Re: Mathematical Logic, Podnieks'page ...
At 15:38 28/06/04 -0400, John M wrote: JM: Science in my terms is the edifice of reductionist imaging (observations) of topically selected models, as it developed over the past millennia: subject to the continually (gradually) evolving (applied) math formalism. Will be back to that. Reply-BM: We surely differ. I am not sure the word science really refers to anything. Scientific attitude exists though. About it the words and expressions like *curiosity*, *modesty*, *clarity*, *willingness to share*, etc.. comes to my mind. I agree there has been, in the human story, attempts to build reductionist theories, but they have all failed, and with comp, by Godel II, it is necessarily so. JM: (MY!) Simplicity is the 'cut-off' from the wholeness in our models. Later you mention the causality: it is similarly a cut-off of all possible (eo ipso 'active') influencings, pointing to the ONE which is the most obvious within our topical cut. We make 'cause' SIMPLE. Reply-BM: I'm afraid I don't understand. JM: Exactly. Comp (? I am not sure if I know what it is indeed) has IMO brisk rules and definite qualia to handle by those rules. Reply-BM: I suspect a terrible confusion due to a probably subtle point which has begin to be clear to me only when I begin to understand the abyssal gap between the notion of total computable function and partial computable function. Or Godel's incompleteness theorems. Cf the diagonalisation posts. COMP is just the (religious? meta-religious?) belief that there exists a level of description of you such that you are not aware of any difference in your life after a digital substitution has been made at that level. (+ Church thesis, + a minimal amount of arithmetical realism). It is the nuance brought by GODEL II which makes COMP not reductionnist. JM: (I evaded: 'quantities'). Which means the omission of aspects OUTSIDE such qualia and rules. Reply-BM: Yes, but apparently just because you evade quantities, it seems to me. JM: The cut-off, ie. limitations, enable comp to become brisk, unequivocal, well defined. Including unidentified and infinite variables, qualia, all sort of influence (quality and strength) - meaning the wholeness-interconnection - makes it more vague than any fuzziness could do (which still stays topical). Reply-BM: Which limitations ? I am not sure I understand. JM: I don't expect this emryonic branch of thinking (30-50years max?) even using the language of the millennia of reductionist development, to compete in briskness with the conventional - what you and others may call: - science. An embryo would recite Godel in a very vague way. Reply-BM: ? You loose me. JM: do we have ANY other knowledge-base? Proof (Popper's no-no) is within the belief system. True is a 1st pers. judgement. Even an 'accepted' 3rd p. truth is 1st p. accepted. Reply-BM: I agree. JM: I haven't (yet?) included the universal mchine into my vocabulary. It is not 'simple' (see above). Reply-BM: Thanks for your admission. It is the key notion of comp. JM: One remark to math vs science: I consider math a human language, a mental activity (again this term!) on its own, (uninhibitied by observational models - only by its intrinsic connotations). Reply-BM: I really do not consider math as a language. Math papers are written (mostly) in English (or in German, French, Russian, etc.). Mathematicians uses abreviations, drawings, and are keen to abstract by the very often use of symbolic variables giving the impression it is a language by itself, but it is not. Mathematicians like Pyhtagore Cantor, would never have hide results if that was only languages. Godel's theorem is often use to defend platonism at least in computer science and arithmetic, and I find the argument compelling. But any book on number theory is enough to illustrate this. Even many physicists agree there is a mathematical reality. The irrationality of the square root of 2 is neither a piece of language, nor a convention, but a (startling) observation. A discovery. JM: Science, however, is a reductionist parcelling of observations - according to the epistemic level of the age, the cognitive inventory and its connectional capabilities of the by that time acquireds. Reply-BM: I understand why you say that (given the amount of reductionnist scientist), but such a reductionnism is the product of a betray of science spirit. We should not confuse the often use reductionnist parcelling of observations, which could be a good method of observation, with the attempt to guess the reality beyond. To be short I would say that science for me is just honesty. The confusion between reality and the parcels is produced by sleepy conscience (of course that occurs all the time, and science asks for ever vigilance). JM: Science applies math in its formalizing of deductions, but such math is quantitatively distorted - adjusted to the models and the observations it pertains to. Which is also subject to the actually
Re: Mathematical Logic, Podnieks'page ...
Reply-BM: We surely differ. I am not sure the word science really refers to anything. Scientific attitude exists though. About it the words and expressions like *curiosity*, *modesty*, *clarity*, *willingness to share*, etc.. comes to my mind. I agree there has been, in the human story, attempts to build reductionist theories, but they have all failed, and with comp, by Godel II, it is necessarily so. 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. 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?). Is science sometimes (often?) malpracticed by agenda driven egos? Certainly, but that doesn't diminish the utility or validity of science well executed. 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. Cheers CMR - insert gratuitous quotation that implies my profundity here -
Re: Mathematical Logic, Podnieks'page ...
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. Hal
Re: Mathematical Logic, Podnieks'page ...
Reply to Bruno's Tuesday, June 29, 2004 10:13 AM
post
Subject: Re: Mathematical Logic, Podnieks'page
Dear Bruno, it seems our ways of expressing
thoughts and sights is so different that in spite of many agreeable
pointsa detailed discussionwould grow out of the framework of the
list.
I want to concentrate on a few minor(?) points -
leaving out the rest of the posts.
Science.
I am in your corner, however I spoke about the
"official" terror of science establishment, the editors, tenure-professors,
Nobel people, etc. control freaks. This type of science is perfectly described
in today's post of CMR in his points, identifying "reductionist
science":
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.
all pertinenet to mind-interpreted and
boundary-enclosed models as observations in the topics we study.
I was shocked when you wrote:
"...I am not sure the word "science"
really refers to anything." and after a while I agreed. Chacqu'un a son go^ut.
Today's fashion is emphasizing in the west the applied math -involved
formalistic 'language' (which is a topic I will come back
to).
I would not degrade the reductionist ways:
whatever we achieved in technology is based on them. (Read e-mail, use a car,
eat cooked food, take an aspirin, etc.) they are just not efficient in
"understanding the world" - anymore.
Simplicity.
In my wholistic view everything is within
unlimited interinfluencing in the universe (this one). No random, no
singularity, so everything is infinitely complex - unless we cut it off into
boundaries of our attention and disregard the off-limits. Then things become
simple.
Special thanks to Hal for his today's post, in
which he emphasized a qualifier ('to them'):
"...input from what might be considered an
external - to them - random oracle." I read this as: 'random', irrelevant as in
'having nothing to do with circumstances of a Turing computability - and ONLY in
this respect. We cut our models to be
considered.
I referred th "The Cause" (one) for effects,
that indeed are the synthesis of unlimited occurrences (influences, two-way
functions) whatsoever, except for our limiting (topical?) boundaries which allow
ONE to be overwhelmingly acknowledged. (Reductionistically).
"evade quantities"
The incomplete 'scientific' (reduced) models
omit connotations beyond their boundaries
(topical, qualia, magnitudes, etc.) so a
definite "quantizing" value should become feasible. It is not the value
(quantity) of the named (concept) item, only of the model in attention.
Formalism works with them and practical results
are obtained for technology. Applied math serves for assuring the equational
'truth' in such 'science'. That's what I called an "edifice" of sci.
(Sorry, 'nonreductionistic' Comp by Godel II
is beyond me).
Limitations:
compare the limited model with the unlimited
(natural?) "maximum model", an image of the named item as connected to the total
of the world. A silly example: you expect the Board of Co. 'C' to vote according
to the well established interest of Co. 'C' (= limited model). Yet board
members are also board members of companies X,Y,Z,R,L,M and have vested interest
in legal processes, educational aspects, international affairs, relatives,
lovers, health problems, perversities, hobbies, so all these influence (in the
wider model) the voting outcome. It may not fit the interest of Co. 'C' at all.
The Chairman cuts off all those esoteric side-interests in a reductionist
limitation and will get the limited-model voting FOR Co.'C' only. It is still
not wholism, just an illustration of thewidening of the
boundaries.
Wholistic thinking is in its early embryonic
stage, has no adequate language, just as a
toddler (sorry for writing embryo) does not
(yet) have the words to confer about Godel.
And I did not even mention understanding, just
the words.
Language I mean as much more than syntax and
semantix, I consider it a way to communicate symbols as they occur in the
development. Matematicians try to describe their "math-language" (ideational
symbolics?) in diverse human vocabulary-talks, yet what they 'think' in is still
math. Feelable, as J.v.N. said. In this respect I value it as aprimary
item in the human mind (not the way Platonists say), comparable maybe to the
mother-tongue.
Not so with 'that' reductionistic
establishment-science I talked about above.
I am strongly with you in the (free)
science-concept with the connotations you mentioned.
I think this was more than I wanted to write onlist.
Thanks for your considerations, it helps in clarifying my obscure thinking.
John
- Original Message -
From:
Bruno Marchal
To: [EMAIL PROTECTED]
Sent:
Subject: Re: Mathematical Logic,
Podnieks'page ...
At
Re: Mathematical Logic, Podnieks'page ...
Science. I am in your corner, however I spoke about the "official" terror of science establishment, the editors, tenure-professors, Nobel people, etc. control freaks. This type of science is perfectly described in today's post of CMR in his points, identifying "reductionist science": With respect, no it's not "reductionist science". It is in fact and precisely, just science. We don't have to like it or find it particularly useful in determining the true "nature" of nature. But that's what it is.A methodwith clearly identifiedacceptable methodology. No more. No less. Qualifying it with adjectives tend totake it out of the realm of a practice and into the morass of a "school", like structuralism, existentialism, Marxism, holism..(pick your ism). I in fact tend towards a holistic philosophy of lifeand world view. ButI don't confuse my model with the practice of science. Rigorous scientific investigation of complexity theory, for example, lends support to my model. But it is the very "complexity" you allude to that limits the utility of the scientific method in generating accurate knowledge about the world(s). This is the dim boundary of that ever expanding circle of knowledge Einstein alluded to. Just beyond it lies the fuzzy but oh so satisfying realm of conjecture. Beyond that lies matters of faith. The End of Science? Hardly, but it does reflect the difficulty we embedded monads (another model of "reality") have in objectifying our world. Fortunately like Democracy, science issignificantly less lousy than all the alternative approaches (including any "ism"one might favor) to gaining knowledge of equally embedded systems. I like, respect and even largely share your apparent philosophy, John. But it ain't science. Cheers CMR- insert gratuitous quotation that implies my profundity here -
Re: Mathematical Logic, Podnieks'page ...
To try to avoid confusion on what I meant I find my model telling me that all metaverses will experience the injection of new information to some non zero degree. Some metaverses are Turing computable between such events. The new information is as if from a random external oracle. The to them was to modify external. If one steps out to the system that contains all metaverses one finds that it is not Turing computable because it is both incomplete and inconsistent. Any metaverse is already incomplete so it is the full system level inconsistency that leaks in as the metaverse evolves trying to complete itself. Each of these leakage events can be looked at as resetting the computer with new program/data. This has interesting potential application. For example if our universe indeed has a maximum informational density then the added information must cause space to expand. As our universe gathers more information the area of its interface with the information in the full system increases so we get a positive feed back situation - The so called Dark Energy and its acceleration effect on the expansion. Hal
