Reviewer 2:
A paradigm is discussed which defines complexity in terms of
"integrity", "structure" and "system". Part of the discussion is
mathematical, the rest being merely philosophical. Despite very
interesting ideas, its content is often inaccurate (for instance:
"Structure is more than just elements and links, it is a kind of
wholeness, a level in the hierarchy of integrity") and conclusions are
hazy ("Functional complexity leads to the numerous forms of Godel's
theorem"). The math parts are a bit basic.
Reply:
Well, I have to admit it. The discussion is mainly methodological,
with minimum mathematics for illustration. It would be nice to
find out which ideas seemed interesting to the reviewer. Still,
I do not see any inacurateness in the contents of the quoted sentence
about structure — actually, it is much more accurate than
the usual mathematical definitions, reducing structures to their
formal models.
Reviewer 2:
My advise would be to read "Chaos and Information Theory: an heuristic
outline", Nicolis and Prigogine, World Scientific, 1990.
Reply:
I am acquainted with the Prigogine's line (and there is a reference
to one of Prigogine's books in the paper). My approach is quite
different — though, of course, I appreciate the value of
Prigogine's ideas for the comprehension of the necessity of
incorporating development in science. However, I suppose that
his theory deals with only one kind of development and is insufficient
in other cases (especially in social sciences). This is a topic for
a special discussion.
By the way, why should I discuss somebody else's views instead of
my own? And why my views should necessarily be based on somebody's
ideas and not on my own thought?
Reviewer 3:
While the subject of making explicit various aspects of the
notion of complexity is an appealing one, I think that the paper lacks
precision in its use of terms, and fails to present a logical and
rigorous argument from well defined contentions to conclusions.
Reply:
The principal goal of the paper is to make the terms related to
complexity more precise, and a new way of definition is suggested,
relating any notions to their hierarchical context. The reviewer
did not understand that, since he is convinced that the only precision
possible is that of syllogistic deduction. However, neither
deduction is the only rigorous argument, nor it is rigorous
indeed, as indicated in my previous paper,
Computability in developing systems. The standard
form of discourse demanded by "scientific" journals is mere
tribute to an obsolete tradition.
Reviewer 3:
In a paper of this kind one would expect to find:
1. In the introduction, a clear statement of the research question
being tackled including how the research builds on the existing body
of research. I would expect to find reference to specific papers
(rather than whole volume citations) defining the point of departure
of the research, what has gone before and what new methods are to be
employed. There is a substantial literature concerning the definition
of complexity.
2. In the body, clear definitions of terms, clear descriptions of
analytical models and methods to be used to make the argument, and an
economy of description demonstrating a clearly worked out argument.
3. A clear conclusion summarising the contribution of the research
and remaining open questions.
Reply:
This is a good summary of bad style. The articles like that pretend
that they really contribute into development of science, while
timidly hiding any valuable thought in the haze of references to
the predecessors. Well, the text should be as clear as possible.
However, following the above formal requirements would rather make
the problem more obfuscated.
-
An overview of previous work on the subject adds nothing to the
contents of the paper, while increasing its size and hiding the author's
intentions. Such historical issues should better be discussed in a
special appendix, or even in a separate paper devoted specifically
to the history of science.
-
For the problems that have not been solved yet, there cannot be any
preliminary formulation. A brief statement of the research question
would restrict the problem to a particular form, which may prove
utterly inadequate in the end. An general indication of the scope
is quite enough for the introduction, and it is the whole body of the
paper that is to exactly specify the problem considered. Scientific
research differs from engineering in that the latter has a list of
properties to achieve in an invention, while the former has to
ramble in the dark to discover the properties yet unknown.
-
Clear definitions are only possible in a very narrow region of research,
where nothing new is to be found, except for more combinations of
the elements already known. Such activity may be of use for some
immediately pragmatic purposes, but it has nothing to do with science.
Likewise, the methods used may only crystallize in the course of their
employment, and not before the research. To demonstrate a clearly worked
and economical argument, one has to solve the problem completely —
which is impossible for any serious problem. Such clear descriptions
appear much later, as simplified accounts for educational needs.
-
A summary of the author's contribution in the conclusion assumes that
some problems have been sovled completely, which is almost never the case.
The only honest summary would be a brief description of what the author
did (not have done) in the body of text — but this is
what the abstract serves for. The author can never list the remaining
open questions, since there is an infinity of such questions, including
those considered in the text. All that can be done is to indicate
which questions are of primary interest for the author, while the
reader may be interested in something quite different.
Reviewer 3:
Instead we find many undefined terms which have precise meaning only
for the author, a set theoretical model that is introduced and then
largely abandoned, and a rambling development which includes a number
of irrelevant metaphysical speculations.
Reply:
The reviewer has not noticed the new type of definition employed in
this work: the categories mutually define each other being used in
the same context, in different positions. This method of definition
is not less precise than the traditional reductions to the previously
introduced notions (which will always have to be somehow defined as well).
An illustration of some points (set theoretical model of structure)
would not be as useful to illustrate a different idea, and there was
no need of sticking to it throughout the paper. "Metaphysical speculations"
(methodological research) are necessary to avoid blind technicality,
aimless manipulation with empty symbols and terms.
Reviewer 3:
The paper demonstrates a lack of understanding of the incremental
nature of scientific investigations and the degree of precision required
for publication in a scientific journal.
Reply:
The reviewer demonstrates a lack of understanding of the impossibility of
incremental evolution in science, and the inevitability of scientific
revolutions. He confuses science with engineering, or mere craftsmanship,
denying any actual creativity.
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