RE: Reasons and Persons
Russell, > > Having said that, I still think it misses the point. The fact that > > Parfit's thought experiments sometimes seem to have a degree of > > scientific plausibility is just a bonus that makes his writing more > > entertaining. Parfit's ideas on personal identity are squarely in the > > tradition of John Locke, who wrote about transfer of "consciousness" > > from one person to another, suggesting that it is this consciousness > > (which importantly includes the donor's memories) which determines > > identity rather than the physical body in which it happens to reside. > > Clearly, this kind of mind transfer was a completely ridiculous notion > > in the 17th century, and probably still is. But technical feasibility > > (or indeed physical possibility) was not part of Locke's argument, nor > > was it used as ammunition against him by his philosophical opponents. > > His argument was that IF it were possible to transfer memory etc. from > > one person to another, THEN the recipient would feel himself to be the > > donor, even though he would notice that he had a completely different > > body. Opponents of this view argue that it is NOT the case that transfer > > of memories etc. from one body to another - WERE it possible - would > > result in transfer of personal identity (see R. & P. chap 10.82 for > > Bernard Williams' thought experiment, for example). > > > > My response to Locke's thought experiment is that the result would a new > person, as embodiment has a strong effect on one's psyche as well. I would > not even predict that the new person is in between those of the donor > and donee, although obviously there would be some elements on common > (memories of the donor for example). You're being too practical. That's fine for scientific speculation, but it can be an impediment in trying to understand philosophers. If I say, "if I were God, I would get rid of all the flies", I am saying something about my attitude to flies; the fact that me becoming God might be a practical and probably a theoretical impossibility is beside the point. Similarly, Parfit's thought experiments are designed to explore the meaning of the term "personal identity", not the likelihood that Star Trek will become reality. Certainly, in the world we live in it is very easy to come up with a reliable *practical* method for verifying a person's identity, such as asking his wife, or via neuronal DNA analysis, or whatever; but this does not really tell us what, in essence, personal identity is. What if, by science or magic, a person were perfectly duplicated? What if, by science or magic, incremental changes were made to a person's mind so that his mental state came to resemble that of a different person? Is it possible to arrive at a definition of personal identity which would yield what everyone would agree is the "right" answer in such cases? Parfit's conclusion is that there is no such definition possible; no objective "truth of the matter" regarding personal identity. What we are left with is something perhaps disturbingly vague: what matters to us in survival is just the feeling of psychological continuity, regardless of what physical processes take place to bring about this feeling. Stathis Papaioannou --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Duplicate email from everything-list
Am I the only one getting duplicate mails from the list? Any clues as to what is going on? cheers colin --~--~-~--~~~---~--~~ 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: Reasons and Persons
Can I add a nuance that seems to be missing from this discourse? What if the original 'programming' or 'configuration' of the neurons (the entire brain including the neuron/astrocyte syncitium) was as a single entity and intrinsically dynamic? That is, the laying down of the brain configuration is to some extent based on the manner(order) of exposure of new information and the net of all prior history. Subsequent recall is then only possible via the brain itself recreating the equivalent to the sensory feeds that originally programmed them and that correspond to that which is required to be recalled. An intrinsically dynamic associative memory would behave like this. We are all used to thinking of things in terms of static 'declarative' (which I think may be a misnomer in brain function, not sure yet) memory. In computers we are all used to dynamic declarative memory in the form of the ubiquitous dynamic RAM (the memory stick) , where the dynamic part is hidden from us in the hardware. We are able to point to a location with a stick and say "that" information is stored "there". But a dynamic associative memory is a very different beast. If this is the case then at any moment during the conversion from one brain configuration to another you would have to duplicate the sensory feeds as well so as to completely duplicate (reprogram) the dynamic transitional states so that you could claim to have properly performed the conversion. If so then a neural level conversion becomes inappropriate as the hardware replacement alone is not taking the characteristics with it that we think are being taken. Neuron by neuron replacement becomes arguably inappropriate to achieve the aim of the thought experiment. The neuron by neuron replacement is possibly a more valid thought experiment tool for the (human <=> philosophical zombie) conversion, but it could be inappropriate for (human A to human B) conversion. Also assumed here is that astrocytes play no role, which is not justified. It would seem that this 'dynamic' aspect provides an nuance currently missing, unless I have misinterpreted things. The real situation could be far more complex than the thought experiment and thus the thought experiment may be impoverishing the discussion by limiting our conclusions. cheers, colin --~--~-~--~~~---~--~~ 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: Reasons and Persons
On Tue, May 30, 2006 at 08:55:19PM +1000, Stathis Papaioannou wrote:
>
> I agree with the comments made by Jesse Mazer and Saibal Mitra, and
> would go further to suggest that there *necessarily* exists a continuous
> series of intermediates between any two minds, if you allow that
> essentially a mind is a mathematical structure - an algorithm or a
> computer program. You are not then restricted to constructing only those
> minds which could in theory be implemented on a human brain, or by
> making sequential changes in one person's brain to arrive at another
> person's brain. Using your PC/ Mac example, this would be like saying
> that although it might not be possible to convert one into the other by
> means of wirecutters and soldering iron, there are a large number of
> possible operating systems between OS X and Windows XP, all running on a
> general purpose computer, which would provide the required gradual
> transition.
Thinking about mind mergers as similar to the genetic cross-over
operation is a possible point of departure (although we do not know
apriori whether minds work that way).
However X-over tends to produce non-viable results, unless restricted
to module boundaries, which is AFAIK how sexual recombination works in
nature.
And my point is that modular cross-over does not provide sufficient
continuity for Parfit's argument to work.
Of course it is entirely possible that the analogy of mind to computer
program, or genetic code is not valid...
One other analogy I thought might be interesting to explore is the game
of converting one English sentence to another by changing one letter
at each step, with the rule that the intervening sentences must be a
grammatically valid English sentence.
This can usually be done, but in what sense are the intervening
sentences "in-between"? And is this a valid analogy for merging minds?
>
> Having said that, I still think it misses the point. The fact that
> Parfit's thought experiments sometimes seem to have a degree of
> scientific plausibility is just a bonus that makes his writing more
> entertaining. Parfit's ideas on personal identity are squarely in the
> tradition of John Locke, who wrote about transfer of "consciousness"
> from one person to another, suggesting that it is this consciousness
> (which importantly includes the donor's memories) which determines
> identity rather than the physical body in which it happens to reside.
> Clearly, this kind of mind transfer was a completely ridiculous notion
> in the 17th century, and probably still is. But technical feasibility
> (or indeed physical possibility) was not part of Locke's argument, nor
> was it used as ammunition against him by his philosophical opponents.
> His argument was that IF it were possible to transfer memory etc. from
> one person to another, THEN the recipient would feel himself to be the
> donor, even though he would notice that he had a completely different
> body. Opponents of this view argue that it is NOT the case that transfer
> of memories etc. from one body to another - WERE it possible - would
> result in transfer of personal identity (see R. & P. chap 10.82 for
> Bernard Williams' thought experiment, for example).
>
My response to Locke's thought experiment is that the result would a new
person, as embodiment has a strong effect on one's psyche as well. I would
not even predict that the new person is in between those of the donor
and donee, although obviously there would be some elements on common
(memories of the donor for example).
--
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Re: Reasons and Persons
On Tue, May 30, 2006 at 03:02:05PM -0700, "Hal Finney" wrote:
>
>
> One way (perhaps the only way) I could see to do it would be for you
> to gradually acquire amnesia, then once you have forgotten your past,
> your personality could gradually change to match Napoleon's, then you
> could gradually recover memory of Napoleon's past.
Yes - I think this is roughly equivalent to the regression to embryo
process I suggested before.
>
> Whether such an extreme case would still support whatever conclusions
> Parfit seeks to draw, I don't know. You're never half-yourself and
> half-Napoleon. Rather, you sort of stop being anybody in the middle
> of the process. I don't think it makes any sense to suppose that you
> could be half-yourself and half-Napoleon.
>
My reading of Parfit was that half-yourself/half-napoleon states were
required. Perhaps others more familiar with Parfit can comment.
> Certainly the physical process Russell quoted could never work,
> because there is no one-to-one correspondence between the neutrons in
> your brain and Napoleons. And each neutron has a distinctive shape.
> If you brought it over unchanged, it would intersect with and overlap
> other cells in the brain, and be non-functional. But if you change its
> shape, it won't be the same neuron in terms of its functional behavior.
> If you brought neurons over from Napoleon's brain but altered them
> in the process to match your own neurons physically and functionally,
> then you would never stop being yourself.
>
> Hal Finney
I'm not sure shape of neurons is sufficient - we can suppose (for the
sake of argument) that nanoscale wires are connected between neurons
on Napoleon's brain and your own, and that once in place, the
neurosurgeon just needs to activate the links 1 by 1 (all 10 billion
of them).
My objection was that there will not be a one-to-one correspondence
between neurons in the two brains. Napoleon probably has a Josephine
neuron that I don't have and so on. So even switching over neurons
will not give half-half states. Instead when the Josephine neuron is
connected to my brain it will probably have some other
function. Indeed as I argue, the most likely result is non-function.
A more likely scenario is that whole modules are swapped at a
time. The human brain is quite modular, a part dedicated to processing
vision, another for smell, another to control the left arm and so
on. Swapping whole modules (assuming sufficient technological prowess)
could well lead to functioning hybrid brains. However the resulting
"in-between" brains do not lie on a spectrum, as is needed for
Parfit's argument. The result is a distinct person in each step. Some
versions may result in split persons, by analogy with the split brain
case - ie if we constructed a brain with my right hemisphere and
Napoleon's left, and left out the connections in between.
Cheers
--
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Re: Ascension (was Re: Smullyan Shmullyan, give me a real example)
Jesse Mazer writes: > The dovetailer is only supposed to generate all *computable* functions > though, correct? And the diagonalization of the (countable) set of all > computable functions would not itself be computable. The dovetailer I know does not seem relevant to this discussion about functions. It generates programs, not functions. For example, it generates all 1 bit programs and runs each for one cycle; then generates all 2 bit programs and runs each for 2 cycles; then generates all 3 bit programs and runs each for 3 cycles; and so on indefinitely. (This assumes that the 3 bit programs include all 2- and 1-bit programs, etc.) In this way all programs get run with an arbitrary number of cycles. These programs differ from functions in two ways. First, programs may never halt and hence may produce no fixed output, while functions must have a well defined result. And second, these programs take no inputs, while functions should have at least one input variable. What do you understand a dovetailer to be, in the context of computable functions? Hal Finney --~--~-~--~~~---~--~~ 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: Reasons and Persons
Jesse Mazer writes: > I agree that Parfit's simple method would probably create a nonfunctional > state in between, or at least the intermediate phase would involve a sort of > split personality disorder with two entirely separate minds coexisting in > the same brain, without access to each other's thoughts and feelings. But > this is probably not a fatal flaw in whatever larger argument he was making, > because you could modify the thought experiment to say something like "let's > assume that in the phase space of all possibe arrangements of neurons and > synapses, there is some continuous path between my brain and Napoleon's > brain such that every intermediate state would have a single integrated > consciousness". There's no way of knowing whether such a path exists (and of > course I don't have a precise definition of 'single integrated > consciousness'), but it seems at least somewhat plausible. One way (perhaps the only way) I could see to do it would be for you to gradually acquire amnesia, then once you have forgotten your past, your personality could gradually change to match Napoleon's, then you could gradually recover memory of Napoleon's past. Whether such an extreme case would still support whatever conclusions Parfit seeks to draw, I don't know. You're never half-yourself and half-Napoleon. Rather, you sort of stop being anybody in the middle of the process. I don't think it makes any sense to suppose that you could be half-yourself and half-Napoleon. Certainly the physical process Russell quoted could never work, because there is no one-to-one correspondence between the neutrons in your brain and Napoleons. And each neutron has a distinctive shape. If you brought it over unchanged, it would intersect with and overlap other cells in the brain, and be non-functional. But if you change its shape, it won't be the same neuron in terms of its functional behavior. If you brought neurons over from Napoleon's brain but altered them in the process to match your own neurons physically and functionally, then you would never stop being yourself. Hal Finney --~--~-~--~~~---~--~~ 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: Reasons and Persons
Russell,
IMO ANY argument ("set of assumptions") "is" truly
believable for people with a mindset that finds it so
(truly believable that is.)
Also Jesse's 'need' for a high level qualia-assignment
is human postulate upon things more than just human.
We have the bad habit to think with our human mind
(some, of course are immune to any thinkng) and accept
our own human delusions as the 'truth' in our
thinking.
But, Alas, how else could we do it?
John M
--- Russell Standish <[EMAIL PROTECTED]> wrote:
>
> Well yes, I suppose there is a set of assumptions
> about persons that
> makes the argument work, the trouble is can we come
> up with a truly
> believable set of assumptions? (My comment also on
> Jesse Mazer's post also).
>
> This is good - it is delving deeper into Parfit's
> argument, exposing
> subtle traps within.
>
> Cheers
>
> On Tue, May 30, 2000 at 03:07:49AM +0200, Saibal
> Mitra wrote:
> >
> > There must exist a ''high level'' program that
> specifies a person in terms
> > of qualia. These qualia are ultimately defined by
> the way neurons are
> > connected, but you could also think of persons in
> terms of the high-level
> > algorithm, instead of the ''machine language''
> level algorithm specified by
> > the neural network.
> >
> > The interpolation between two persons is more
> easily done in the high level
> > language. Then you do obtain a continuous path
> from one person to the other.
> > For each intermediary person, you can then try to
> ''compile'' the program to
> > the corresponding neural network.
> >
>
> --
>
> A/Prof Russell Standish Phone 8308
> 3119 (mobile)
> Mathematics 0425
> 253119 (")
> UNSW SYDNEY 2052
> [EMAIL PROTECTED]
> Australia
> http://parallel.hpc.unsw.edu.au/rks
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> prefix 02
>
>
>
>
>
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Re: Ascension (was Re: Smullyan Shmullyan, give me a real example)
George Levy wrote: > > >Bruno Marchal wrote: > > >Meanwhile, I > >would like to ask George and the others if they have a good > >understanding of the present thread, that is on the fact that growing > >functions has been well defined, that each sequence of such functions > >are well defined, and each diagonalisation defines quite well a precise > >programmable growing function (growing faster than the one in the > >sequence it comes from). > >Just a tiny effort, and I think we will have all we need to go into the > >"heart of the matter", and to understand why comp makes our "universe" > >a godelized one in the Smullyan sense. > > > > > >To speak only for myself, I think I have a sufficient understanding of >the thread. Essentially you have shown that one cannot form a set of all >numbers/functions because given any set of numbers/functions it is >always possible, using diagonalization, to generate new >numbers/functions: the Plenitude is too large to be a set. This leads to >a problem with the assumption of the existence of a Universal Dovetailer >whose purpose is to generate all functions. I hope this summary is >accurate. > >George The dovetailer is only supposed to generate all *computable* functions though, correct? And the diagonalization of the (countable) set of all computable functions would not itself be computable. 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: Ascension (was Re: Smullyan Shmullyan, give me a real example)
Bruno Marchal wrote: >Meanwhile, I >would like to ask George and the others if they have a good >understanding of the present thread, that is on the fact that growing >functions has been well defined, that each sequence of such functions >are well defined, and each diagonalisation defines quite well a precise >programmable growing function (growing faster than the one in the >sequence it comes from). >Just a tiny effort, and I think we will have all we need to go into the >"heart of the matter", and to understand why comp makes our "universe" >a godelized one in the Smullyan sense. > > To speak only for myself, I think I have a sufficient understanding of the thread. Essentially you have shown that one cannot form a set of all numbers/functions because given any set of numbers/functions it is always possible, using diagonalization, to generate new numbers/functions: the Plenitude is too large to be a set. This leads to a problem with the assumption of the existence of a Universal Dovetailer whose purpose is to generate all functions. I hope this summary is accurate. George --~--~-~--~~~---~--~~ 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: Ascension (was Re: Smullyan Shmullyan, give me a real example)
Quentin Anciaux wrote: > Hi, > > >From what you've said about dovetailing before, you don't have to have > > > > just a single sequence in order to dovetail. You can jump among > > multiple sequences. I have yet to understand how you could dovetail on > > something that is not effective. > > I think dovetailing is possible because the dovetailer only complete sequences > at infinity. So when you construct the matrice on which you > will "diagonalize", you are already diagonilizing it at the same time. > Example: when you have the first number of the first growing function, you > can also have the first number of the diagonalize function (by adding 1) and > the first number of the diagonalize*diagonalize function and ... ad recursum. > By dovetailing you execute in fact everything in "parallel" but all infinites > sequences are only completed at infinity. > > Quentin Anciaux OK. Thanks. But so far we have done only effective diagonalization. I'll follow along as Bruno goes step by step. Also, it seems to me even with non-effective diagonalization there will be another problem to solve: When we dovetail, how do we know we are getting sufficient (which means indefinite) level of substitution in finite amount of computation? (Also, I am waiting for a good explanation of how Church Thesis comes into this.) Again, I'll wait for the step by step argument. 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: Ascension (was Re: Smullyan Shmullyan, give me a real example)
Hi, >From what you've said about dovetailing before, you don't have to have > > just a single sequence in order to dovetail. You can jump among > multiple sequences. I have yet to understand how you could dovetail on > something that is not effective. I think dovetailing is possible because the dovetailer only complete sequences at infinity. So when you construct the matrice on which you will "diagonalize", you are already diagonilizing it at the same time. Example: when you have the first number of the first growing function, you can also have the first number of the diagonalize function (by adding 1) and the first number of the diagonalize*diagonalize function and ... ad recursum. By dovetailing you execute in fact everything in "parallel" but all infinites sequences are only completed at infinity. Quentin Anciaux --~--~-~--~~~---~--~~ 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: Ascension (was Re: Smullyan Shmullyan, give me a real example)
Tom Caylor wrote: > It sounds like the cute theorem says that you can keep dividing up the > natural numbers like this forever. > Oops. I slipped in an actual infinity when I said "forever". Perhaps I should have said "indefinitely" ;) 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: Ascension (was Re: Smullyan Shmullyan, give me a real example)
Bruno Marchal wrote: > > OK. And you are right, I could have done this without mentioning the > constructive ordinal. But it is worth mentioning it, even at this early > stages, because they will reappear again and again. > Note that all those infinite but constructive ordinal are all countable > (in bijection with N), and even constructively so. Note also, if you > haven't already done so, that omega is just N, the set of natural > numbers. I will soon give a more set-theoretical motivation for those > ordinals. OK. I feel power sets coming. > > Actually there is a cute theorem about constructive ordinal. Indeed > they are equivalent to the recursive (programmable) linear > well-ordering on the natural numbers. Examples: > > An order of type omega: the usual order on N (0<1<2<3<4<5<6<...) > > An order of type omega+1 : just decide that 0 is bigger than any non > null natural numbers: > > 1<2<3<4<5<6< <0 > > It is recursive in the sense that you can write a program FORTRAN (say) > capable of deciding it. For example such a program would stop on "yes" > when asked if 4<8, and "no" if you ask 0<8, etc. > > An order of type omega+omega: just decide that all odd numbers are > bigger than the even ones, and take the usual order in case the two > numbers which are compared have the same parity: > > 0<2<4<6<8<10< . 1<3<5<7<9<... > > An order of type omega+omega+omega: just decide that multiple of 3 are > bigger than the multiple of two, themselves bigger than the remaining > numbers: > > 1<5<7<11<13<14<17<... 0<2<4<6<8<10<... 3<6<9<12<15<... > > Again it should be easy to write a Fortran program capable of deciding > that order (that is to decide for any x and y if x < y with that > (unusual) order. > > Exercise: could you find an order of type omega*omega? (Hint: use the > prime numbers). > You could use the Sieve of Eratosthenes (spelling?): 2*1<2*2<2*3<... 3*1<3*3<3*5<(all multiples of 3 that are not multiples of 2)... 5*1<5*5<5*7<(all multiples of 5 that are not multiples of 3 or 2)... It sounds like the cute theorem says that you can keep dividing up the natural numbers like this forever. > Those omega names are quite standard. > > > > > OK. So we haven't left the finite behind yet. It makes intuitive > > sense to me that you can diagonalize till the cows come home, staying > > within countability, and still not be done. Otherwise infinity > > wouldn't be infinite. > > > > On the tricky question, it also makes intuitive sense that you can > > sequence effectively on all computable growing functions. This is > > because the larger the growing function gets, the more uncovered space > > (gaps) there are between the computable functions. Any scheme for > > generating growing functions will also leave behind every-growing > > uncomputed gaps. Very unmathematical of me to be so vague, but you've > > already given us the answer, and I know you will fill in the gaps. :) > > I will. Unfortunately this week is full of duty charges. Meanwhile, I > would like to ask George and the others if they have a good > understanding of the present thread, that is on the fact that growing > functions has been well defined, that each sequence of such functions > are well defined, and each diagonalisation defines quite well a precise > programmable growing function (growing faster than the one in the > sequence it comes from). > Just a tiny effort, and I think we will have all we need to go into the > "heart of the matter", and to understand why comp makes our "universe" > a godelized one in the Smullyan sense. > > > I meant that it makes intuitive sense that you *cannot* sequence > > effectively on all computable growing functions. > > You are right. But would that mean we cannot dovetail on all growing > computable functions? I let you ponder this "not so easy" question. > > Bruno > > PS About Parfit, I have already said some time ago in this list that I > appreciate very much its "Reasons and Persons" book, but, in the middle > of the book he makes the statement that we are "token", where it > follows---[easily? not really: you need the movie graph or some strong > form of Occam]--- that comp makes us type, even abstract type. It just > happens that from a first person point of view we cannot take ourselves > as type because we just cannot distinguish between our many instances > generated by the Universal Dovetailer. A similar phenomenon occur > already with the quantum. But from the point of view of this thread, > this is an anticipation. The things which look the more like token, > with the comp hyp, are the numbers. This makes the second half part of > Parfit's book rather inconsistent with comp, but, still, his analysis > of personal identity remains largely genuine. (I don't like at all his > use of the name "reductionism" in that context, also, it's quite > misleading). > > http://iridia.ulb.ac.be/~marchal/ >From what you've said about dovetailing before, you don't have to have just a single seq
Re: Smullyan Shmullyan, give me a real example
Bruno, It's been a long holiday weekend here in the US, Bruno, thank you for your reply, and your patience for my responce. Fromconventional math, everything you said was correct, put to me by a co-list friend as .. should I offer you a financial reimbursement for your answer: "1m$ that is: 0m$" :-) . Well, I'm not sending you 1m$, but I will continue commentary. Consider for a moment, the possibility that the entire used ediface of mathematics is an analog of Abbott's "Flatland". That though we may think we are 'calculating' in a completely identified domain, that the 'environment' of mathematics is extensive in new ways, and that there are new/different operators needed to access the extended mathematics. Consider G.Cantor. Suppose I said that not only are Aleph>0 regions of math calculations, but that addional functions make all of those infinities - calculation accessible. That 'normal math' still applies .. but if and only if .. notated as referencing each frame-of-reference Aleph n. That to segue (equationally transduce) from any Aleph to any Aleph requires additional notations marks, in order to keep separate what Aleph the immediate notation referneces, or, mores into or out of. You remarked that it is absurd to : > "From (-5)^2 = 5^2 you will not infer that 5 = (-5), right?" Actually, what I suggest does -relate- to this question. We make such presumption about positive or absolute value numeration that when we do back-functioning we overlook relations and information that might be inconvenient or cumbersome to treat. Such as differentiating an already integrated operation. That pesky throw-away scalar transform value of (+C) is unceremoniously thrown out because we assume is to be a non-consequential shift- or spatial-translation factor that needn't be considered in mathematical generalization. When we take a square-root, we ignore the minus signs option. When we look at quantum equations, we keep the positive set and ignore the negative set .. which in and of itself is contrary to quantum-math philosophy .. where all variables are included, even if anti-thetical. [M and not-M are concurrent rather than computationally mutually exclusive.] A closing thought for this morning (possible discussion of particulars being left for another day): --from an off-list letter, same list-subject " Dear __ , I am broaching a substantially new logic. "1m$ that is: 0m$" -is- a patent absurdity in current math. The version that I came up with essentially restructures the analysis of mathematics as comparisons of dimensions. I did one analysis around the pythagorean theorem that results in a statement b=b^2 for any and all numbers, b. [with the autonomous inclusion of new +/- markers that arrive everytime a dimension is added to or calculated to.] What is missing in math notation are markers that help a person to remember they may be co-navigating several different dimensional fields at the same time, where the left side of an equation is in 'm' dimensions and the right in 'other than m' dimensions, yet the equation is valid. The trouble persists if the notations presume that native dimensionality on both sides is identical. In -that- presumption, the numbers have to match conventional math concepts and no such thing as " b=b^2 for any and all numbers, b" is allowed or even sensible. It is like trying to have perfect translation among human languages. Not possible. It's only when we convert languages into the larger information network of memes, that 'equal translation' makes sense. That's what I'm doing. Identifying a core realm of 'information' (albeit, mathematical notions, concepts, information) that can transduce as real and valid 'equalities' across the equals sign. When the realm of dimensions is recognized as the larger realm of mathematical memes. If a person doesn't do that shift of consciousness/sensibilities, they'll never 'get it'. ... but I see a shining country of mathematics that no one else seems to recognize .. yet. Jamie" Bruno, I know you are still going to treat this line of thought/conversation as sophomoric. A natural reaction. I can assure you it is 'of significance' however. Best Regards, Jamie Rose Bruno Marchal wrote: > > Le 26-mai-06, à 02:50, James N Rose a écrit : > > An example at the core of it is a most simplistic > > definition/equation. > > > > 1^1 = 1^0 > > > > [one to the exponent one equals one to the exponent zero] > > > > To all mathematicians, this is a toss-out absurdity, with > > no 'real meaning'. n^0 is a convenience tool at best ; > > n^0 = 1, because 1= (n^m)/(n^m) = n^(m-m) = n^0. > Or better n^0 = the number of functions from the empty > set (cardinal 0) to the set with cardinal n. This > justifies also 0^0 = 1 (there is one (empty) > function from the empty set to the empty set). > > > along with 'n/0 is 'undefined''. We note the consistent/
RE: platinum-eaters and alien abductees
Perhaps what you are in part getting at is the difference between statements of opinion or value, on the one hand, and statements of fact (either empirical or logical truths) on the other. The distinction seems to have come late in the history of Western philosophy (the British Empiricists, particularly David Hume), and it still isn’t appreciated by most non-philosophers. There is a sense in which the former type of statement can be turned into the latter, if we accept some axiom against which statements of value can be tested; however, the axiom is commonly either unrecognized or falsely accorded the status of an empirical or logical truth. Stathis Papaioannou Jef Albright writes: Finally, the very notion of continuity of personal identity, which is necessary if "survival" is to have any meaning, is just as much a product of evolutionary expedience. That is, it is no more logically necessary that an organism is the "same" individual from one moment to the next than it is logically necessary that an organism will strive to survive from one moment to the next. Those organisms which run away when a predator approaches because they believe they will be the same individual in the next moment will thrive, while those which believe that the organism with their approximate shape, memories, position etc. in the next moment is a completely different individual, and don't care if that other individual gets eaten, will die out. Such considerations do not apply to most of the devices that humans produce, which "replicate" on the basis of usefulness rather than a desire to survive and have progeny. A car does not care if it is wrecked for spare parts for use in another car, or a modern sculpture, or whatever, while even a non-sentient organism such as a bacterium is essentially a machine with no purpose other than maintaining its structural integrity from moment to moment and producing exact copies of itself. I want to add that while I agree with Stathis' remarks, we can abstract this further and thereby resolve some of the popularly conceived paradoxes of personal identity and of morality if we consider that what we really want is to promote our *values* into the future. This explains how one can rationally sacrifice one's life for one's family or the good of the greater group on the principle that this is consistent with promoting the kind of world one (and by extension, most others) would like to live in. It also resolves the paradox of taking actions today for the benefit of a self in the future, without the unrealistic requirement of static personal identity. Of course, we tend to think of these actions as "good" because we are enmeshed in and a product of the very process of evolution that tends to promote "what works" into the future. - Jef --~--~-~--~~~---~--~~ 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: Reasons and Persons
I agree with the comments made by Jesse Mazer and Saibal Mitra, and
would go further to suggest that there *necessarily* exists a continuous
series of intermediates between any two minds, if you allow that
essentially a mind is a mathematical structure - an algorithm or a
computer program. You are not then restricted to constructing only those
minds which could in theory be implemented on a human brain, or by
making sequential changes in one person's brain to arrive at another
person's brain. Using your PC/ Mac example, this would be like saying
that although it might not be possible to convert one into the other by
means of wirecutters and soldering iron, there are a large number of
possible operating systems between OS X and Windows XP, all running on a
general purpose computer, which would provide the required gradual
transition.
Having said that, I still think it misses the point. The fact that
Parfit's thought experiments sometimes seem to have a degree of
scientific plausibility is just a bonus that makes his writing more
entertaining. Parfit's ideas on personal identity are squarely in the
tradition of John Locke, who wrote about transfer of "consciousness"
from one person to another, suggesting that it is this consciousness
(which importantly includes the donor's memories) which determines
identity rather than the physical body in which it happens to reside.
Clearly, this kind of mind transfer was a completely ridiculous notion
in the 17th century, and probably still is. But technical feasibility
(or indeed physical possibility) was not part of Locke's argument, nor
was it used as ammunition against him by his philosophical opponents.
His argument was that IF it were possible to transfer memory etc. from
one person to another, THEN the recipient would feel himself to be the
donor, even though he would notice that he had a completely different
body. Opponents of this view argue that it is NOT the case that transfer
of memories etc. from one body to another - WERE it possible - would
result in transfer of personal identity (see R. & P. chap 10.82 for
Bernard Williams' thought experiment, for example).
Stathis Papaioannou
> -Original Message-
> From: everything-list@googlegroups.com [mailto:everything-
> [EMAIL PROTECTED] On Behalf Of Russell Standish
> Sent: Monday, 29 May 2006 8:22 PM
> To: everything-list@googlegroups.com
> Subject: Re: Reasons and Persons
>
>
> On Mon, May 29, 2006 at 07:15:33PM +1000, Stathis Papaioannou wrote:
> >
> > I don't see why you are so sure about the necessity of passing
through
> > non-functional brain structures going from you to Napoleon. After
all,
> > there is a continuous sequence of intermediates between you and a
> > fertilized ovum, and on the face of it you have much more in common
> > mentally and physically with Napoleon than with a fertilized ovum.
> > However, technical feasibility is not the point. The point is that
*if*
> > (let's say magically) your mind were gradually transformed, so that
your
>
> We need to be a bit more precise than "magically". In Parfit's book he
> talks about swapping out my neurons for the equivalent neurons in
> Napoleon's brain. Sure this is not exactly technically feasible at
> present, but for thought experiment purposes it is adequate, and
> suffices for doing the teleporting experiment.
>
> The trouble I have is that Napoleon's brain will be wired completely
> differently to my own. Substituting enough of his neurons and
> connections will eventually just disrupt the functioning of my brain.
>
> Perhaps there is some other way of passing through functioning brain
> states, but not in the way Parfit describes it. Perhaps there is a way
> going through a sequence of brains states to when I was an embryo,
> then reversing the process via developing Napoleon's brain. But would
> each stage be conscious? It is still debatable whether children under
> the age of 12 months are conscious (eg in the sense of being
> self-aware), let alone the mind of a foetus.
>
> All I can say is that things are definitely more subtle than Parfit
was
> implying.
>
>
> --
>
--
> --
> A/Prof Russell Standish Phone 8308 3119 (mobile)
> Mathematics 0425 253119 (")
> UNSW SYDNEY 2052 [EMAIL PROTECTED]
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Re: Ascension (was Re: Smullyan Shmullyan, give me a real example)
Le 30-mai-06, à 03:14, Tom Caylor a écrit : > OK. I see that so far (above) there's no problem. (See below for > where I still have concern(s).) Here I was taking a fixed N, but G is > defined as the diagonal, so my comparison is not valid, and so my proof > that G is infinite for a fixed N is not valid. I was taking G's > assignment of an ordinal of omega as being that it is in every way > larger than all Fi's, but in fact G is larger than all Fi's only when > comparing G(n) to Fn(n), not when comparing G(Nfixed) to Fi(N) for all > i's. Right. > OK. I think you are just throwing me off with your notation. Do you > have to use transfinite ordinals (omega) to do this? Couldn't you just > stay with successively combining and diagonalizing, like below, without > using omegas? > > G(n) = Fn(n)+1 > Gi(n) = G(...G(n)), G taken i times > Then instead of using more and more additional letters, just add > subscripts... > H1(n) = Gn(n)+1 > H1i(n) = H1(...H1(n)), H1 taken i times > H2(n) = H1n(n)+1 > H2i(n) = H2(...H2(n)), H2 taken i times > > Then the subscripts count the number of diagonalizations you've done, > and every time you do the Ackermann thing, instead of adding an omega > you add another subscript. Then it continues ad infinitum. You can > do the Ackermann thing with the *number* of subscripts, i.e. do the > Ackermann thing on the number of times you've done the Ackermann > thing... etc. > > This may just be a technical point, but it doesn't seem precise to do > very much arithmetic with ordinals, like doing omega [omega] omega, > because you're just ordering things, and after a while you forget the > computations that are being performed. I can see that it works for > just proving that you can continue to diagonalize and grow, which is > what you're doing. I just don't want to be caught off guard and > suddenly realize you've slipped actual infinities in without me > realizing it. I don't think you have. OK. And you are right, I could have done this without mentioning the constructive ordinal. But it is worth mentioning it, even at this early stages, because they will reappear again and again. Note that all those infinite but constructive ordinal are all countable (in bijection with N), and even constructively so. Note also, if you haven't already done so, that omega is just N, the set of natural numbers. I will soon give a more set-theoretical motivation for those ordinals. Actually there is a cute theorem about constructive ordinal. Indeed they are equivalent to the recursive (programmable) linear well-ordering on the natural numbers. Examples: An order of type omega: the usual order on N (0<1<2<3<4<5<6<...) An order of type omega+1 : just decide that 0 is bigger than any non null natural numbers: 1<2<3<4<5<6< <0 It is recursive in the sense that you can write a program FORTRAN (say) capable of deciding it. For example such a program would stop on "yes" when asked if 4<8, and "no" if you ask 0<8, etc. An order of type omega+omega: just decide that all odd numbers are bigger than the even ones, and take the usual order in case the two numbers which are compared have the same parity: 0<2<4<6<8<10< . 1<3<5<7<9<... An order of type omega+omega+omega: just decide that multiple of 3 are bigger than the multiple of two, themselves bigger than the remaining numbers: 1<5<7<11<13<14<17<... 0<2<4<6<8<10<... 3<6<9<12<15<... Again it should be easy to write a Fortran program capable of deciding that order (that is to decide for any x and y if x < y with that (unusual) order. Exercise: could you find an order of type omega*omega? (Hint: use the prime numbers). Those omega names are quite standard. > > OK. So we haven't left the finite behind yet. It makes intuitive > sense to me that you can diagonalize till the cows come home, staying > within countability, and still not be done. Otherwise infinity > wouldn't be infinite. > > On the tricky question, it also makes intuitive sense that you can > sequence effectively on all computable growing functions. This is > because the larger the growing function gets, the more uncovered space > (gaps) there are between the computable functions. Any scheme for > generating growing functions will also leave behind every-growing > uncomputed gaps. Very unmathematical of me to be so vague, but you've > already given us the answer, and I know you will fill in the gaps. :) I will. Unfortunately this week is full of duty charges. Meanwhile, I would like to ask George and the others if they have a good understanding of the present thread, that is on the fact that growing functions has been well defined, that each sequence of such functions are well defined, and each diagonalisation defines quite well a precise programmable growing function (growing faster than the one in the sequence it comes from). Just a tiny effort, and I think we will have all we need to go into the "heart of the matter", and
