Re: Mathematical Logic, Podnieks'page ...

From: Bruno Marchal <>
Date: Tue, 29 Jun 2004 16:13:07 +0200

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.

Received on Tue Jun 29 2004 - 10:10:11 PDT

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