one correspondence with N.
This is the definition of uncountable.  However, just because the set
of infinite length integers is uncountable, or even equivalent in
cardinality to the set of real numbers, doesn't mean they are real
numbers.  There are other sets that have the same cardinality as the
set of real numbers, 2^aleph_0, for instance the set of all subsets of
N.  Granted, there are (undecidable) mysteries involved, as Jesse has
alluded to, when we start trying to sort out all of the possible
infinite beasts, and this is partly why the Continuum Hypothesis is
such a mystery.  But with the given definitions of countable and
uncountable, infinite length integers are uncountable, and so not in
N.  Conversely, just because you can *start* counting the reals
(starting with the rationals), and you can *start* counting the
infinite integers, and it would take forever (just like counting
the integers would take forever) doesn't mean they are countable.  We
need some kind of definition like the one-to-one correspondence
definition of Cantor to distinguish countable/uncountable.

Tom

Quentin Anciaux wrote:
 Hi, thank you for your answer.

 But then I have another question, N is usually said to contains positive
 integer number from 0 to +infinity... but then it seems it should contains
 infinite length integer number... but then you enter the problem I've shown,
 so N shouldn't contains infinite length positive integer number. But if they
 aren't natural number then as the set seems uncountable they are in fact
 real number, but real number have a decimal point no ? so how N is
 restricted to only finite length number (the set is also infinite) without
 infinite length number ?

 Thanks,
 Quentin

 On 7/13/06, Tom Caylor [EMAIL PROTECTED] wrote:
 
 
  I think my easy answer is to say that infinite numbers are not in N.  I
  like to think of it with a decimal point in front, to form a number
  between 0 and 1.  Yes you have the rational numbers which eventually
  have a repeating pattern (or stop).  But you also have in among them
  the irrational numbers which are uncountable. (Hey this reminds me of
  the fi among the Fi.)
 
  To ask what is the next number after an infinite number, like
  1...1... is similar asking what is the next real number after
  0.1...1...
 
  Tom
 
 


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Re: Infinities, cardinality, diagonalisation

2006-07-13 Thread Tom Caylor

Technically, I should say that countable means that the set can be put
into a one-to-one correspondence with *a subset of* N, to include
finite sets.

Tom

Tom Caylor wrote:
 N is defined as the positive integers, {0, 1, 2, 3, ...}, i.e. the
 *countable* integers.   (I am used to starting with 1 in number
 theory.)  N does not include infinity, neither the countable infinity
 aleph_0 nor any other higher infinity.  Infinite length integers
 fall into this category of infinities.  As you have shown, the infinite
 length integers cannot be put in a one-to-one correspondence with N.
 This is the definition of uncountable.  However, just because the set
 of infinite length integers is uncountable, or even equivalent in
 cardinality to the set of real numbers, doesn't mean they are real
 numbers.  There are other sets that have the same cardinality as the
 set of real numbers, 2^aleph_0, for instance the set of all subsets of
 N.  Granted, there are (undecidable) mysteries involved, as Jesse has
 alluded to, when we start trying to sort out all of the possible
 infinite beasts, and this is partly why the Continuum Hypothesis is
 such a mystery.  But with the given definitions of countable and
 uncountable, infinite length integers are uncountable, and so not in
 N.  Conversely, just because you can *start* counting the reals
 (starting with the rationals), and you can *start* counting the
 infinite integers, and it would take forever (just like counting
 the integers would take forever) doesn't mean they are countable.  We
 need some kind of definition like the one-to-one correspondence
 definition of Cantor to distinguish countable/uncountable.

 Tom

 Quentin Anciaux wrote:
  Hi, thank you for your answer.
 
  But then I have another question, N is usually said to contains positive
  integer number from 0 to +infinity... but then it seems it should contains
  infinite length integer number... but then you enter the problem I've shown,
  so N shouldn't contains infinite length positive integer number. But if they
  aren't natural number then as the set seems uncountable they are in fact
  real number, but real number have a decimal point no ? so how N is
  restricted to only finite length number (the set is also infinite) without
  infinite length number ?
 
  Thanks,
  Quentin
 
  On 7/13/06, Tom Caylor [EMAIL PROTECTED] wrote:
  
  
   I think my easy answer is to say that infinite numbers are not in N.  I
   like to think of it with a decimal point in front, to form a number
   between 0 and 1.  Yes you have the rational numbers which eventually
   have a repeating pattern (or stop).  But you also have in among them
   the irrational numbers which are uncountable. (Hey this reminds me of
   the fi among the Fi.)
  
   To ask what is the next number after an infinite number, like
   1...1... is similar asking what is the next real number after
   0.1...1...
  
   Tom
  
  


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(offlist) Bruno's argument

2006-07-13 Thread Stathis Papaioannou


Quentin,

I think I can follow Bruno's UDA up to the point of the point where he shows that comp = no material world exists. You seem to understand it and you aren't Bruno (at least, I assume you're not Bruno: none of us on this list can really be sure of these things, can we? ;). Would you be kind enough to explain it to me?

Stathis



 From: [EMAIL PROTECTED] To: everything-list@googlegroups.com Subject: Re: SV: Only Existence is necessary? Date: Wed, 12 Jul 2006 21:40:20 +   Hi,  1Zwrote: Iwilltakethestuffthatseemssolidtomeasprimaryrealityuntil demostrated otherwise.  Thiswasnotthepoint...thepointwastomakeyouunderstandthat Brunohasprovedthat*IF*computationalismistrue*THEN*primary realitydoesnotexists!Itevendoesn'tmeananythinginthis context.  Sothepointisnotthatyouacceptornotcomputationalismand stuffy/notstuffystuff...Itisjustthatifyouaccept computationalismyoucannotacceptaprimaryreality...Ifyoudonot (asitseems)thenit'snormal,butyoucannotclaimcomputationalism atthesametime,Brunoprovedthatitisnotcompatible.  Regards, Quentin   
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Re: Theory of Nothing available

2006-07-13 Thread [EMAIL PROTECTED]

Russell,

Congratulations on the publication of your book! I look forward to
getting the hard copy in my hands, as long PDF documents give me
headaches. The Australian Booksurge website does not seem to be
working, so I'll try again later and use one of the other sites to
order the book if it's still a problem.

Stathis Papaioannou


Russell Standish wrote:
 I'm pleased to announce that my book Theory of Nothing is now for
 sale through Booksurge and Amazon.com. If you go to the Booksurge
 website (http://www.booksurge.com, http://www.booksurge.co.uk for
 Brits and http://www.booksurge.com.au for us Aussies) you should get
 the PDF softcopy bundled with the hardcopy book, so you can
 start reading straight away, or you can buy the softcopy only for a
 reduced price. The prices are USD 16 for the hardcopy, and USD 7.50
 for the softcopy.

 In the book, I advance the thesis that many mysteries about reality can be
 solved by connecting ideas from physics, mathematics, computer
 science, biology and congitive science. The connections flow both ways
 - the form of fundamental physics is constrained by our psyche, just
 as our psyche must be constrained by the laws of physics.

 Many of the ideas presented in this book were developed over the years
 in discussions on the Everything list. I make extensive references
 into the Everything list archoives, as well as more traditional scientific and
 philosophical literature. This book may be used as one man's synthesis
 of the free flowing and erudite discussions of the Everything list.

 Take a look at the book. I should have Amazon's search inside
 feature wokring soon. In the meantime, I have posted a copy of the
 first chapter, which contains a precis of the main argument, at
 http://parallel.hpc.unsw.edu.au/rks/ToN-chapter1.pdf

 --
 *PS: A number of people ask me about the attachment to my email, which
 is of type application/pgp-signature. Don't worry, it is not a
 virus. It is an electronic signature, that may be used to verify this
 email came from me if you have PGP or GPG installed. Otherwise, you
 may safely ignore this attachment.

 
 A/Prof Russell Standish  Phone 8308 3119 (mobile)
 Mathematics  0425 253119 ()
 UNSW SYDNEY 2052   [EMAIL PROTECTED]
 Australiahttp://parallel.hpc.unsw.edu.au/rks
 International prefix  +612, Interstate prefix 02
 


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