### Re: A calculus of personal identity

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

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

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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---

### Re: Infinities, cardinality, diagonalisation

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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---

### Re: Infinities, cardinality, diagonalisation

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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---

### Re: Infinities, cardinality, diagonalisation

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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---

### (offlist) Bruno's argument

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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---

### Re: Theory of Nothing available

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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---