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 points a detailed discussion would grow out of the framework of the list.
I want to concentrate on a few minor(?) points - leaving out the rest of the posts.
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.
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).
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 the widening 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 a primary 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.
----- Original Message -----
Subject: 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 achieved level of epistemic enrichment.

Reply-BM:   Only logicians formalize, and then use informal mathematics (like any mathematicians), but it just happen they are working  *on* formal systems and machines.


Reply via email to