Re: Intensionality (was: The Riemann Zeta Pythagorean TOE)
Le 05-avr.-06, à 23:14, [EMAIL PROTECTED] (Tom) wrote : Another categorization of this dichotomy could be the Plato universals corresponding to Intensional definitions and the possible, vs. the Aristotle particulars corresponding to the Extensional definitions and the actual. The Intensional can also be associated with mathematical descriptions and algorithmic complexity, whereas Extensional is when something is defined by listing all of its components without assigning any order to it or doing any information compression. I think that it takes a person to do the Intensional, to assign order, beauty or meaning. My belief is that we as finite persons cannot reduce that to numbers, fully understanding it in a reductionist way. I think this is what Stephen was getting at with Intensionality, and perhaps what is also called simple apprehension, intuition. I guess this could be Bruno's distinction between the inside view (G) of only the world that is accessible to us through proof, versus being able to somehow comprehend truth, beauty and order directly (G*). Careful. Both G and G* gives third person, and thus objective, intellectual, outside, ... views. G is terrestrial or effective, and G* is divine (still effective, but not from the machine's point of view). The inside view are given by defining the new boxes (corresponding to hypostases in Plotinus). The first person inside view (soul) is given by Bp p, the sensible soul is given by Bp Dp p. I will come back on this soon or later. Many (including myself times ago) got that wrong. I agree it is a bit confusing. I think there might be some confusion sometimes with what math and numbers are about. I think that math is about Intensionality, seeing truth, beauty and order. By definition, this is saying that we are leaving out a lot of the particulars, we are compressing information. Yes but almost like Plotinus, I do believe that matter is already compressed information, and that there is no real particular. Comp leads naturally to a Many Types No Token interpretation of arithmetic. Some people (particularly the reductionist view) say that math brings us closer to understanding everything about the universe. Before Godel, you can think like that. Since Godel we know that any mathematical theory is just a tool to open doors on bigger mysteries and Unknown. About numbers, we know really nothing, but after Godel we know, at least ,that we know nothing (assuming we are consistent, in some way). They look at numbers and say wow numbers are very precise, so this means we can do the same thing with the universe. But numbers are not so precise. If this is counterintuitive wait for my post 'the herat of the matter to George Levy. I will explain where does the Universal Dovetailer (UD) comes from and why does the UD needs necessarily to dovetail, and this is related with the fact that numbers are not so precise, and that there is an infinity of information hidden there. Perhaps in a way math does bring us closer or give us a better understanding, but I think it is wrong to believe that closer means that we can have a goal of actually understanding everything. Right, but modern (post-Godel) math shows the contrary. The more we know, the less we know! The *learning* machine ignorance can be described by the corona G* minus G. But as the machine learns new information, G get bigger, but G* get still bigger, and consequently, the corona get itself still bigger too. We have to be modest. It is like Zeno's paradox, yes we are getting closer, but what does that mean? I think that we have to always take the humble stance that there will always be something that we don't understand. I think you are right, but more can be said. You are right from purely logico-arithmetical reason.This provides effective information for finding mathematical structure bearing on what we don't understand, a little bit like physicists talking about the universe. 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 -~--~~~~--~~--~--~---
Re: Intensionality (was: The Riemann Zeta Pythagorean TOE)
Le 05-avr.-06, à 22:35, Quentin Anciaux a écrit : Hi, Le Mercredi 5 Avril 2006 22:07, John M a écrit : Stephen: right on! (onwards, of course). I did not mention the arts. Express art by numbers and you killed the art. It is not a question to describe art by numbers... I'd say it is totally unrelated, in a materialistic view don't you think you would kill the art by describing it at molecular interaction level ? Well said. Also expressing art by number can mean a lot of things. Today, you have movies and pictures and music on DVDs, and strictly speaking you get only a number on those DVDs. More interesting: to let the numbers express themselves: here are many primes expressing themselves through 1, 2, 3 ... up to 100 zeros of the wavy/spectral Zeta function: http://www.math.ucsb.edu/~stopple/primesmusic.mp3 I know there are much more fascinating pieces of music composed by numbers. Including one which looks like Scarlatti Baroc Music, but I don't find it currently. The only problem I have with this idea (numbers...) is like I said in the other mail I don't understand where *meaning* come from. This is certainly mysterious. We can encode information in numbers, but without an observer/person (as Tom said) the information is meaningless... OK, but (obviously if we assume comp) the universal machine can play the role of the observer/person. It can decode numbers including itself, but then only partially, so that it faces and can infer the infinity of our ignorance. Without comp, I just point on the fact that meaning is as mysterious as a product of relations between numbers than as relations between atoms, wavesor your molecular interactions or actually anything third person describable. UDA shows that with comp, meaning is *more* mysterious when related to matter than related to (many) numbers. yet Tom said a person is an higher level system. Hmmm so numbers are the primary things that generates person that generates meaning which generates numbers ? (I hope I'm not to unclear) No. I mean you are not unclear for me. You got the point, it seems to me. Numbers generate numbers which generate numbers ... meaning appears from the point of views of relative number sequences or relative computational states ... 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 -~--~~~~--~~--~--~---
Re: Intensionality (was: The Riemann Zeta Pythagorean TOE)
Stephen: right on! (onwards, of course). I did not mention the arts. Express art by numbers and you killed the art. Maybe I misunderstand the idea, but a representation by (any kind and length of) numbers is (in my mind at least) rational. Art is not. Emotions (some of them) are not necessarily either. I feel in the 'numbers represented world' some sort of uniformity-trend which does not cope with the infinite 'tastes' of the qualia we may imagine into the world. The unrestricted variety cannot be formulated into just certain rules. How can 'numbers' comply with 'non-numbers' related connotations? Can 'numbers' express the 'non-number' ideas? Similar questions were raised already here - I do not recall explanations to my satisfaction. Maybe MY fault. John M --- Stephen Paul King [EMAIL PROTECTED] wrote: Hi Tom, Your post has inspired a thought for me that I have been struggling for years to generate! Where is Intensionality instantiated in Arithmetic Realism, or any form of Platonism? To re-phrase in folk-speak: How is to whom-ness present in a number? I find in http://en.wikipedia.org/wiki/Intension the idea that refers to the set of all possible things which a word could describe., thus intensionality for a number would be the set (???) of all possible other numbers that it could encode, which has a nice algorithmic flavor; but let's go to extensionality: extension (or denotation) refers to the set of all actual things which the word actually describes. How do numbers *distinguish* (if I am permitted to use that word) between *possibility* and *actuality*? Is the bush what Bruno is beating around? Onward! Stephen - Original Message - From: [EMAIL PROTECTED] To: everything-list@googlegroups.com Cc: [EMAIL PROTECTED] Sent: Monday, April 03, 2006 5:20 PM Subject: Re: The Riemann Zeta Pythagorean TOE Quentin: I don't know from your wink at the end whether you are half-serious or not. But just in case (and Bruno can do better than I can on this), I think I can correctly appeal to Peano's distinction between mathematical and linguistic paradox. The meaning of the symbols is defined at a higher level than the encoding itself. Your statement turns on the word chosen, which is a verb. This goes back to my other post in this thread that, in order to keep from going into an infinite regress of meaninglessness, defining meaning ultimately requires a person. 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: Intensionality (was: The Riemann Zeta Pythagorean TOE)
Another categorization of this dichotomy could be the Plato universals corresponding to Intensional definitions and the possible, vs. the Aristotle particulars corresponding to the Extensional definitions and the actual. The Intensional can also be associated with mathematical descriptions and algorithmic complexity, whereas Extensional is when something is defined by listing all of its components without assigning any order to it or doing any information compression. I think that it takes a person to do the Intensional, to assign order, beauty or meaning. My belief is that we as finite persons cannot reduce that to numbers, fully understanding it in a reductionist way. I think this is what Stephen was getting at with Intensionality, and perhaps what is also called simple apprehension, intuition. I guess this could be Bruno's distinction between the inside view (G) of only the world that is accessible to us through proof, versus being able to somehow comprehend truth, beauty and order directly (G*). I think there might be some confusion sometimes with what math and numbers are about. I think that math is about Intensionality, seeing truth, beauty and order. By definition, this is saying that we are leaving out a lot of the particulars, we are compressing information. Some people (particularly the reductionist view) say that math brings us closer to understanding everything about the universe. They look at numbers and say wow numbers are very precise, so this means we can do the same thing with the universe. Perhaps in a way math does bring us closer or give us a better understanding, but I think it is wrong to believe that closer means that we can have a goal of actually understanding everything. It is like Zeno's paradox, yes we are getting closer, but what does that mean? I think that we have to always take the humble stance that there will always be something that we don't understand. 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: Intensionality (was: The Riemann Zeta Pythagorean TOE)
Le 04-avr.-06, à 04:35, Stephen Paul King a écrit : x-tad-bigger /x-tad-biggerx-tad-biggerHow do numbers *distinguish* (if I am permitted to use that word) between */x-tad-biggerx-tad-biggerpossibility/x-tad-biggerx-tad-bigger* and */x-tad-biggerx-tad-biggeractuality/x-tad-biggerx-tad-bigger*? Is the bush what Bruno is beating around? /x-tad-bigger I guess so. For a machine, an *actuality* is just a possibility seen from some inside point of view. It is the basic idea refered by the term indexical in the philosophical literature. An expression like Here and now I am myself is tautologically true for such a machine, despite the fact that here, now and myself will change their meanings with respect to each observer moments. 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 -~--~~~~--~~--~--~---
Re: Intensionality (was: The Riemann Zeta Pythagorean TOE)
Hi Tom, Your post has inspired a thought for me that I have been struggling for years to generate! Where is Intensionality instantiated in Arithmetic Realism, or any form of Platonism? To re-phrase in folk-speak: How is "to whom-ness" present in a number? I find in http://en.wikipedia.org/wiki/Intensionthe idea that "refers to the set of all possible things which a word could describe.", thus intensionality for a number would be the set (???) of all possible other numbers that it could encode, which has a nice algorithmic flavor; but let's go to extensionality: "extension (or denotation) refers to the set of all actual things which the word actually describes". How do numbers *distinguish* (if I am permitted to use that word) between *possibility* and *actuality*? Is the"bush" what Bruno is "beating around"? Onward! Stephen - Original Message - From: [EMAIL PROTECTED] To: everything-list@googlegroups.com Cc: [EMAIL PROTECTED] Sent: Monday, April 03, 2006 5:20 PM Subject: Re: The Riemann Zeta Pythagorean TOE Quentin:I don't know from your wink at the end whether you are half-serious or not.But just in case (and Bruno can do better than I can on this), I think I can correctly appeal to Peano's distinction between mathematical and linguistic paradox. The meaning of the symbols is defined at a higher level than the encoding itself. Your statement turns on the word "chosen", which is a verb. This goes back to my other post in this thread that, in order to keep from going into an infinite regress of meaninglessness, defining meaning ultimately requires a person.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 -~--~~~~--~~--~--~---
