Re: Theory of Nothing available
Russell Congratulation on your book. I intend to buy the hard copy. I can't wait to read it! George 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 > > > --~--~-~--~~~---~--~~ 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: Diagonalization (solution-sequel)
Bruno Marchal wrote: > Hi Tom, > > I will comment your (important imo) first and last paragraph, for > avoiding making the post too much long and technical. > > > > Le 14-juil.-06, à 12:30, Tom Caylor a écrit : > > > > But with Church's Thesis how could it be machine or language dependent? > > Another way of arguing without the "+ 1" is this: Define G(n) = Fn(n) > > for all n. If G is in the list of Fi's, then G=Fk for some fixed k. > > So Fk(n) = Fn(n) for all n. Now if all you're thinking of is a matrix > > of numbers Fx(y) (a lookup table if you will) with rows numbered by x, > > and columns numbered by y, then this doesn't seem problematic (unless > > you introduce the "+ 1"). But such a lookup table is infinite and > > therefore is not allowed as the code of a computable function. You > > need code for the functions Fi. Specifically, you need code for the > > function Fk (=G). What does this code look like, even in a universal > > sense? Well Fk(n) = G(n) = Fn(n) for all n, so Fk would have to have > > some code to compute Fk(1)=F1(1), Fk(2)=F2(2), Fk(3)=F3(3), ...Fk(k)=?, > > ... > > How does Fk *ever* know what to compute for Fk(k)? This is actually > > rather funny to me. It's like me being my own grandpa. It seems that > > there already is a case of G(n) not being defined for n=k, even without > > the "+ 1". > > > Remember that the Fi are the partial computable function. You can > generate the set of codes, written in some universal language, of all > those functions. To fix the idea I choose often the universal language > fortran, but choose any of your favorite one. > > Let us then define, like you propose, the diagonal function G by G(n) = > Fn(n). > Now the Fn are fortran generable, and they are partially computable. So > it is easy to write a program computing G: > > > > Begin > read x; > generate (by using the lexicographic order) the code of the Fi up to > the code of Fx; > ouput the result of applying the xth program on x; (or > equivalently compute Fx(x), or just call > the universal function u(x,x) if you recall it). > End > - > > > Now this is a finite fortran program. So it belongs to the list of > codes of the program Fi, and you can find that code, so you can find > the indice k of the function Fk = G through the explicit program above. > > So, now, you can apply G on k, giving G(k) = Fk(k). > > This does not give any information (unlike with G(x) = Fx(x) + 1 where > you get a proof that this G is undefined on its own code). Your G > (where G(x) = Fx(x) could be, or not, defined on its own code). > You've written a sort of intuitive code for G above, where you say "generate". But if G = Fk, then when we go to explicitly write the code for G, when we get to "generate the code for Fk" what to we write? Fk *is* G. So we start generating G from the beginning until we again get to the part "generate the code for Fk" and then we do this forever. It's sort of like at dinner when I ask my son or daughter what they did today, and they tell me everything they did starting with "I woke up and made my bed...", and jokingly they finally say, "...and then sat down for dinner and told you, 'I woke up and made my bed...' ..." But of course they finally stop and laugh, instead of going forever. This is where I'm stumped. You say that we escape the diagonalization and the program runs forever (because 0 is not equal to 1). I'm trying to get a firm handle on what is actually going on here. Is there some intuitive definition that is causing an ambiguity, just like the definition of a function itself, as in my previous post? Tom > > Yes: it is a little bit like you can be your own grandpa in > computerland. If you find this magic, what will you say when I will > explain Kleene Second Recursion Theorem. But indeed, what is lovely > here is that we start from a very well-founded structure (N), and the > comp constraint already forces us to admit some non-well founded > substructure. That is why I say often to Stephen that I find it > premature to start from some non well-founded set theory, because this > is like adding magic at the start, where on the contrary, here we see > we cannot avoid it from purely arithmetical reasons. But deeply enough, > here, Stephen is right I would say (I mean "comp-right"). > > > > > > > > > > I get your point, that if you assume Church Thesis, all of these neat > > things are possible "intuitively/mechanically". I guess my first > > paragraph of this post reveals that I am uncomfortable with the > > vagueness of this "intuitively/mechanically". > > > That is normal. It is perhaps related to what I have just say today in > the "Rép : Infinities, cardinality, diagonalisation post, where I gave > a non technical argument showing that we cannot even define what > "finite" means. So, it could be hard indeed to *define* what is meant > by "computable function from N to N". It will entirely be based on the > in
Re: Re: Fermi's Paradox
Stathis: glad you agree with my wording. Several evolutionists (both Darwin-based and post-Darwinians) disagreed =- some fetish 'natural selection' in fitness maps, some swore to ADAPTATION, a sort of self organizing for a purpose. Besides I think I exceed the conventional 'evolution' in the extent of (as a history pf the process) from the 'occurrence' of a universe till its dissipation (into - as my narrative says) into the invariant plenitude of infinite symmetry where it came from. I am really glad that I could finally word my position into a simple formulation that sounds acceptable to you. (Of course 'offspring' stands for reaction-product and the entire image is not restricted to live features - whatever these may be). John - Original Message - From: "Stathis Papaioannou" <[EMAIL PROTECTED]> To: Sent: Wednesday, July 12, 2006 1:36 AM Subject: RE: Re: Fermi's Paradox John Mikes writes: > "My" mutation story is based on interactive responses to the ceaseless > changes of "the rest of the world" producing variations in offsprings. > Some more compatible than others. > The variations with more 'fitness'(?) will proliferate more abundantly so > they are the "successful" ones. Scientists consider most variations still > as "the same" species and in their intermittent snapshots realize > "changes" as mutation - towards a better adapted fitness for survival. The > reverse way to how it happened. But it looks like that. No creature > realizes a 'better way to survive' and has a wing or fin let grow out for > that purpose. > The variants of the species "select" themselves for a better proliferation > in the ever changing circumstances of the environment. The '[unsuccessful > do not even show up (e.g. the calf with 5 feet: it was eaten by the wolf > before copulating age). That's the theory of evolution. Are you agreeing or disagreeing? Stathis Papaioannou _ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.1.394 / Virus Database: 268.9.10/386 - Release Date: 7/12/2006 --~--~-~--~~~---~--~~ 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: A calculus of personal identity
Stathis Papaioannou wrote: > I am not so sure that the standard model of personal identity with which we > are familiar would be > a universal standard. Imagine intelligent beings evolved from hive insects > which go through > several radically different life stages, frequently share genetic information > with each other > like bacteria, identify self and others via pheromones which can change or be > transferred to > other individuals... the possibilities are endless. These beings would have > an utterly alien > psychology, ethics, aesthetics, and probably also an utterly alien sense of > what it means to be a > person, including what it means to be the same person from one life stage to > another. However, if > they were intelligent, they would come up with the same scientific truths as > us, even if they > thought about them very differently, because such truths are in a fundamental > sense > observer-independent. > > Perhaps we have reached a consensus of sorts (Brent and Lee, let me know if > you disagree): > evolution has given us brains hardwired with a sense of continuity of > personal identity over time > for very good reasons, but it could have been otherwise, and it would not > have been inconsistent > with any logical or empirical fact about the world had it been otherwise. I agree, except I don't see how evolution could have worked it out otherwise for our kind of animal. Your thought-experimental day-people took supernatural intervention to evolve. Assuming that their outward behavoir comported with personal continuity; I'm not sure how much their inner narrative could differ from our own. To what degree could they really worry (an emotion) about their future circumstance without feeling that they would *be* that future person. Is there anything to continuity of personal identity besides a) the third-person continuity of body, memory, personality and b) the emotions related to anticipation of pain, pleasure, etc. You make a good point though that a species like the social insects must have a different kind of feeling of identity - if any. Richard Hofstader imagined an intelligent ant colony in which the mind supervened on the spatial and chemical interactions among individuals of the colony. This has also been addressed in fiction. Greg Egan wrote a short story about a person who woke up in a different body every morning. Stanislaw Lem, in one of his Star Diaries stories, has the hero land on a planet where everyone changes societal roles each day. Brent Meeker --~--~-~--~~~---~--~~ 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
Bruno Marchal wrote:
> Hi Quentin, Tom and List,
>
>
> Of course, N is the set of finite positive integers:
>
> N = {0, 1, 2, 3, ...}.
>
> An infinite set A is countable or enumerable if there is a computable
> bijection between A and N.
>
>
> Forgetting temporarily the number zero, all finite number can be put in
> the shapes:
>
>
> |
> ||
> |||
>
> |
> ||
> |||
>
> ...
>
>
> This raises already an infinitely difficult problem: how to define
> those finite numbers to someone who does not already have some
> intuition about them. The answer is: IMPOSSIBLE. This is part of the
> failure of logicism, the doctrine that math can be reduced to logic.
> technically this can be explained through mathematical logic either
> invoking the incompleteness phenomenon, or some result in model theory
> (for example Lowenheim-Skolem results).
>
> But it is possible to experience somehow that impossibility by oneself
> without technics by trying to define those finite sequence of strokes
> without invoking the notion of finiteness.
>
> Imagine that you have to explain the notion of positive integer, or
> natural number greater than zero to some extraterrestrials A and B. A
> is very stubborn, and B is already too clever (as you will see).
>
> So, when you present the sequence:
>
> | || ||| ...
>
> A replies that he has understood. Numbers are the object "|",and the
> object "||", and the object "|||", and the object "...". So A conclude
> there are four numbers. You try to correct A by saying that "..." does
> not represent a number, but does represent some possibility of getting
> other numbers by adding a stroke "|" at their end. From this A
> concludes again that there is four numbers: |, ||, |||, and . You
> try to explain A that "..." really mean to can continue to add the "|";
> so A concludes that there are five numbers now. So you will try to
> explain to A that "..." means you can continue to add the "I" as many
> times as you want.
Here is where I believe the crux is: "..." means you can continue to
add the "I" as many times as you want. Actually, this is equivalent
to: "..." means you can continue to add the "I" as many times as you
want and you can. It's just a little redundant to say it that way.
Now A and B *know*, as well as anyone can even know, what finite means.
All they have to do is perform some experimentation to get the idea
that, after a while of adding "I" they eventually get tired and/or
loose interest, so they have to *stop*. What's so difficult about
understanding what stopping is? Even the word "finite" has "fin" in
it, i.e. "end". The notion is defined by invariance. Something
similar (invariant) is happening (adding "I" at one step is considered
the same action as adding "I" in another step) and then the invariance
disappears, i.e. the adding of the "I" is no longer happening.
> From this A will understand that the set of numbers
> is indefinite: it is
>
> {|, ||, |||, , |} or {|, ||, |||, , |, ïï} or some
> huge one but similarly ... finite.
>
> Apparently A just doesn't grasp the idea of the infinite.
>
> B is more clever. After some time he seems to grasp the idea of "...",
> and apparently he does understand the set {|, ||, |||, , |,
> ...}. But then, like in Tom's post, having accepted the very idea of
> infinity through the use of "...", B, in some exercise, can accept the
> infinite object
>
>
>
> |...
>
> itself as a number. How will you explain him that he has not the right
> to take this as a finite number. He should add that the rule,
> consisting in adding a stroke "|" at the end of a number (like
> "|||"), can only be applied a finite number of times. OK, but the
> problem was just that: how to define "a finite number"
>
> The modern answer is that this is just impossible. The set of positive
> integers N cannot be defined univocally in any finite way.
>
> This can take the form of some theorem in mathematical logic. For
> example: it is not possible to define the term "finite" in first order
> classical logic. There is not first order logic theory having finite
> model for each n, but no infinite models.
> You can define "finite" in second order logic, but second order logic
> are defined through the intuition of finiteness/non-finiteness, so this
> does not solve the problem.
>
> This can be used to show that comp will make the number some absolute
> mystery.
>
> Now, note that B, somehow, can consider the generalized number:
>
>
>
> |...
>
> as a number. Obviously, this corresponds to our friend the *ordinal
> omega*. From the axiom that you get a number by adding a stroke at its
> end: you will get
>
> omega+1, as
>
>
>
> |...|
>
> omega+2, as
>
>
> ||
RE: Re: A calculus of personal identity
Stathis writes > I am not so sure that the standard model of personal identity with which we > are familiar would be a universal standard. Imagine intelligent beings evolved from hive insects which go through several radically different life stages, frequently share genetic information with each other like bacteria, identify self and others via pheromones which can change or be transferred to other individuals... the possibilities are endless. These beings would have an utterly alien psychology, ethics, aesthetics, and probably also an utterly alien sense of what it means to be a person, including what it means to be the same person from one life stage to another. < Yes, I think that that is right. > However, if they were intelligent, they would come up with the same > scientific truths as us, even if they thought about them very differently, because such truths are in a fundamental sense observer-independent. < Right. > Perhaps we have reached a consensus of sorts (Brent and Lee, let me know if > you disagree): evolution has given us brains hardwired with a sense of continuity of personal identity over time for very good reasons, but it could have been otherwise, < Otherwise in the sense that if we were like insects (instead of mammals, or maybe just large primate-like creatures), yes, we might not have this lingering notion that we are the same people from day to day. And the sense that (I claim) young people have that they will not be the same people when they are old. > and it would not have been inconsistent with any logical or empirical fact > about the > world had it been otherwise. Yes, that seems so too: though no tribe of humans (or even lions, for that matter) would ever develop the notion of "day-persons" (see Mike Perry's book, Forever For All for his independent discussion of day-persons), that is indeed a contingent fact of evolution. > On the other hand, evolution has also given us brains which tend to believe > that the Earth is flat and that there is an absolute up and down in the universe, also for fairly good reasons. However, in the latter case, the received belief *is* inconsistent with empirical facts about the world. < Only inconsistent, of course, when data became available that was not available in the EEA (Environment of Early Adapteness). > This is a basic, and I think not immediately obvious, difference between > beliefs about personal identity and logical or empirical facts. < I would agree. Lee --~--~-~--~~~---~--~~ 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: Diagonalization (solution-sequel)
Hi Tom, I will comment your (important imo) first and last paragraph, for avoiding making the post too much long and technical. Le 14-juil.-06, à 12:30, Tom Caylor a écrit : But with Church's Thesis how could it be machine or language dependent? Another way of arguing without the "+ 1" is this: Define G(n) = Fn(n) for all n. If G is in the list of Fi's, then G=Fk for some fixed k. So Fk(n) = Fn(n) for all n. Now if all you're thinking of is a matrix of numbers Fx(y) (a lookup table if you will) with rows numbered by x, and columns numbered by y, then this doesn't seem problematic (unless you introduce the "+ 1"). But such a lookup table is infinite and therefore is not allowed as the code of a computable function. You need code for the functions Fi. Specifically, you need code for the function Fk (=G). What does this code look like, even in a universal sense? Well Fk(n) = G(n) = Fn(n) for all n, so Fk would have to have some code to compute Fk(1)=F1(1), Fk(2)=F2(2), Fk(3)=F3(3), ...Fk(k)=?, ... How does Fk *ever* know what to compute for Fk(k)? This is actually rather funny to me. It's like me being my own grandpa. It seems that there already is a case of G(n) not being defined for n=k, even without the "+ 1". Remember that the Fi are the partial computable function. You can generate the set of codes, written in some universal language, of all those functions. To fix the idea I choose often the universal language fortran, but choose any of your favorite one. Let us then define, like you propose, the diagonal function G by G(n) = Fn(n). Now the Fn are fortran generable, and they are partially computable. So it is easy to write a program computing G: Begin read x; generate (by using the lexicographic order) the code of the Fi up to the code of Fx; ouput the result of applying the xth program on x; (or equivalently compute Fx(x), or just call the universal function u(x,x) if you recall it). End - Now this is a finite fortran program. So it belongs to the list of codes of the program Fi, and you can find that code, so you can find the indice k of the function Fk = G through the explicit program above. So, now, you can apply G on k, giving G(k) = Fk(k). This does not give any information (unlike with G(x) = Fx(x) + 1 where you get a proof that this G is undefined on its own code). Your G (where G(x) = Fx(x) could be, or not, defined on its own code). Yes: it is a little bit like you can be your own grandpa in computerland. If you find this magic, what will you say when I will explain Kleene Second Recursion Theorem. But indeed, what is lovely here is that we start from a very well-founded structure (N), and the comp constraint already forces us to admit some non-well founded substructure. That is why I say often to Stephen that I find it premature to start from some non well-founded set theory, because this is like adding magic at the start, where on the contrary, here we see we cannot avoid it from purely arithmetical reasons. But deeply enough, here, Stephen is right I would say (I mean "comp-right"). I get your point, that if you assume Church Thesis, all of these neat things are possible "intuitively/mechanically". I guess my first paragraph of this post reveals that I am uncomfortable with the vagueness of this "intuitively/mechanically". That is normal. It is perhaps related to what I have just say today in the "Rép : Infinities, cardinality, diagonalisation post, where I gave a non technical argument showing that we cannot even define what "finite" means. So, it could be hard indeed to *define* what is meant by "computable function from N to N". It will entirely be based on the intuition of natural (finite) number. Intuitively a function is computable if you can explain (to some "idiot") in a finite time, or on a finite piece of paper, how to compute that function in a finite time, and this on any (finite) input. This is vague, of course. And this vagueness is what has given to Alonzo Church the motivation for *defining* the computable functions by those definable in LAMBDA(*). Now Stephen K. Kleene was not convinced, and tried to refute that "definition", by finding (by diagonalisation) a computable function not in the list of the LAMBDA functions (showing also that this was more a scientific (refutable) thesis than a definition). It is only when Kleene realized that the list of LAMBDA functions was closed for the diagonalization procedures that he realized that Church's "definition" could be *true*, and he became an ardent defenders of that thesis. He is the one who will make the label "Church's Thesis" (the most commonly used by logicians). In other words, just what is a function in the intuitive/mechanical sense? So I have just said it above, and with Church thesis you can "define" a computable function by "a function programmable in your favorite universal language". For all known universal procedure/system/language/machine it has
Re: Infinities, cardinality, diagonalisation (errata)
Le 14-juil.-06, à 14:34, Bruno Marchal a écrit :
> Hi Quentin, Tom and List,
>
>
> Of course, N is the set of finite positive integers:
>
> N = {0, 1, 2, 3, ...}.
>
> An infinite set A is countable or enumerable if there is a computable
> bijection between A and N.
Please suppress the "computable" in that last sentence.
Bruno
> ~---
http://iridia.ulb.ac.be/~marchal/
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Re: Infinities, cardinality, diagonalisation
Hi Quentin, Tom and List,
Of course, N is the set of finite positive integers:
N = {0, 1, 2, 3, ...}.
An infinite set A is countable or enumerable if there is a computable bijection between A and N.
Forgetting temporarily the number zero, all finite number can be put in the shapes:
|
||
|||
|
||
|||
...
This raises already an infinitely difficult problem: how to define those finite numbers to someone who does not already have some intuition about them. The answer is: IMPOSSIBLE. This is part of the failure of logicism, the doctrine that math can be reduced to logic. technically this can be explained through mathematical logic either invoking the incompleteness phenomenon, or some result in model theory (for example Lowenheim-Skolem results).
But it is possible to experience somehow that impossibility by oneself without technics by trying to define those finite sequence of strokes without invoking the notion of finiteness.
Imagine that you have to explain the notion of positive integer, or natural number greater than zero to some extraterrestrials A and B. A is very stubborn, and B is already too clever (as you will see).
So, when you present the sequence:
| || ||| ...
A replies that he has understood. Numbers are the object "|",and the object "||", and the object "|||", and the object "...”. So A conclude there are four numbers. You try to correct A by saying that "..." does not represent a number, but does represent some possibility of getting other numbers by adding a stroke "|" at their end. From this A concludes again that there is four numbers: |, ||, |||, and . You try to explain A that "..." really mean to can continue to add the "|"; so A concludes that there are five numbers now. So you will try to explain to A that "..." means you can continue to add the "I" as many times as you want. From this A will understand that the set of numbers is indefinite: it is
{|, ||, |||, , |} or {|, ||, |||, , |, ïï} or some huge one but similarly ... finite.
Apparently A just doesn't grasp the idea of the infinite.
B is more clever. After some time he seems to grasp the idea of "...", and apparently he does understand the set {|, ||, |||, , |, ...}. But then, like in Tom's post, having accepted the very idea of
infinity through the use of "...", B, in some exercise, can accept the infinite object
|...
itself as a number. How will you explain him that he has not the right to take this as a finite number. He should add that the rule, consisting in adding a stroke "|" at the end of a number (like "|||"), can only be applied a finite number of times. OK, but the problem was just that: how to define "a finite number"
The modern answer is that this is just impossible. The set of positive integers N cannot be defined univocally in any finite way.
This can take the form of some theorem in mathematical logic. For example: it is not possible to define the term "finite" in first order classical logic. There is not first order logic theory having finite model for each n, but no infinite models.
You can define "finite" in second order logic, but second order logic are defined through the intuition of finiteness/non-finiteness, so this does not solve the problem.
This can be used to show that comp will make the number some absolute mystery.
Now, note that B, somehow, can consider the generalized number:
|...
as a number. Obviously, this corresponds to our friend the *ordinal omega*. From the axiom that you get a number by adding a stroke at its end: you will get
omega+1, as
|...|
omega+2, as
|...||
omega+3
|...|||
...
omega+omega
||...||...
...
omega+omega+omega
||...||...||...
...
omega*omega
|||...|||...|||...|||...|||...|||...|||...|||...|||...|||...|||...|||...|||...|||...|||...|||...|||...|||... ...
... and this generate a part of the constructive countable ordinals.
And we stay in the domain of the countable structure, unless you decide to go up to the least non countable ordinals and beyond. For doing this properly you need some amount of (formal) set theory. In all case, what "..." expressed is unavoidably ambiguous.
Bruno
Le 13-juil.-06, à 15:29, Quentin Anciaux a écrit :
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 infi
RE: Re: A calculus of personal identity
I am not so sure that the standard model of personal identity with which we are familiar would be a universal standard. Imagine intelligent beings evolved from hive insects which go through several radically different life stages, frequently share genetic information with each other like bacteria, identify self and others via pheromones which can change or be transferred to other individuals... the possibilities are endless. These beings would have an utterly alien psychology, ethics, aesthetics, and probably also an utterly alien sense of what it means to be a person, including what it means to be the same person from one life stage to another. However, if they were intelligent, they would come up with the same scientific truths as us, even if they thought about them very differently, because such truths are in a fundamental sense observer-independent. Perhaps we have reached a consensus of sorts (Brent and Lee, let me know if you disagree): evolution has given us brains hardwired with a sense of continuity of personal identity over time for very good reasons, but it could have been otherwise, and it would not have been inconsistent with any logical or empirical fact about the world had it been otherwise. On the other hand, evolution has also given us brains which tend to believe that the Earth is flat and that there is an absolute up and down in the universe, also for fairly good reasons. However, in the latter case, the received belief *is* inconsistent with empirical facts about the world. This is a basic, and I think not immediately obvious, difference between beliefs about personal identity and logical or empirical facts. Stathis Papaioannou > Date: Wed, 12 Jul 2006 17:25:07 -0700> From: [EMAIL PROTECTED]> To: everything-list@googlegroups.com> Subject: Re: A calculus of personal identity> > > Stathis Papaioannou wrote:> > Brent Meeker writes:> > > > > >> I would say that what makes a statement like "we're the same person from moment to moment" true> >> is that it's an inference from, or a part of, a model of the world that is "true" in the> >> provisional sense of scientific theories, i.e. it subsumes and predicts many emprically> >> verified observations (e.g. if I wake you up in the middle of the night and ask you your name> >> you'll reply 'Stathis') and it has not made any falsified predictions. So in this sense we> >> could say that our model of personhood is better than that of the day-people - not in the sense> >> that we can show theirs is false, but in the sense that ours has greater predictive power and> >> scope.> > > > > > If I were a day-person and you woke me in the middle of the night, I would say that the person> > who went to bed last night was Stathis-1 and the person now awake is Stathis-2. I would agree> > that Stathis-1 and Stathis-2 are comprised of mostly the same matter and have similar mental> > attributes, but the fact remains, the brains of my species have evolved so that waking up from> > sleep makes them believe they are a new person. This isn't a model or a theory; it's more like> > reporting that I'm hungry, or frightened. Philosophical problems arise when this feeling of> > continuity of identity (or lack of it) is equated with some empirical fact. It happens that in> > our own evolution physical and mental continuity has been strongly correlated with the subjective> > feeling of continuity of identity, and it is tempting to say that therefore physical and mental> > continuity is equivalent to or (slightly weaker) necessitates continuity of identity. However,> > this default model that we all use day to day is flawed on two counts. Firstly, the correlation> > is not necessary, but contingent on evolutionary circumstances. It is easy enough to imagine> > rational beings like the day-people who have a completely different approach to personal> > identity. Secondly, the default model is not even internally consistent, as shown in duplication> > thought experiments. If I am to be duplicated tomorrow and one of the copies tortured, I am> > worried; but when tomorrow comes, and I am not tortured, I am relieved. How is it that I "become"> > one or other copy when my mental continuity with both is the same? There is no ambiguity in the> > empirical facts, but there is ambiguity in how I experience continuity of identity - because> > these are two different things and there is no simple, consistent relationship between them.> > Well, the default model, personal continuity, is consistent absent duplications...and there ain't > any yet.> > My example of waking you up and asking your name was a weak one. I agree with Lee that the test of > a model is in the behavoir it predicts (and not just the vocal behavoir). And on that basis I think > the model of personal continuity would be a better one, and you might even convince a day-person of > it; Just the reverse of trying convince people here that there isn't *really* continuity. Of course > if they didn't act as if th
Re: Diagonalization (solution-sequel)
Bruno Marchal wrote:
> Le 10-juil.-06, à 21:55, Tom Caylor a écrit :
>
> >>
> >> With Church thesis, Fortran is a Universal Language, and a fortran
> >> "interpreter" is a Universal Machine, where Universal means it
> >> computes
> >> (at least) all computable functions. Fortran programs are recursively
> >> (computably, mechanically, effectively) enumerable, so
> >>
> >> G = Fn(n) + 1
> >>
> >> is programmable, notably in fortran. So there is fortran code for G
> >> and
> >> it exists in the enumeration
> >> of all fortran programs. So there is a number k such that G = Fk. So
> >> G(k) = Fk(k) = Fk(k) + 1. So Fk(k) cannot be defined and it makes the
> >> Universal Machine run for ever (crash). So, the notorious "other
> >> beasts" are the *partial* recursive function. They are functions from
> >> *subset* of N, called domain, in N.
> >
> > OK. I noticed that you can get the Universal Machine (UM) to run for
> > ever even without the "+ 1". If I think of the program for G as a big
> > "case statement" with cases 1, 2, 3, to infinity, then the case for k
> > will contain the code for, or better yet a call to (hence the name
> > "recursive"?), Fk(k), but if we state by defining even G = Fn(n) (even
> > without the "+ 1") then this is equivalent to calling G(k)... But then
> > when we call G(k) we end up back in the "k case" again, calling G(k)
> > again,... forever.
>
>
> I'm not sure. I'm afraid your argument could be machine or language
> dependent.
>
But with Church's Thesis how could it be machine or language dependent?
Another way of arguing without the "+ 1" is this: Define G(n) = Fn(n)
for all n. If G is in the list of Fi's, then G=Fk for some fixed k.
So Fk(n) = Fn(n) for all n. Now if all you're thinking of is a matrix
of numbers Fx(y) (a lookup table if you will) with rows numbered by x,
and columns numbered by y, then this doesn't seem problematic (unless
you introduce the "+ 1"). But such a lookup table is infinite and
therefore is not allowed as the code of a computable function. You
need code for the functions Fi. Specifically, you need code for the
function Fk (=G). What does this code look like, even in a universal
sense? Well Fk(n) = G(n) = Fn(n) for all n, so Fk would have to have
some code to compute Fk(1)=F1(1), Fk(2)=F2(2), Fk(3)=F3(3), ...Fk(k)=?,
...
How does Fk *ever* know what to compute for Fk(k)? This is actually
rather funny to me. It's like me being my own grandpa. It seems that
there already is a case of G(n) not being defined for n=k, even without
the "+ 1".
> >
>
> >
> >>
> >> The key point now, is that the recursively enumerable sequence "Fi"
> >> give us a sort of coordinate system for reasoning about programs. To
> >> fix some Universal machine or language is the equivalent of fixing
> >> some
> >> reference frame in geometry. And then we can reason in a way which
> >> does
> >> not depend on which Universal Machine has been chosen.
> >>
> >> Now Fi denotes just the partial function programmed by the ith fortran
> >> program. So Fi has a domain. It is written Wi. That is: Wi = domain of
> >> Fi.
> >>
> >> Exercises:
> >> 1) show that
> >> A) all the Wi are recursively enumerable (mechanically generable = in
> >> the range of a total computable function, or empty).
> >> B) all the recursively enumerable sets are among the Wi
> >>
> >
> > I don't have time to word together arguments for all of these, but I
> > drew pictures. Let's see. Each Wi is a subset of N, so it is easy to
> > see how each Wi could be in (a subset of) the range (output) of a
> > function from N to N, so A follows.
>
>
> You are too much quick here. The set R of codes of total computable
> functions is also a subset of N, but this does not entail R is the
> range of a total computable function. The diag2 and diag3 already
> showed that R cannot be such a range. Oops, I realize I should not have
> said "in the range of some Fi" but "the range of some Fi" (my fault).
>
OK. For 1A I'm not sure whether you mean "{the whole set of Wi's} is
RE", or "each and every {Wi, for a given i} is RE". I think you mean
the first one. I think that we have to use the fact that the set of
Fi's is RE (=the range of a total computable function). However, I
can't see how that would make the set of domains Wi for all i, RE. I
was thinking along the lines of a composition of two total computable
functions would be a total computable function, but it seems that the
Fi's and Wi's apples and oranges, since the Fi's are the (code of?)
functions, and the Wi's are the domains of the Fi's.
>
> >
> > Each RE set is a subset of N. But it is not just any subset of N, is
> > it? Likewise the set of all Wi's cannot be the set of *all* subsets of
> > N, can it? This would be not enumerable.
>
> Right.
>
This was trying to address 1B. I have a feeling that "all the RE sets
being among the Wi" has something to do with the Church Thesis
statement (below) about all partial computable functions being among
the Fi.
Re: SV: Only Existence is necessary?
Le 12-juil.-06, à 18:06, 1Z a écrit : > > I mean that is what material exists regardless of any mathematical > justification. So this is your main hypothesis: what is material exist. Now my problem is that a term like "material" is very vague in physics, and I would say experimentally vague since the birth of experimental quantum philosophy (EPR, Bell, Shimoni, Feynman, Deutsch, Bennett ...). The big problem with the notion of *primary* matter = how to relate "1-experiences" with "3-experiments". The naïve idea of attaching consciousness to physical activity leads to fatal difficulties. > >> Well, why not, if that is your definition. I understand better why you >> say you could introduce "matter" in Platonia. Plato would have >> disagree >> in the sense that "matter" is the shadow of the ideal intelligible >> reality. > > What is material exists. Whether Platonia exists > is another matter. It is for Platonism to justify itslef > in terms of the concrete reality we find oursleves in, > not for concrete reality to be justify itself in terms > of Platonia. It depends of the assumptions you start from. > The "intelligible" is a quasi-empiricist mathematical epistemology. > Mathematicians are supposed by Platonists to be able to "perceive" > mathematical > truth with some extra organ. That is naïve platonism. Already condemned by Plato himself and most of his followers. Read Plotinus for more on this (especially Ennead V). > >> I don't understand what you mean by "numbers don't exist at all". > > Well, I've never seen one. Again that would be a critics of naïve Platonism. As I have said: "number n exists in Platonia" means just that the proposition "number n exists" is true. For example I believe that the equation x^2 - 61y^2 = 1 admits integers solutions independently of any things related to me. > >> Numbers exists in Platonia in the sense that the classical proposition >> "4356667654090987890111 is prime or 4356667654090987890111 is not >> prime" is true there. > > It's true here. why bring Platonia into it ? I don't understand what you mean by "4356667654090987890111 is prime or not" is true here. Is it false or meaningless on the moon? is it false or meaningless beyond the solar system? is it false or meaningless beyond the Milky Way? > >>> they they cannot even produce the mere appearance of a physical >>> world, >>> as Bruno requires. >> >> Why? > > What doesn't exist at all cannot underpin the existence of anything -- > even of an illusion. I do agree with you. But, once we assume comp, we can attach consciousness to sheaf of computational histories (abstract computations which can be defined precisely from the Fi and the Wi: more in the diagonalization posts). Those computations are entirely defined by infinite sets of true relations among numbers. You could perhaps wait I define the "Kleene predicate" in the diagonalization posts. or read the beautiful work of Matiazevitch on the diophantine equations. A set of numbers is RE, i.e. is a Wi set, if and only if it is given by the zero of a diophantine polynomial. In *all* situation, when I say a number exists, or when I say a sequence of numbers exists, I only mean that the proposition expressing that existence is true independently of me or you. > >> With Church thesis all computations, as defined in computer >> science (not in physics), exists in Platonia, exactly in the same >> sense >> that for the prime numbers above. > > That is a most unhelpful remark. All you said above is > that true mathematical sentences have truth-values > independent of you. You have now started treating > that as a claim about existence. It is as if > your are using "is true" and "exists" as synonyms. You did not read carefully what I have said. I am just using "exists" as a quantifier (in first or second order logic). Exists n P(n) = truth of "exists n P(n)". I believe that there is an infinity of twin primes ... or not, independently of the fact that mathematicians on this planet or elsewhere will solve, or not, that (currently open) problem. > >> And I do provide evidence that "rational unitary transform" could be >> the mathematical computations winning the measure-battle in Platonia. > > > Huh How can you have a battle without time ? By using varieties of theoretical computer science notion of convergence. If you want, I am using the integers themselves for measuring complexity of computations. The UDA shows that if you are in the comp state S, then your "consistent extensions" are defined by a measure on all computations going through that state S. It is a static well defined mathematical set. A type of computation wins the measure-battle if it has a reasonable measure. > >> This would explain not only the existence of computations with >> self-aware observers, but also they relative stability.@ >> But MUCH more can be said, from Solovay theorem (justifying the modal >> logics G and
Re: Theory of Nothing available
HI Russell,
Bravo for your publication. I hope you have take into account some
remarks I made :)
Like Stathis I will wait for an hard copy ...
Regards,
Bruno
Le 14-juil.-06, à 04:16, [EMAIL PROTECTED] a écrit :
>
> 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]
>> Australia
>> http://parallel.hpc.unsw.edu.au/rks
>> International prefix +612, Interstate prefix 02
>> --
>> --
>
>
> >
>
http://iridia.ulb.ac.be/~marchal/
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