Re: Mathematical Logic, Podnieks'page ...
At 09:02 29/06/04 -0700, CMR wrote: Here's one reasonably functional definition of science: sci·ence( P ) Pronunciation Key (sns) n. 1. The observation, identification, description, experimental investigation, and theoretical explanation of phenomena. 2. Such activities restricted to a class of natural phenomena. 3. Such activities applied to an object of inquiry or study. BM: OK. That is very large. You know there are borderline. Bohr has dismiss the EPR paper as metaphysics, and he did that by imposing its own metaphysics, etc. And of course such a definition is a user-description, it is not an attempt to define it for a deeper epistemological study. What *is* science, is also a object of inquiry. CMR: I find its not uncommon for those who may chafe at the inconvenient constraints of science as defined above to be somewhat dismissive of its special utility in generating knowledge about our world(s). The creationists often leverage this tactic, for instance. Just as often the label science is co-opted by occultists to lend credibility to otherwise incredible claims They'd all like to cast it as just another world view intrinsically no more valuable than any other. But it's not.. It's not because science as a methodology ignores that which is by necessity matters of faith, be it religion, mysticism, metaphysics (or Platonism?). BM: Absolutely. Science as a methodology ignores that which is by necessity matters of faith. But how many scientist are aware that the existence of a *physical* universe is a matter of faith? Many scientist quickly consider (like Bohr) question which they cannot solve or formulate in the language of their field as metaphysical, but in general the frontier between science and metaphysics are either methodological or metaphysical, or historical. Also, why do you put platonism along with faith. The level of clarity and seriousness of a text like the Thaetetus is rarely met these days. And Plato has less ontological commitment than Aristotle, and many scientists today keep some Aristotelian act of faith without ever mentionning it, apparently they are not aware of their act of faith. *This* is unscientific attitude, no? CMR: Is science sometimes (often?) malpracticed by agenda driven egos? Certainly, but that doesn't diminish the utility or validity of science well executed. BM: Surely John and me were a little ambiguous in our discussion on science. I thought we were discussing what science *is*, not the shape of actual human science. That's why I say science is merely the product of inquiry, humility, and curisosity. In front of unsolved hard problem, it is also the ability to recognize our prejudice, and to keep an open mind. CMR: Any and all philosophers, mystics and mathemiticians can and are welcome to minimize, reject and even appropriate science as they will. And so it should be in a free society. But if and when they claim their faith-based musings are scientific or as good as same, then they are charlatans in deed as well as name, IMHO. BM: I agree 100% (if you add physicists, biologists, ... in your list). The pity, today, is that most scientist are specialized, and their keep their scientific attitude only in their discipline, and lack it completely once they talk about anything outside (except perhaps on soccer). In particular a lot of naturalist (materialist, physicalist), like Changeux, are just totally UNscientific when they pretend that all honest scientist should be naturalist, or materialist, ... The same for the platonist. Platonism is unscientifical only when it is presented as being the only way science should be. But naturalism or platonism per se are quite respectable views or departure point. Now the UDA shows that the first is logically incompatible with the computationalist hyp., the other is not. Have you see this? Also, you said that your are not platonist. Could you tell me how you understand the proposition that the number seventeen is prime. (I want just be sure I understand your own philosophical hypothesis). Bruno http://iridia.ulb.ac.be/~marchal/
Re: Mathematical Logic, Podnieks'page ...
At 12:42 29/06/04 -0400, Hal Ruhl wrote: I have enjoyed my first looks at Podnieks' page. Bruno thanks for the URL . My issue is that my model while it has changed many times seems to persistently return me to the idea that while some metaverses may be otherwise Turing computable all metaverses are subject to input from what might be considered an external - to them - random oracle. The system that embeds these metaverses - a dual simultaneous existence of a Nothing and an Everything seems inconsistent and incomplete so its not Turing computable as I understand the term. This seems to put my view in conflict with Comp. If your system is inconsistent then it is obviously Turing computable (just write a generator of ALL arithmetical formula). But I am not sure your system is inconsistent. Well, I am not sure it is a system, or perhaps you just fail to present it as such, probably. Bruno
Re: Mathematical Logic, Podnieks'page ...
Dear Hal, Could the Nothing be a generalization of the notion of the Null or Empty set? One question that I have is what moves? It seems that I am merely re-asking Zeno's question... How is motion, whether it is the UD moving infinitely slowly from string to string or your example of a shackwave, what is the reason MOTION exists? What necessitates motion and change a priori? Stephen - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, June 30, 2004 12:18 PM Subject: Re: Mathematical Logic, Podnieks'page ... Hi Bruno: At 09:34 AM 6/30/2004, you wrote: If your system is inconsistent then it is obviously Turing computable (just write a generator of ALL arithmetical formula). But I am not sure your system is inconsistent. Well, I am not sure it is a system, or perhaps you just fail to present it as such, probably. Bruno As for my model and its system I was referring to my post of June 8 which because I can not get on the escribe site to get the URL right now I have copied below. Ok so if I accept that the Everything half of the system is Truing computable what about the Nothing half which is the incomplete part. In this case there is no output. So if indeed evolving metaverses are the result of an interaction between the two then they can only be incomplete and evolve inconsistently. xx Prior post: 1) Given that the following definitions are sound: The Everything: That which contains all. The Nothing: That which is empty of all. A Something: A division of the Everything into two subparts. 2) These are unavoidable because at least one must exist 3) They are interdependent so that you can not have one without the whole set. 4) Notice that Definition is the same as establishing a boundary between what a thing is and another thing that is all that the first thing is not. 5) The Nothing has a logical problem: It can not answer any meaningful question about itself including the unavoidable one of its own stability. 6) To answer this unavoidable question the Nothing must at some point penetrate the boundary between itself and the Everything in an attempt to complete itself. 7) However, the boundary is permanent as required by the definitions and a Nothing remains. 8) Thus the penetration process repeats in an always was and always will be manner. 8) The boundary penetration produces a shock wave [a boundary] that moves into the Everything as the old example of Nothing tries to complete itself. This divides the Everything into two evolving somethings - evolving multiverses. Notice that half the multiverses are contracting. 9) Notice that the Everything also has a logical problem. Looking at the same meaningful question of its own stability it contains all possible answers because just one would constitute a selection i.e. net internal information which is not an aspect of the all content of the Everything. Thus the Everything is inconsistent. 10) Thus the motion of a shock wave boundary in the Everything must be consistent with this inconsistency - That is the motion is at least partly random. 11) Some of these evolving Somethings will admit being modeled as UD's with true noise.
Re: Mathematical Logic, Podnieks'page ...
Greetings Bruno and Kory, Also, you said that your are not platonist. Could you tell me how you understand the proposition that the number seventeen is prime. (I want just be sure I understand your own philosophical hypothesis). A quick aside: It might be better not to even use the term platonist in these discussions, because it means at least two different things. It can be used to refer to Plato's essentialism - the idea that there's a world of Forms in which exists (for instance) the Ideal Horse, and all physical horses represent imperfect copies of this Horse. This is certainly a more elaborate belief than mathematical realism (or arithmetical realism, or computational realism). One can be a mathematical realist without being an essentialist. I am. So some people would call me a Platonist, and some wouldn't, but that's just a disagreement about a definition. I prefer just to use the term mathematical realism or essentialism, depending on what I'm talking about. There would seem to be some difference of opinion on this view: Mathematical realism holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. The term Platonism is used because such a view is seen to parallel Plato's belief in a heaven of ideas, an unchanging ultimate reality that the everday world can only imperfectly approximate. Plato's view probably derives from Pythagoras, and his followers the Pythagoreans, who believed that the world was, quite literally, built up by the numbers. This idea may have even older origins that are unknown to us. http://www.fact-index.com/p/ph/philosophy_of_mathematics.html I'd have to agree that mathematical realism smacks of essentialism to me as well. Thus my reservations regarding it. But my real point here is that, for myself, all isms including Platonism are merely maps (models?) and the world the territory, to paraphrase Korzybski. Mathematics is, I believe, one of those maps. Hard pressed for a label, I'd guess that I probably fit most well as a non-Aristotelian if anything (but I'm not sure they'd have me). But in truth I tend to be like bacterium where my world view is like it's genome: I take a little here, a little there from various compatible isms and assimilate the parts that seem to fit well, averaging across many maps to better grok the territory. Ultimately though, I suppose my main man would be Socrates, if I had to choose one (and apparently I just did). Plato would have done well to assimilate more of his mentor's methodology, IMHO. He might have been more competitive with the Ionians had he done so. On the science topic: Natural History magazine this month has an article on the anthropic universe, the cosmological constant and cosmology. It cites the multi-verse as one theory gaining popularity in explaining the constant's otherwise apparently arbitrary value. The author quotes Tegmark as well as some soft multi-versers and of course the skeptics who tend to see a meta-verse solution as a cop-out and, in at least one view, akin to a religious mythological tale. These last bemoan what they see as a premature abandonment of rigourous physics methodology in pursuit of an instant TOE. To this lot the rumors of the end of science are greatly exaggerated, I would imagine. Look, all I know is that the world(s) apparently proceeds from state to state and exihibits patterns of varying degrees of order and (psuedo/) randomness. I suspect that this is likely the consequence of simple underlying rules or a single rule. Thus the world contains information, IMHO. That these patterns map reasonably (remarkably?) well to a meme that we call mathematics and that first appeared at a recent juncture(s) of that procession seems clear. Am I a mathematical realist? You tell me.. Cheers CMR - insert gratuitous quotation that implies my profundity here -
Re: Spam Alert: Re: Mathematical Logic, Podnieks'page ...
CMR:( I quote your earlier points here about 'science' to explain why I called them reductionistic.) 1. The observation, identification, description, experimental investigation,and theoretical explanation of phenomena.2. Such activities restricted to a class of natural phenomena.3. Such activities applied to an object of inquiry or study. #1 works with (observed/able) phenomena: models according to our epistemic enrichment at the time of study. Identification, description, especially explanation is topical, observing the boundaries within which we stay put - disregarding the rest - (whether known or unknown) within our reduced models. This is what I call 'thereduction of the total'. It is even enhanced in #2, "restricted to the chosen class" - while #3 puts the crown on its reductionistic head: applying activities [only?] to the limited (topical, boundary-enclosed) models. If your vocabulary sais different from reduction of the total into limited models, we have to smoke the calumet for using different vocabularies in peace. You wrote: "A methodwith clearly identifiedacceptable methodology. No more. No less." And I seek understanding. I don't believe to find it in your "scientism"G. I may have used the wrong adverb: not "reductionist science", only "science" as we know it.Conventional. It is a topically reduced segregated-parcelled modeling of nature into topics all considered assubstantial units - while really in an interconnected total where separating barriers exist only in our organizing effort. Complexity is a loaded historical noumenon, almost as unidentifiable as consciousness. I am not talking about the "reductionistic limited models" that are complex, have a theory and work in a formalism of acknowledging the limited model values as 'complete values' in the equational math treatment. If I have to use the word, I mean the complexity of the total in unabridged interinfluencingreciprocity. The word allows flexible semantics. I prefer to say wholeness. Not even 'hole-ism'. It is hard to skip the belief-system we were brainwashed into during our early studies. Maybe you can find more in http://pages.prodigy.net/jamikes/SciRelMay00.html This was written before I foramlized my thinking about reductionism, but applicable. And NO End of Science! The good old reductionist edifice is very good and useful, a NEW WAY of doing scientific activity may be in the works. Give it 2-300 years. "[Conventional]...science issignificantly less lousy than all the alternative approaches ..." which is not good enough for me. Finally as you could see from all the above: Igladlyagree with your final remark: "I like, respect and even largely share your apparent philosophy, John. But it ain't science." I hope so and appreciate the preceding to it. John M - Original Message - From: CMR To: [EMAIL PROTECTED] Cc: John M Sent: Tuesday, June 29, 2004 5:06 PM Subject: Spam Alert: Re: Mathematical Logic, Podnieks'page ...
