Re: Numbers, Machine and Father Ted
Le 11-nov.-06, à 19:07, 1Z a écrit : Bruno Marchal wrote: Le 11-nov.-06, à 01:09, 1Z a écrit : No, because there are no possible worlds where (2^32582657)-1 is not a prime number. This is for me a typical arithmetical realist statement. Most philosophers who use the possible worlds terminology do nothing PW's actually exist. Of course it is AR in the sense of appealing to mind-independent truth. And of course it remains unclear whether your AR is a claim about truth, or about existence. It depends on the sense of the term existence. But frankly such discussion is premature. It is probably a 1004 fallacy, like those who were condemning the old quantum mechanics, after its birth, because it is philosophically unclear. I think you should study the comp-theory before arguing about its interpretation. You are introducing nuances, like the difference between 2 exists is true and '2 exists' which, although not uninteresting per se, are too much involved considering the existence of a precise (refutable) new theory of mind/matter. You still want it both ways: keeping comp and primary material reality, but I have already argued in detail that this cannot work in any reasonable way. No you haven't. You argument requires an assumption of Platonism as well as computationalism. Computationalism alone is compatible with materialism. I need only A or ~A. You can call it classical computationalism. I prefer to call it comp, because the reasoning goes through even with weaken form of classical logic (that is I can use the intuitionist excluded middle principle for arithmetic instead: ~~(A v ~A)). I do believe the formalist philosophy has been shown dead wrong after Godel, but in case you have trouble with what I call platonism or even plotinism you could for all practical purpose adopt formalism temporarily. In that case I will say that an ideal lobian machine (in her chatty mode) is an arithmetical platonist if she asserts A v ~A for any arithmetical proposition A. This could help to proceed, and then we can come back on discussing on the interpretation problem of the formalism. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ 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?hl=en -~--~~~~--~~--~--~---
Re: To observe is to......EC
Le 12-nov.-06, à 03:43, Colin Geoffrey Hales a écrit : As I stuff my head with the bird menagerie, and try to see if I need to breed a new bird, I find that EC is best thought of as a form of combinatorics (as you thought, Bruno!). You should use combinators instead of combinatorics because most people will confuse those two very different branches of math. Combinators are just sort of lambda terms without variable. Is there anyone out there who has any intuitions as to which bird(s) would correspond to 'coherence' or 'symmetry breaking'? All eliminators, like the kestrel, introduce some irreversibility in the computations. Duplicators, like the warbler, can break symmetry in their own ways. I find that I must have some sort of 'adjacency' or 'proximity' applicator. Perhaps, with the bird metaphor, I need birds that have selective hearing and hear better those birds that are closer, where 'closer' means 'I can hear you'. Ah ah! I guess you need to type your lambda terms (or the combinators). Then you will be able to benefit from the very extraordinary relation between lambda terms and proofs known as the Curry Howard isomorphism. This is in fashion today and you will find many interesting papers about this on the net. The Curry Howard iso provides also a relation between weak logic and computations. BTW there are more and more genuine quantum lambda calculus, but from the point of view of extracting physics from computations this can be seen as a form of treachery. The most typical models for lambda are cartesian closed category. Actually lambda calculus provides a deep computer science motivation for the whole of category theory, but this is a bit advanced logic perhaps. There are good books by Lambek, Asperti Longo, etc. Also... is there a 'Nothing' or a 'Vanishing' bird? If a 'normal form' completely dissappears to 'Nothing', then its normal form is 'Nothing'. Trying to axiomatise 'Nothing' seems a tad tricky, but I'm getting an idea of what it might be. Kestrelling to a Konstant 'nothing' seems useful but I'm not sure how to formalise it or whether that is the right way to think of it. The confusing difference is between 'doing nothing' and 'being nothing'. There are programming languages which allow the empty program, but to my knowledge this does not make sense in lambda or combinators. I will think about this ... I can't believe what I just wrote, but they are serious questions from a newbie combinatoricist. Patience is required. Sure. Wish you luck. Funny how these things work out. I know it sounds a little obtuse, but I'm going to leave it there for now. If anyone wants a nice 'programmers intro' to Lambda Calc: Michaelson G. 1989. An introduction to functional programming through Lambda calculus. Nice bird intro here: http://users.bigpond.net.au/d.keenan/Lambda/ That is good indeed (but not quite standard). There is also the Smullyan pocket book: How to Mock a Mockingbird?. The birdy names of the combinators comes from it. And then the best (because the only one :) intro to combinators on the list: http://www.mail-archive.com/everything-list@eskimo.com/msg05920.html http://www.mail-archive.com/everything-list@eskimo.com/msg05949.html http://www.mail-archive.com/everything-list@eskimo.com/msg05953.html http://www.mail-archive.com/everything-list@eskimo.com/msg05954.html http://www.mail-archive.com/everything-list@eskimo.com/msg05955.html http://www.mail-archive.com/everything-list@eskimo.com/msg05956.html http://www.mail-archive.com/everything-list@eskimo.com/msg05957.html http://www.mail-archive.com/everything-list@eskimo.com/msg05958.html http://www.mail-archive.com/everything-list@eskimo.com/msg05959.html http://www.mail-archive.com/everything-list@eskimo.com/msg05961.html A summary and a follow up of those post can be found in my last (Elsevier) paper which I should put on my webpage or send to ArXiv.org. (Please, ask me personally a copy if you want a free print quickly). The best textbook on (untyped) lambda calculus remains, imo, the book by Barendregt (North Holland). (If you read it, and if you are not mathematician, please jump over the first chapter which is very difficult and not useful for the beginners). Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ 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?hl=en -~--~~~~--~~--~--~---
Natural Order Belief
Brent Meeker wrote: Tom Caylor wrote: Brent Meeker wrote: An excellent essay. I agree with almost everything you wrote; and you put it very well. Would you mind if I cross posted it to Vic Stenger's AVOID-L mailing list. You can check out the list here: http://www.colorado.edu/philosophy/vstenger/ Although Victor Stenger doesn't use the word anti-natural, the following equation is what he is assuming in his atheistic arguments: supernatural = anti-natural. Therefore he thinks that a proof of theism would amount to finding a violation of natural law. Since he finds no such violation (which I would argue is a circular argument based on the definition of natural) he claim this proves atheism beyond a reasonable doubt (what is the measure of certainty/uncertainty?). In terms of Bruno's provability, this is akin to saying that a proof of the existence of a non-trivial G*/G can be obtained by finding an inconsistency in G. This does not make sense. This is like saying the only god that can exist is an inconsistent god. A theist God (as opposed to a deist God) is one who intervenes in the natural order, i.e. does miracles. Stenger will readily admit that his argument does not apply to a deist God. Brent Meeker The problem (or challenge :) is that the meaning of natural order is open to much debate, especially here on the Everything List. Everything is up for grabs, so much so that it can be a challenge to figure out where any order comes from, resulting in problems such as white rabbits. When we start with Everything, the problem is not just How can anything interesting happen (like life, not to mention our stereotypical 'miracles'? (the something-from-nothing question), but also How can any order be birthed out of the plenitudinous sea of disorder? So in this Everything context, not having the whole picture of what the natural order is implies a lack of knowledge of what it would be to intervene on the natural order. Of course if we're talking about theism, then the nature of intervention is limited by certain parameters related to whatever god is supposedly intervening. These parameters are a function of contingent aspects, such as, in the case of the biblical God's universe, the presence of evil and sacrificial love. But such facts are probably considered too contingent for a List like this, where Everything is supposed to be impersonal. (Is it?) Unfortunately, as Blaise Pascal noted, if the solution to the problem of evil is based on contingent facts, then staying at a general metaphysical (Everything) level is not going to get us in contact with the solution.One possible insight that we can get from Everything-level discussion, if the thinker is willing to accept it, is to realize that a solution based on contingent facts in history is not ruled out by general philosophical thought about Everything. Another insight is to realize that there is no solution to the problem of evil (or the mind-body problem...) at the (non-contingent) Everything level. And if there's no solution to a problem that is part of the universe, then perhaps the (impersonal) Everything approach is not sufficient for dealing with everything. Getting back to the more impersonal question, as has been observed on this List multiple times, there is a problem with discerning the source of order in the universe. Where does this natural order come from that we can make laws about it, and predict nature's actions fairly accurately, at least for our purposes? Why is it that we aren't destroyed by savage white rabbits out of nowhere? Proposed explanations include the use of ideas such as the Anthropic Principle, Occam's Razor, some kind of measure, numbers, local order at the expense of disorder somewhere else far away, etc. So again, in the light of this lack of understanding, it seems pretty presumptuous for us to say that there must not be interventions in the natural order simply because we don't see any as we've defined them. (Then we trap ourselves even more when we attach the label natural order to Everything we observe, whether we can explain it naturally or not.) Perhaps the following analogy will help to open up the possibilities (not probabilities!) in our brains. This is from C.S. Lewis as he put it in his book Miracles. Tom Let us suppose a race of people whose peculiar mental limitation compels them to regard a painting as something made up of little coloured dots which have been put together like a mosaic. Studying the brushwork of a great painting through their magnifying glasses, they discover more and more complicated relations between the dots, and sort these relations out, with great toil, into certain regularities. Their labour will not be in vain. These regularities will in fact work; they will cover most of the facts. But if they go on to conclude that any departure from them would be unworthy of the painter, and an arbitrary breaking of his own rules, they
Re: Natural Order Belief
Tom Caylor wrote: Brent Meeker wrote: Tom Caylor wrote: Brent Meeker wrote: An excellent essay. I agree with almost everything you wrote; and you put it very well. Would you mind if I cross posted it to Vic Stenger's AVOID-L mailing list. You can check out the list here: http://www.colorado.edu/philosophy/vstenger/ Although Victor Stenger doesn't use the word anti-natural, the following equation is what he is assuming in his atheistic arguments: supernatural = anti-natural. Therefore he thinks that a proof of theism would amount to finding a violation of natural law. Since he finds no such violation (which I would argue is a circular argument based on the definition of natural) he claim this proves atheism beyond a reasonable doubt (what is the measure of certainty/uncertainty?). In terms of Bruno's provability, this is akin to saying that a proof of the existence of a non-trivial G*/G can be obtained by finding an inconsistency in G. This does not make sense. This is like saying the only god that can exist is an inconsistent god. A theist God (as opposed to a deist God) is one who intervenes in the natural order, i.e. does miracles. Stenger will readily admit that his argument does not apply to a deist God. Brent Meeker The problem (or challenge :) is that the meaning of natural order is open to much debate, especially here on the Everything List. I'd say it's almost only on the Everything List that it is much debated. Which of course because once you postulate that everything (in some sense or another) happens, you are then faced with the question of why what actually happens is so regular. Everything is up for grabs, so much so that it can be a challenge to figure out where any order comes from, resulting in problems such as white rabbits. When we start with Everything, the problem is not just How can anything interesting happen (like life, not to mention our stereotypical 'miracles'? (the something-from-nothing question), but also How can any order be birthed out of the plenitudinous sea of disorder? So in this Everything context, not having the whole picture of what the natural order is implies a lack of knowledge of what it would be to intervene on the natural order. Of course if we're talking about theism, then the nature of intervention is limited by certain parameters related to whatever god is supposedly intervening. These parameters are a function of contingent aspects, such as, in the case of the biblical God's universe, the presence of evil and sacrificial love. But such facts are probably considered too contingent for a List like this, where Everything is supposed to be impersonal. (Is it?) Unfortunately, as Blaise Pascal noted, if the solution to the problem of evil is based on contingent facts, then staying at a general metaphysical (Everything) level is not going to get us in contact with the solution.One possible insight that we can get from Everything-level discussion, if the thinker is willing to accept it, is to realize that a solution based on contingent facts in history is not ruled out by general philosophical thought about Everything. There is a very simple and widely accepted solution to the problem of evil - there is no omnipotent, benevolent God. Another insight is to realize that there is no solution to the problem of evil (or the mind-body problem...) at the (non-contingent) Everything level. And if there's no solution to a problem that is part of the universe, then perhaps the (impersonal) Everything approach is not sufficient for dealing with everything. Getting back to the more impersonal question, as has been observed on this List multiple times, there is a problem with discerning the source of order in the universe. Actually Vic has just published a book on the subject, The Comprehensible Cosmos. I recommend it. Where does this natural order come from that we can make laws about it, and predict nature's actions fairly accurately, at least for our purposes? Why is it that we aren't destroyed by savage white rabbits out of nowhere? Proposed explanations include the use of ideas such as the Anthropic Principle, Occam's Razor, some kind of measure, numbers, local order at the expense of disorder somewhere else far away, etc. So again, in the light of this lack of understanding, it seems pretty presumptuous for us to say that there must not be interventions in the natural order simply because we don't see any as we've defined them. (Then we trap ourselves even more when we attach the label natural order to Everything we observe, whether we can explain it naturally or not.) Perhaps the following analogy will help to open up the possibilities (not probabilities!) in our brains. This is from C.S. Lewis as he put it in his book Miracles. Tom Let us suppose a race of people whose peculiar mental limitation compels them to regard a painting as
